From 1ea92f93e0dd5a8254fd3b0df5cc84ccdb4e505b Mon Sep 17 00:00:00 2001
From: SIPB
Date: Sun, 8 Dec 2024 01:58:46 -0500
Subject: More work on blog.md, move images to img folder

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 blog.md                          |  181 +-
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 index.html                       |  447 +-
 insane-shortest-paths.ipynb      |  451 +-
 loss                             | 8388 ++++++++++++++++++++++++++++++++++----
 model.pth                        |  Bin 422298 -> 1233035 bytes
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 transformer_shortest_paths.ipynb | 3603 +++++++++++++++-
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 delete mode 100644 fine-tuning-2d-histogram.png
 delete mode 100644 fine-tuning-loss.png
 create mode 100644 finetune.dot
 delete mode 100644 grokking.png
 create mode 100644 img/embeddings.svg
 create mode 100644 img/finetune.svg
 create mode 100644 img/test.svg
 create mode 100644 img/train.svg
 delete mode 100644 test-2d-histogram.png
 create mode 100644 test.dot
 create mode 100644 train.dot
 delete mode 100644 training-2d-histogram.png
 delete mode 100644 training-loss.png

diff --git a/blog.md b/blog.md
index c599f21..10333f9 100644
--- a/blog.md
+++ b/blog.md
@@ -1,7 +1,7 @@
 ---
 build: pandoc blog.md --citeproc --katex -s -o index.html
 mkzip: zip project.zip index.html *.png
-title: "6.7960 Project: Investigating Off-Distribution Generalization of Transformers"
+title: "Discovering Graph Algorithms Using Transformers"
 bibliography: blog.bib
 link-citations: true
 ---
@@ -14,25 +14,15 @@ Anthony Wang, Alek Westover, Kevin Zhao
 {xy,alekw,kevinmz}\@mit.edu
 </div>
 
-## Goals
+## Motivation
 
-Recently, LLMs have been developing very fast, and with that comes the concern of aligning the models to output true and productive statements. One common approach for ensuring this is to have a human in the loop rewarding the model for true outputs (e.g. RLHF), but one drawback to this problem is that humans can be poor judges of truthfulness. As LLMs become more capable, there might not even exist experts that are good judges of whether the model's outputs, such as difficult mathematical proofs, are truthful. So, we'd like to propose a potential solution to this issue via **off-distribution generalization** - applying human-like intuition to solve problems not in the dataset. Paul Christiano [proposed an experiment](https://www.alignmentforum.org/posts/BxersHYN2qcFoonwg/experimentally-evaluating-whether-honesty-generalizes?commentId=dsDA2BWpHPdgLvaXX) about shortest paths in a graph; our project is essentially to implement Christiano's proposed experiment. To the best of our knowledge, although there has been research in applying machine learning for different variations of graph searches [@10.5555/3666122.3666260], no one has done our exact experiment yet.
+Transformers--the architecture that powers LLMs--can do incredible feats: trained on hundreds of gigabytes of raw text, they can learn to hold natural conversations, reason about the physical world, and write code. Skeptics argue that LLMs are simply memorizing their datasets without gaining any deeper understanding. For instance, GPT's o1 model, achieving 90th percentile on Codeforces, struggles with simple but bizarre algorithms problems such as "find the subarray of a 2D array with the minimum average". In this project, we hope to explore **when off-distribution generalization happens in a transformer**. Paul Christiano proposed an experiment [here](https://www.alignmentforum.org/posts/BxersHYN2qcFoonwg/experimentally-evaluating-whether-honesty-generalizes?commentId=dsDA2BWpHPdgLvaXX) about shortest paths in a graph to investigate this, so we decided to become the first to implement his experiment and put transformers' generalization abilities to the test.
 
-It is generally desirable for LLMs to output true statements. A current approach for ensuring this is to have a human in the loop rewarding the model for true outputs (e.g. RLHF); however, humans can be poor judges of truthfulness. We enjoy many cognitive biases and might employ superficial heuristics when judging truthfulness. A further challenge is that as LLMs develop further, there might not even exist experts that can correctly judge the accuracy and truthfulness of sophisticated outputs such as difficult mathematical proofs.
+LLMs are notorious for making up complete nonsense, so we also hope that our project can shed light on when truthfulness generalizes. It's generally desirable for LLMs to output true statements. One current approach for ensuring this is to have a human in the loop rewarding the model for true outputs (e.g. RLHF). However, humans can be poor judges of truthfulness and have many cognitive biases and superficial heuristics. A further challenge is that as LLMs become more capable, there might not even exist experts that are good judges of whether the models outputs, such as difficult mathematical proofs, are truthful. For instance, most Task Rabbit workers would probably be hard pressed to evaluate whether a difficult mathematical proof produced by an LLM is true. The entire mathematical community has been known on occasion to [believe false statements for many years](https://en.wikipedia.org/wiki/Grunwald%E2%80%93Wang_theorem).
 
-One approach to solving this problem is to reward an LLM for truthful behavior on simple inputs, and then hoping that the LLM generalizes its truthful behavior for more complex inputs where humans cannot provide helpful labels. Deep learning models often perform remarkable feats of off-distribution generalization -- for instance, a model trained to transform hand drawn cats into images of cats might be able to handle a "cat" with three eyes in an intuitive way. We might hope that generalizing truthfully is simple, thus promoted by "Occam's Razor", and aim to investigate that with this project.
+One possible solution is to reward an LLM for truthful behavior on simple inputs, and then hope that the LLM generalizes its truthful behavior for more complex inputs where humans cannot provide helpful labels. Deep learning models can be remarkably good at off-distribution generalization--for instance, a model trained to transform hand drawn cats into images of cats might be able to handle a "cat" with three eyes in an intuitive way. We might hope that generalizing truthfully is simple, thus promoted by "Occam's Razor".
 
-COMMENT FROM KEVIN -- synthesize from intorduction
-
-### Task
-
-We will use a synthetic task to test our hypothesis that models will generalize truthfully off-distribution. The synthetic task is computing the distance between various vertices in an input graph. Our experiment will have three parts:
-
-1. Pre-train a transformer to predict the distance between two fixed vertices $s,t$ on graphs with $n\in [8, 32)$ vertices.
-2. Fine-tune a transformer to predict the distances between $s,t'$ for any $t'$ which is on the shortest path from $s$ to $t$, but only do fine-tuning on graphs with $n\in [8,16)$ vertices.
-3. Test whether the transformer can accurately predict the distances between $s,t'$ for any $t'$ on the shortest path from $s$ to $t$ for graphs with $n\in [16,32)$ vertices.
-
-### Related Work
+## Related Work
 
 COMMENT FROM ALEK 
 -- please remove all mentions of graph neural networks -- that is BS: there is no actual reason why you'd ever use a Neural network to solve shortest paths, the point of choosing a synthetic task is because there is a **simple ground truth** which makes it easy to evaluate whether or not our model is performing correctly. We'd also hoped that the simplicity of the task would make it more feasible to do with a limited compute budget, but apparently this task was too hard for our architecture.
@@ -44,82 +34,58 @@ There has been some research into the algorithmic optimization of GNNs and how t
 
 - Tutsoy uses a graph-theory-based approach to model the epidemiological characteristics of infectious diseases, such as COVID-19 [@10.1109/TPAMI.2023.3256421]. We understand from his paper how GNN optimization may also be useful in researching novel diseases.
 
-## Methods
-
-### Algorithm for Shortest Paths
-
-The standard algorithm to find the shortest path in a graph between a source numbered as $u$ and sink numbered as $v$ is **breadth-first search (BFS)**. The BFS algorithm maintains a mapping of visited vertices to their distances with respect to $u$, and each run of the algorithm goes through all the vertices newly visited in the previous run, and for each vertex, visits any of its unvisited neighbors. The algorithm terminates once either $v$ is visited or the set of newly visited vertices in a single run is empty.
-
-We will use this algorithm to verify the accuracy of our machine learning approach. Given $V$ vertices and $E$ edges, the runtime of this algorithm is thus $O(V + E)$; however, a machine learning approach may do better in time through parallelism, although at the expense of using much more memory.
-
-### Data
-
-We will represent an $n$ vertex, $m$ edge unweighted, undirected graph as sequence of the endpoints of the $m$ edges, so $[a_1,b_1,a_2,b_2,\ldots,a_m,b_m]$ represents a graph with the edges $\{(a_i,b_i)\}$ for $1 \leq i \leq m$. We will pad all sequences to be the same length using the padding token 0.
-
-The full input to our model will additionally add the target vertex after the padding tokens. The model is tasked with predicting the length of the shortest path between vertex 1 and the target vertex $t$. If no such path exists, we define the length to be $n+1$ which represents infinity. For example, an input-output pair for our model could look like $[1, 3, 3, 2, 0, 0, 0, 0, 2]$ and $2$ respectively.
-
-We have three separate datasets.
-
-- **Pre-train data**: For each $n \in [8,32)$, we will generate several graphs on $n$ vertices. We generate these graphs by inserting $2n$ random edges into the graph. We always set the target vertex to be $2$ here.
-- **Fine-tune data**: For each $n \in [8,16)$, we will generate several graphs on $n$ vertices. We generate these graphs by inserting $2n$ random edges into the graph. We select the target vertex to be a random vertex on the shortest path from $1$ to $2$.
-- **Generalization testing data**: The same as the fine-tune data, except we sample $n \in [16,32)$ instead.
-
-We wrote some Python code to generate the data during the training loop, but Python is slow and the data generation wasted a lot of time during training. To get around this, we pre-generated the data before training and made our Python code multithreaded to speed it up.
-
-### Architecture
-
-TODO: honestly not much to say here since it's a pretty typical arch
-
-We plan to use a standard transformer architecture. We will ensure that the number of layers in our transformer is at least the diameter of the graph. By doing this, we ensure that there is an extremely simple circuit --- namely BFS --- that the transformer could in theory learn to perform the task. Note that if the transformer actually learns a simple circuit to perform this task, then it seems more likely to generalize well. This is also our intuition for why it should be possible to fine tune on a small amount of data for finding shortest paths to other vertices besides $2$ -- it seems like the model should be computing these other distances as intermediate values in its computation to find the distance to vertex $2$.
-
-### Embeddings
-
-Since the order of the edges in the input does not matter, we did not use positional encodings. Each edge $(u,v)$ where $u < v$ is embedded to a dimension of $d$ where the first $\frac{d}{2}$ elements are the learned embedding of $u$ and the last $\frac{d}{2}$ elements are the learned embedding of $v$. For the target vertex $t$, we also embedded to dimension $d$, where the first $\frac{d}{2}$ elements are the learned embedding of $t$ and the last $\frac{d}{2}$ are a learned embedding of a special token.
-
-## Training
-
-For our model, we used a model dimension of 64, four layers, and two heads per layer, for a total of 200545 parameters in bfloat16 which corresponds to around 3.2e6 bits. The number of possible graphs on 15 vertices generated using our procedure is approximately
 
-$$\frac{\binom{15}{2}^{15}}{15!} = 1.59\cdot10^{18}.$$
-
-This is because there are $\binom{15}{2}$ choices for each of the 15 edges and we don't care about the order of the edges. This is only an approximation because some edges might be duplicated. Each graph has an answer between 1 and 15 which requires around 4 bits, so memorizing all the answers requires $4\cdot1.59\cdot10^{18} = 6.36\cdot10^{18}$, which is $2\cdot10^{12}$ times larger than our model size.
 
+## Task
 
+Our synthetic task is simple: compute the distance between various vertices in an input graph. To test off-distribution generalization, our experiment has three steps.
 
-We used MSE loss, the Adam optimizer, a learning rate of 8e-4, and a batch size of 131072 for 8000 unique randomly generated batches. Our final MSE loss was approximately 0.3555.
+1. **Pre-train** a transformer to predict the distance between vertices $1$ and $2$ in graphs with $n \in [3,15]$ vertices.
 
-![](training-loss.png)
+<div style="text-align:center">
+![](img/train.svg)
+</div>
 
-![](training-2d-histogram.png)
+2. **Fine-tune** a transformer to predict the distances between vertex $1$ to $t$ for any $t$ on the shortest path from $1$ to $2$, but only do fine-tuning on graphs with $n \in [3,7]$ vertices.
 
-One pattern we consistently noticed during training is that the model often gets stuck and plateaus for many epochs before rapidly decreasing. For instance, this happened between epochs 100 and 300 in the graph above:
+<div style="text-align:center">
+![](img/finetune.svg)
+</div>
 
-![](grokking.png)
+3. **Test** whether the transformer can accurately predict the distances between $1$ to $t$ for any $t \leq 7$ on the shortest path from $1$ to $2$ for graphs with $n \in [3,15]$ vertices.
 
-"grokking" hypothesis: it's memorizing all length 2 paths?
+<div style="text-align:center">
+![](img/test.svg)
+</div>
 
-TODO: training curves for 1, 2, 3 length paths
+### Algorithm for Shortest Paths
 
-### Potential Mathematical Approaches to Shortest Paths? Delete this?
+The standard algorithm to find the shortest path in a graph between vertices $u$ and $v$ is **breadth-first search (BFS)**, taught in every intro algorithms class. Initially, BFS starts at $u$, and at each phase, explores a farther layer of vertices from $u$. During a phase, BFS goes through every vertex in the current layer and adds any of their unvisited neighbors to the next layer. The algorithm terminates once we reach $v$ or if the next layer is empty. For a graph with $V$ vertices and $E$ edges, the runtime of BFS is $O(V + E)$. BFS gives us an easy and fast way to find the ground truth answer for any graph, so that we can verify the accuracy of our machine learning approach.
 
-Another way one can think of the shortest path of a graph is using a *matrix* to record which vertices are connected. Given vertices numbered $1$ to $V$, we denote the **adjacency matrix** $\textbf{M}$ of dimensions $V \times V$ as the matrix with element $\textbf{M}_{i, j} = 1$ if vertices $i$ and $j$ are connected by an edge and $\textbf{M}_{i, j} = 0$ if they are not. Now, we note that (1) For all $k$, $(\textbf{M}+I)^k_{i, j} = 0$ if and only if there exists no path from the vertex numbered $i$ to the vertex numbered $j$ that is distance $k$ or less due to Markov matrix processes. As a result, if the distance between vertices numbered $i$ and $j$ is $d$, then $\text{min}\left((\textbf{M}+I)^k_{i, j}, 1\right) = 1$ if $k \ge d$ and $\text{min}\left((\textbf{M}+I)^k_{i, j}, 1\right) = 0$ if $k < d$. 
+We hope that our model can learn BFS or some other simple, generalizable algorithm for shortest paths, because the model can't just pull some magic number out of a hat but intuitively needs to count or list the vertices on the shortest path from $1$ to $2$. In fact, we will show how to hand-craft a set of weights to implement BFS in a transformer, so it's indeed theoretically possible for a transformer to achieve 100% accuracy.
 
-With this information, because the distance between any two vertices is at most $V-1$ in a graph with $V$ vertices, we note that the *distance* matrix turns out to be simply $$\textbf{D} = \textbf{1}_{V \times V} \cdot V - \Sigma_{i=0}^{V-1}\text{min}\left((\textbf{M}+I)^k_{i, j}, 1\right).$$ The runtime to compute this is $O(V)$, although it will take more space to compute all powers of $\textbf{M}$.
+### Data
 
-## Fine tuning results
+We'll represent an $n$ vertex, $m$ edge unweighted, undirected graph as sequence of the endpoints of the $m$ edges, so $[a_1,b_1,a_2,b_2,\ldots,a_m,b_m]$ represents a graph with the edges $\{(a_i,b_i)\}$ where $a_i < b_i$ for $1 \leq i \leq m$. All sequences are padded to the same length using the padding token $0$.
 
-After receiving our initial results, we fine-tuned with a learning rate of 1e-5, also with MSE and the same batch size. Our final results are shown in the images below.
+The full input to our model additionally includes the target vertex $t$ after the padding tokens. The label to an input is the length of the shortest path from $1$ to $t$. If no such path exists, we define the length to be $n+1$ which represents infinity. For example, the input $[1, 3, 3, 4, 2, 4, 2, 3, 0, 0, 0, 0, 3]$ has the label $2$.
 
-![](fine-tuning-loss.png)
+<div style="text-align:center">
+![](img/finetune.svg)
+</div>
 
-![](fine-tuning-2d-histogram.png)
+We have three datasets for each step.
 
-![](test-2d-histogram.png)
+1. **Pre-train data**: For each $n \in [3,15]$, we generated an equal number of graphs on $n$ vertices, with $t = 2$. Each graph was created by choosing $n$ random edges.
+2. **Fine-tune data**: For each $n \in [3,7]$, we generated an equal number of graphs on $n$ vertices each with a random $t$ on the shortest path from $1$ to $2$. Again, each graph was created by choosing $n$ random edges.
+3. **Generalization test data**: The same as the fine-tune data, except we sample $n \in [3,15]$ and $t \leq 7$.
 
-Memorization? Do some math here to compute how many bits required to memorize 1, 2, 3
+We wrote some Python code to generate the data during the training loop, but Python is excruciatingly slow and data generation wasted a lot of training time. Our solution was to pre-generate the data before training using a multithreaded version of our Python code.
 
 ## Complicated explicit transformer formula for shortest paths
 
+TODO: Kevin or Alek
+
 ```py
 # Configuration
 NVTXS = 16
@@ -221,9 +187,7 @@ class SillyTransformer(nn.Module):
         return final_output
 ```
 
-It looked like the fine tuning results weren't as meaningful because TODO: ALEK
 
-## Customizing a Transformer
 
 After much deliberation, we decided the next step for us was to customize a transformer, writing it ourselves. We observed that we wished for the transformer to do similar work as a BFS. As a result, we decided to work with the following transformer, for a graph with $n$ vertices $v_1, v_2, \cdots, v_n$:
 
@@ -241,8 +205,81 @@ Specifically, we see that $\text{NBR}_{i}$ is a $n \times 1$ vector detailing wh
 
 This iterates through all the vertices, and at the end, we may see what run we are on to update $V_{\text{OUT}}$.
 
+## Perturbing the Weights
+
+SLT folks like to think about geometry of loss landscape CITE
+So we did an experiment where we mess with the weights. 
+
+Findings: XXX
+
+
+## Our Model
+
+### Architecture
+
+We used a standard transformer architecture. To ensure that it can in theory learn BFS, we ensured that the number of layers in our transformer exceeds the diameter of the input graphs.
+
+Since the order of the edges in the input doesn't matter, we did not use positional encodings. Each edge $(a,b)$ is embedded to dimension $d$ where the first $\frac{d}{2}$ elements are the learned embedding of $a$ and the last $\frac{d}{2}$ elements are the learned embedding of $b$. For the target vertex $t$, we pair it with the special token $TARGET$ and embed $(t,TARGET)$ in the same way.
+
+<!-- https://cocreate.csail.mit.edu/r/sxArTEXiAgJshznmm -->
+![](img/embeddings.svg)
+
+### Training
+
+To match the BFS transformer as closely as possible, we used a model dimension of $64$, $11$ layers, and $2$ heads per layer, for a total of 550433 parameters. In 32-bit float precision, that corresponds to around $1.76\cdot10^6$ bits. The number of possible graphs on 15 vertices generated using our procedure is approximately
+
+$$\frac{\binom{15}{2}^{15}}{15!} = 1.59\cdot10^{18}.$$
+
+This is because there are $\binom{15}{2}$ choices for each of the 15 edges and we don't care about the order of the edges. This is only an approximation because some edges might be duplicated. Each graph has an answer between 1 and 15 which requires around 4 bits, so memorizing all the answers requires $4\cdot1.59\cdot10^{18} = 6.36\cdot10^{18}$ bits, which is $3.61\cdot10^{12}$ times larger than our model size.
+
+To train the model, we used MSE loss, the Adam optimizer, a learning rate of $3\cdot10^{-4}$, and a batch size of $2^{15}$ for one billion randomly generated graphs. A training run takes roughly eight hours to run on a Radeon 7900 XTX graphics card. Our final MSE loss was $0.000555$.
+
+TODO: use https://mpld3.github.io/index.html to make interactive plots
+
+![](training-loss.png)
+
+![](training-2d-histogram.png)
+
+One pattern we consistently noticed during training is that the model often gets stuck and plateaus for many epochs before rapidly decreasing. For instance, this happened between epochs 100 and 300 in the graph above:
+
+![](grokking.png)
+
+"grokking" hypothesis: it's memorizing all length 2 paths?
+
+TODO: cite Neel Nanda grokking modular addition
+
+TODO: CRAZY!!! training curves for 1, 2, 3 length paths
+
+One pitfall we encountered during training is that we initially used bfloat16 to save VRAM, but our huge batch size caused loss-of-precision problems and made training very difficult. It took us two weeks to debug this until we found that switching to float32 improved training significantly.
+
+## Fine tuning results
+
+After receiving our initial results, we fine-tuned with a learning rate of 1e-5, also with MSE and the same batch size. Our final results are shown in the images below.
+
+![](fine-tuning-loss.png)
+
+![](fine-tuning-2d-histogram.png)
+
+![](test-2d-histogram.png)
+
+TODO: get new graphs
+
+It's pretty good!!!
+
+Can only generalize to target vertices from 2 to 7 since 8 through 15 didn't appear in the fine-tune data
+
+but this still means it
+
 ## Conclusion
 
+however, a machine learning approach may do better in time through parallelism, although at the expense of using much more memory.
+**TODO: ALEK: this is BS. If you want a parallel algorithm for BFS, here's one https://en.wikipedia.org/wiki/Parallel_single-source_shortest_path_algorithm**
+
 just do bfs lol
 
+**Future Work**
+There are a couple of other things that we could try to learn shortest paths better and maybe see more generalization. 
+- Chain of thought
+- Train model to output a path, not just the distance. Give it partial points for outputting anything that is a legitimate path (i.e., consists of real edges) and more points for getting the distance correct. 
+
 ## References
diff --git a/fine-tuning-2d-histogram.png b/fine-tuning-2d-histogram.png
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diff --git a/finetune.dot b/finetune.dot
new file mode 100644
index 0000000..f80b54b
--- /dev/null
+++ b/finetune.dot
@@ -0,0 +1,9 @@
+graph G {
+  1 [color=blue];
+  2 [color=red];
+  3 [color=green];
+  1 -- 3 [color=red];
+  4 -- 3;
+  2 -- 4;
+  2 -- 3 [color=red];
+}
diff --git a/grokking.png b/grokking.png
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diff --git a/img/embeddings.svg b/img/embeddings.svg
new file mode 100644
index 0000000..6e7b510
--- /dev/null
+++ b/img/embeddings.svg
@@ -0,0 +1,37 @@
+<?xml version="1.0" encoding="utf-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="451.1200256347656 187.3000030517578 532.1399841308594 229.5599822998047" width="532.1399841308594px" height="229.5599822998047px">
+<style>
+.pen line { stroke-linecap: round }
+.pen polyline { stroke-linecap: round; stroke-linejoin: round; fill: none }
+.grid { stroke-width: 0.96; stroke: #c4e3f4 }
+text { font-family: "Roboto Slab", serif }
+@font-face { font-family: "Roboto Slab"; src: url("https://fonts.gstatic.com/s/robotoslab/v34/BngMUXZYTXPIvIBgJJSb6ufN5qU.woff2") format("woff2"); font-style: normal; font-weight: 500; font-display: swap; unicode-range: U+0-FF, U+131, U+152-153, U+2BB-2BC, U+2C6, U+2DA, U+2DC, U+304, U+308, U+329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD; }
+</style>
+<g class="grid"/>
+<rect data-id="6xjpYJRwx2i9Lk4ka" x="566.4" y="188.79999999999998" width="37.75999999999999" height="226.55999999999997" stroke="black" stroke-width="3" stroke-linejoin="round" fill="none"/>
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diff --git a/img/train.svg b/img/train.svg
new file mode 100644
index 0000000..ef63aac
--- /dev/null
+++ b/img/train.svg
@@ -0,0 +1,127 @@
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diff --git a/index.html b/index.html
index efec318..fd5f74f 100644
--- a/index.html
+++ b/index.html
@@ -4,7 +4,7 @@
   <meta charset="utf-8" />
   <meta name="generator" content="pandoc" />
   <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
-  <title>6.7960 Project: Investigating Off-Distribution Generalization of Transformers</title>
+  <title>Discovering Graph Algorithms Using Transformers</title>
   <style>
     html {
       color: #1a1a1a;
@@ -271,74 +271,51 @@
 </head>
 <body>
 <header id="title-block-header">
-<h1 class="title">6.7960 Project: Investigating Off-Distribution
-Generalization of Transformers</h1>
+<h1 class="title">Discovering Graph Algorithms Using Transformers</h1>
 </header>
 <!-- Guidelines: https://www.dropbox.com/scl/fi/bet8enscln8ue36kd8t17/final_project_guidelines.pdf?rlkey=knd19cnumk51ho1y9crno56ib&e=2&dl=0 -->
 <div style="text-align:center">
 <p>Anthony Wang, Alek Westover, Kevin Zhao</p>
 <p>{xy,alekw,kevinmz}@mit.edu</p>
 </div>
-<h2 id="goals">Goals</h2>
-<p>Recently, LLMs have been developing very fast, and with that comes
-the concern of aligning the models to output true and productive
-statements. One common approach for ensuring this is to have a human in
-the loop rewarding the model for true outputs (e.g. RLHF), but one
-drawback to this problem is that humans can be poor judges of
-truthfulness. As LLMs become more capable, there might not even exist
-experts that are good judges of whether the model’s outputs, such as
-difficult mathematical proofs, are truthful. So, we’d like to propose a
-potential solution to this issue via <strong>off-distribution
-generalization</strong> - applying human-like intuition to solve
-problems not in the dataset. Paul Christiano <a
-href="https://www.alignmentforum.org/posts/BxersHYN2qcFoonwg/experimentally-evaluating-whether-honesty-generalizes?commentId=dsDA2BWpHPdgLvaXX">proposed
-an experiment</a> about shortest paths in a graph; our project is
-essentially to implement Christiano’s proposed experiment. To the best
-of our knowledge, although there has been research in applying machine
-learning for different variations of graph searches <span
-class="citation" data-cites="10.5555/3666122.3666260">(<a
-href="#ref-10.5555/3666122.3666260" role="doc-biblioref">Zang et al.
-2024</a>)</span>, no one has done our exact experiment yet.</p>
-<p>It is generally desirable for LLMs to output true statements. A
-current approach for ensuring this is to have a human in the loop
-rewarding the model for true outputs (e.g. RLHF); however, humans can be
-poor judges of truthfulness. We enjoy many cognitive biases and might
-employ superficial heuristics when judging truthfulness. A further
-challenge is that as LLMs develop further, there might not even exist
-experts that can correctly judge the accuracy and truthfulness of
-sophisticated outputs such as difficult mathematical proofs.</p>
-<p>One approach to solving this problem is to reward an LLM for truthful
-behavior on simple inputs, and then hoping that the LLM generalizes its
-truthful behavior for more complex inputs where humans cannot provide
-helpful labels. Deep learning models often perform remarkable feats of
-off-distribution generalization – for instance, a model trained to
-transform hand drawn cats into images of cats might be able to handle a
-“cat” with three eyes in an intuitive way. We might hope that
-generalizing truthfully is simple, thus promoted by “Occam’s Razor”, and
-aim to investigate that with this project.</p>
-<p>COMMENT FROM KEVIN – synthesize from intorduction</p>
-<h3 id="task">Task</h3>
-<p>We will use a synthetic task to test our hypothesis that models will
-generalize truthfully off-distribution. The synthetic task is computing
-the distance between various vertices in an input graph. Our experiment
-will have three parts:</p>
-<ol type="1">
-<li>Pre-train a transformer to predict the distance between two fixed
-vertices <span class="math inline">s,t</span> on graphs with <span
-class="math inline">n\in [8, 32)</span> vertices.</li>
-<li>Fine-tune a transformer to predict the distances between <span
-class="math inline">s,t&#39;</span> for any <span
-class="math inline">t&#39;</span> which is on the shortest path from
-<span class="math inline">s</span> to <span
-class="math inline">t</span>, but only do fine-tuning on graphs with
-<span class="math inline">n\in [8,16)</span> vertices.</li>
-<li>Test whether the transformer can accurately predict the distances
-between <span class="math inline">s,t&#39;</span> for any <span
-class="math inline">t&#39;</span> on the shortest path from <span
-class="math inline">s</span> to <span class="math inline">t</span> for
-graphs with <span class="math inline">n\in [16,32)</span> vertices.</li>
-</ol>
-<h3 id="related-work">Related Work</h3>
+<h2 id="motivation">Motivation</h2>
+<p>Transformers–the architecture that powers LLMs–can do incredible
+feats: trained on hundreds of gigabytes of raw text, they can learn to
+hold natural conversations, reason about the physical world, and write
+code. Skeptics argue that LLMs are simply memorizing their datasets
+without gaining any deeper understanding. For instance, GPT’s o1 model,
+achieving 90th percentile on Codeforces, struggles with simple but
+bizarre algorithms problems such as “find the subarray of a 2D array
+with the minimum average”. In this project, we hope to explore
+<strong>when off-distribution generalization happens in a
+transformer</strong>. Paul Christiano proposed an experiment <a
+href="https://www.alignmentforum.org/posts/BxersHYN2qcFoonwg/experimentally-evaluating-whether-honesty-generalizes?commentId=dsDA2BWpHPdgLvaXX">here</a>
+about shortest paths in a graph to investigate this, so we decided to
+become the first to implement his experiment and put transformers’
+generalization abilities to the test.</p>
+<p>LLMs are notorious for making up complete nonsense, so we also hope
+that our project can shed light on when truthfulness generalizes. It’s
+generally desirable for LLMs to output true statements. One current
+approach for ensuring this is to have a human in the loop rewarding the
+model for true outputs (e.g. RLHF). However, humans can be poor judges
+of truthfulness and have many cognitive biases and superficial
+heuristics. A further challenge is that as LLMs become more capable,
+there might not even exist experts that are good judges of whether the
+models outputs, such as difficult mathematical proofs, are truthful. For
+instance, most Task Rabbit workers would probably be hard pressed to
+evaluate whether a difficult mathematical proof produced by an LLM is
+true. The entire mathematical community has been known on occasion to <a
+href="https://en.wikipedia.org/wiki/Grunwald%E2%80%93Wang_theorem">believe
+false statements for many years</a>.</p>
+<p>One possible solution is to reward an LLM for truthful behavior on
+simple inputs, and then hope that the LLM generalizes its truthful
+behavior for more complex inputs where humans cannot provide helpful
+labels. Deep learning models can be remarkably good at off-distribution
+generalization–for instance, a model trained to transform hand drawn
+cats into images of cats might be able to handle a “cat” with three eyes
+in an intuitive way. We might hope that generalizing truthfully is
+simple, thus promoted by “Occam’s Razor”.</p>
+<h2 id="related-work">Related Work</h2>
 <p>COMMENT FROM ALEK – please remove all mentions of graph neural
 networks – that is BS: there is no actual reason why you’d ever use a
 Neural network to solve shortest paths, the point of choosing a
@@ -367,170 +344,113 @@ href="#ref-10.1109/TPAMI.2023.3256421" role="doc-biblioref">Tutsoy
 2023</a>)</span>. We understand from his paper how GNN optimization may
 also be useful in researching novel diseases.</p></li>
 </ul>
-<h2 id="methods">Methods</h2>
+<h2 id="task">Task</h2>
+<p>Our synthetic task is simple: compute the distance between various
+vertices in an input graph. To test off-distribution generalization, our
+experiment has three steps.</p>
+<ol type="1">
+<li><strong>Pre-train</strong> a transformer to predict the distance
+between vertices <span class="math inline">1</span> and <span
+class="math inline">2</span> in graphs with <span class="math inline">n
+\in [3,15]</span> vertices.</li>
+</ol>
+<div style="text-align:center">
+<p><img src="img/train.svg" /></p>
+</div>
+<ol start="2" type="1">
+<li><strong>Fine-tune</strong> a transformer to predict the distances
+between vertex <span class="math inline">1</span> to <span
+class="math inline">t</span> for any <span class="math inline">t</span>
+on the shortest path from <span class="math inline">1</span> to <span
+class="math inline">2</span>, but only do fine-tuning on graphs with
+<span class="math inline">n \in [3,7]</span> vertices.</li>
+</ol>
+<div style="text-align:center">
+<p><img src="img/finetune.svg" /></p>
+</div>
+<ol start="3" type="1">
+<li><strong>Test</strong> whether the transformer can accurately predict
+the distances between <span class="math inline">1</span> to <span
+class="math inline">t</span> for any <span class="math inline">t \leq
+7</span> on the shortest path from <span class="math inline">1</span> to
+<span class="math inline">2</span> for graphs with <span
+class="math inline">n \in [3,15]</span> vertices.</li>
+</ol>
+<div style="text-align:center">
+<p><img src="img/test.svg" /></p>
+</div>
 <h3 id="algorithm-for-shortest-paths">Algorithm for Shortest Paths</h3>
-<p>The standard algorithm to find the shortest path in a graph between a
-source numbered as <span class="math inline">u</span> and sink numbered
-as <span class="math inline">v</span> is <strong>breadth-first search
-(BFS)</strong>. The BFS algorithm maintains a mapping of visited
-vertices to their distances with respect to <span
-class="math inline">u</span>, and each run of the algorithm goes through
-all the vertices newly visited in the previous run, and for each vertex,
-visits any of its unvisited neighbors. The algorithm terminates once
-either <span class="math inline">v</span> is visited or the set of newly
-visited vertices in a single run is empty.</p>
-<p>We will use this algorithm to verify the accuracy of our machine
-learning approach. Given <span class="math inline">V</span> vertices and
-<span class="math inline">E</span> edges, the runtime of this algorithm
-is thus <span class="math inline">O(V + E)</span>; however, a machine
-learning approach may do better in time through parallelism, although at
-the expense of using much more memory.</p>
+<p>The standard algorithm to find the shortest path in a graph between
+vertices <span class="math inline">u</span> and <span
+class="math inline">v</span> is <strong>breadth-first search
+(BFS)</strong>, taught in every intro algorithms class. Initially, BFS
+starts at <span class="math inline">u</span>, and at each phase,
+explores a farther layer of vertices from <span
+class="math inline">u</span>. During a phase, BFS goes through every
+vertex in the current layer and adds any of their unvisited neighbors to
+the next layer. The algorithm terminates once we reach <span
+class="math inline">v</span> or if the next layer is empty. For a graph
+with <span class="math inline">V</span> vertices and <span
+class="math inline">E</span> edges, the runtime of BFS is <span
+class="math inline">O(V + E)</span>. BFS gives us an easy and fast way
+to find the ground truth answer for any graph, so that we can verify the
+accuracy of our machine learning approach.</p>
+<p>We hope that our model can learn BFS or some other simple,
+generalizable algorithm for shortest paths, because the model can’t just
+pull some magic number out of a hat but intuitively needs to count or
+list the vertices on the shortest path from <span
+class="math inline">1</span> to <span class="math inline">2</span>. In
+fact, we will show how to hand-craft a set of weights to implement BFS
+in a transformer, so it’s indeed theoretically possible for a
+transformer to achieve 100% accuracy.</p>
 <h3 id="data">Data</h3>
-<p>We will represent an <span class="math inline">n</span> vertex, <span
+<p>We’ll represent an <span class="math inline">n</span> vertex, <span
 class="math inline">m</span> edge unweighted, undirected graph as
 sequence of the endpoints of the <span class="math inline">m</span>
 edges, so <span
 class="math inline">[a_1,b_1,a_2,b_2,\ldots,a_m,b_m]</span> represents a
-graph with the edges <span class="math inline">\{(a_i,b_i)\}</span> for
-<span class="math inline">1 \leq i \leq m</span>. We will pad all
-sequences to be the same length using the padding token 0.</p>
-<p>The full input to our model will additionally add the target vertex
-after the padding tokens. The model is tasked with predicting the length
-of the shortest path between vertex 1 and the target vertex <span
-class="math inline">t</span>. If no such path exists, we define the
-length to be <span class="math inline">n+1</span> which represents
-infinity. For example, an input-output pair for our model could look
-like <span class="math inline">[1, 3, 3, 2, 0, 0, 0, 0, 2]</span> and
-<span class="math inline">2</span> respectively.</p>
-<p>We have three separate datasets.</p>
-<ul>
+graph with the edges <span class="math inline">\{(a_i,b_i)\}</span>
+where <span class="math inline">a_i &lt; b_i</span> for <span
+class="math inline">1 \leq i \leq m</span>. All sequences are padded to
+the same length using the padding token <span
+class="math inline">0</span>.</p>
+<p>The full input to our model additionally includes the target vertex
+<span class="math inline">t</span> after the padding tokens. The label
+to an input is the length of the shortest path from <span
+class="math inline">1</span> to <span class="math inline">t</span>. If
+no such path exists, we define the length to be <span
+class="math inline">n+1</span> which represents infinity. For example,
+the input <span class="math inline">[1, 3, 3, 4, 2, 4, 2, 3, 0, 0, 0, 0,
+3]</span> has the label <span class="math inline">2</span>.</p>
+<div style="text-align:center">
+<p><img src="img/finetune.svg" /></p>
+</div>
+<p>We have three datasets for each step.</p>
+<ol type="1">
 <li><strong>Pre-train data</strong>: For each <span
-class="math inline">n \in [8,32)</span>, we will generate several graphs
-on <span class="math inline">n</span> vertices. We generate these graphs
-by inserting <span class="math inline">2n</span> random edges into the
-graph. We always set the target vertex to be <span
-class="math inline">2</span> here.</li>
+class="math inline">n \in [3,15]</span>, we generated an equal number of
+graphs on <span class="math inline">n</span> vertices, with <span
+class="math inline">t = 2</span>. Each graph was created by choosing
+<span class="math inline">n</span> random edges.</li>
 <li><strong>Fine-tune data</strong>: For each <span
-class="math inline">n \in [8,16)</span>, we will generate several graphs
-on <span class="math inline">n</span> vertices. We generate these graphs
-by inserting <span class="math inline">2n</span> random edges into the
-graph. We select the target vertex to be a random vertex on the shortest
-path from <span class="math inline">1</span> to <span
-class="math inline">2</span>.</li>
-<li><strong>Generalization testing data</strong>: The same as the
-fine-tune data, except we sample <span class="math inline">n \in
-[16,32)</span> instead.</li>
-</ul>
+class="math inline">n \in [3,7]</span>, we generated an equal number of
+graphs on <span class="math inline">n</span> vertices each with a random
+<span class="math inline">t</span> on the shortest path from <span
+class="math inline">1</span> to <span class="math inline">2</span>.
+Again, each graph was created by choosing <span
+class="math inline">n</span> random edges.</li>
+<li><strong>Generalization test data</strong>: The same as the fine-tune
+data, except we sample <span class="math inline">n \in [3,15]</span> and
+<span class="math inline">t \leq 7</span>.</li>
+</ol>
 <p>We wrote some Python code to generate the data during the training
-loop, but Python is slow and the data generation wasted a lot of time
-during training. To get around this, we pre-generated the data before
-training and made our Python code multithreaded to speed it up.</p>
-<h3 id="architecture">Architecture</h3>
-<p>TODO: honestly not much to say here since it’s a pretty typical
-arch</p>
-<p>We plan to use a standard transformer architecture. We will ensure
-that the number of layers in our transformer is at least the diameter of
-the graph. By doing this, we ensure that there is an extremely simple
-circuit — namely BFS — that the transformer could in theory learn to
-perform the task. Note that if the transformer actually learns a simple
-circuit to perform this task, then it seems more likely to generalize
-well. This is also our intuition for why it should be possible to fine
-tune on a small amount of data for finding shortest paths to other
-vertices besides <span class="math inline">2</span> – it seems like the
-model should be computing these other distances as intermediate values
-in its computation to find the distance to vertex <span
-class="math inline">2</span>.</p>
-<h3 id="embeddings">Embeddings</h3>
-<p>Since the order of the edges in the input does not matter, we did not
-use positional encodings. Each edge <span
-class="math inline">(u,v)</span> where <span class="math inline">u &lt;
-v</span> is embedded to a dimension of <span
-class="math inline">d</span> where the first <span
-class="math inline">\frac{d}{2}</span> elements are the learned
-embedding of <span class="math inline">u</span> and the last <span
-class="math inline">\frac{d}{2}</span> elements are the learned
-embedding of <span class="math inline">v</span>. For the target vertex
-<span class="math inline">t</span>, we also embedded to dimension <span
-class="math inline">d</span>, where the first <span
-class="math inline">\frac{d}{2}</span> elements are the learned
-embedding of <span class="math inline">t</span> and the last <span
-class="math inline">\frac{d}{2}</span> are a learned embedding of a
-special token.</p>
-<h2 id="training">Training</h2>
-<p>For our model, we used a model dimension of 64, four layers, and two
-heads per layer, for a total of 200545 parameters in bfloat16 which
-corresponds to around 3.2e6 bits. The number of possible graphs on 15
-vertices generated using our procedure is approximately</p>
-<p><span class="math display">\frac{\binom{15}{2}^{15}}{15!} =
-1.59\cdot10^{18}.</span></p>
-<p>This is because there are <span
-class="math inline">\binom{15}{2}</span> choices for each of the 15
-edges and we don’t care about the order of the edges. This is only an
-approximation because some edges might be duplicated. Each graph has an
-answer between 1 and 15 which requires around 4 bits, so memorizing all
-the answers requires <span class="math inline">4\cdot1.59\cdot10^{18} =
-6.36\cdot10^{18}</span>, which is <span
-class="math inline">2\cdot10^{12}</span> times larger than our model
-size.</p>
-<p>We used MSE loss, the Adam optimizer, a learning rate of 8e-4, and a
-batch size of 131072 for 8000 unique randomly generated batches. Our
-final MSE loss was approximately 0.3555.</p>
-<p><img src="training-loss.png" /></p>
-<p><img src="training-2d-histogram.png" /></p>
-<p>One pattern we consistently noticed during training is that the model
-often gets stuck and plateaus for many epochs before rapidly decreasing.
-For instance, this happened between epochs 100 and 300 in the graph
-above:</p>
-<p><img src="grokking.png" /></p>
-<p>“grokking” hypothesis: it’s memorizing all length 2 paths?</p>
-<p>TODO: training curves for 1, 2, 3 length paths</p>
-<h3
-id="potential-mathematical-approaches-to-shortest-paths-delete-this">Potential
-Mathematical Approaches to Shortest Paths? Delete this?</h3>
-<p>Another way one can think of the shortest path of a graph is using a
-<em>matrix</em> to record which vertices are connected. Given vertices
-numbered <span class="math inline">1</span> to <span
-class="math inline">V</span>, we denote the <strong>adjacency
-matrix</strong> <span class="math inline">\textbf{M}</span> of
-dimensions <span class="math inline">V \times V</span> as the matrix
-with element <span class="math inline">\textbf{M}_{i, j} = 1</span> if
-vertices <span class="math inline">i</span> and <span
-class="math inline">j</span> are connected by an edge and <span
-class="math inline">\textbf{M}_{i, j} = 0</span> if they are not. Now,
-we note that (1) For all <span class="math inline">k</span>, <span
-class="math inline">(\textbf{M}+I)^k_{i, j} = 0</span> if and only if
-there exists no path from the vertex numbered <span
-class="math inline">i</span> to the vertex numbered <span
-class="math inline">j</span> that is distance <span
-class="math inline">k</span> or less due to Markov matrix processes. As
-a result, if the distance between vertices numbered <span
-class="math inline">i</span> and <span class="math inline">j</span> is
-<span class="math inline">d</span>, then <span
-class="math inline">\text{min}\left((\textbf{M}+I)^k_{i, j}, 1\right) =
-1</span> if <span class="math inline">k \ge d</span> and <span
-class="math inline">\text{min}\left((\textbf{M}+I)^k_{i, j}, 1\right) =
-0</span> if <span class="math inline">k &lt; d</span>.</p>
-<p>With this information, because the distance between any two vertices
-is at most <span class="math inline">V-1</span> in a graph with <span
-class="math inline">V</span> vertices, we note that the
-<em>distance</em> matrix turns out to be simply <span
-class="math display">\textbf{D} = \textbf{1}_{V \times V} \cdot V -
-\Sigma_{i=0}^{V-1}\text{min}\left((\textbf{M}+I)^k_{i, j},
-1\right).</span> The runtime to compute this is <span
-class="math inline">O(V)</span>, although it will take more space to
-compute all powers of <span class="math inline">\textbf{M}</span>.</p>
-<h2 id="fine-tuning-results">Fine tuning results</h2>
-<p>After receiving our initial results, we fine-tuned with a learning
-rate of 1e-5, also with MSE and the same batch size. Our final results
-are shown in the images below.</p>
-<p><img src="fine-tuning-loss.png" /></p>
-<p><img src="fine-tuning-2d-histogram.png" /></p>
-<p><img src="test-2d-histogram.png" /></p>
-<p>Memorization? Do some math here to compute how many bits required to
-memorize 1, 2, 3</p>
+loop, but Python is excruciatingly slow and data generation wasted a lot
+of training time. Our solution was to pre-generate the data before
+training using a multithreaded version of our Python code.</p>
 <h2
 id="complicated-explicit-transformer-formula-for-shortest-paths">Complicated
 explicit transformer formula for shortest paths</h2>
+<p>TODO: Kevin or Alek</p>
 <div class="sourceCode" id="cb1"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Configuration</span></span>
 <span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>NVTXS <span class="op">=</span> <span class="dv">16</span></span>
 <span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>MAXDIST <span class="op">=</span> NVTXS <span class="op">+</span> <span class="dv">1</span></span>
@@ -629,9 +549,6 @@ explicit transformer formula for shortest paths</h2>
 <span id="cb1-96"><a href="#cb1-96" aria-hidden="true" tabindex="-1"></a>        canreach <span class="op">=</span> src[:, <span class="dv">0</span>, START_OUT:START_OUT <span class="op">+</span> NVTXS]</span>
 <span id="cb1-97"><a href="#cb1-97" aria-hidden="true" tabindex="-1"></a>        final_output <span class="op">=</span> <span class="dv">1</span> <span class="op">+</span> torch.<span class="bu">sum</span>(<span class="dv">1</span> <span class="op">-</span> canreach, dim<span class="op">=</span><span class="dv">1</span>)</span>
 <span id="cb1-98"><a href="#cb1-98" aria-hidden="true" tabindex="-1"></a>        <span class="cf">return</span> final_output</span></code></pre></div>
-<p>It looked like the fine tuning results weren’t as meaningful because
-TODO: ALEK</p>
-<h2 id="customizing-a-transformer">Customizing a Transformer</h2>
 <p>After much deliberation, we decided the next step for us was to
 customize a transformer, writing it ourselves. We observed that we
 wished for the transformer to do similar work as a BFS. As a result, we
@@ -686,8 +603,95 @@ class="math inline">i</span>th entry is nonzero.</p>
 <p>This iterates through all the vertices, and at the end, we may see
 what run we are on to update <span
 class="math inline">V_{\text{OUT}}</span>.</p>
+<h2 id="perturbing-the-weights">Perturbing the Weights</h2>
+<p>SLT folks like to think about geometry of loss landscape CITE So we
+did an experiment where we mess with the weights.</p>
+<p>Findings: XXX</p>
+<h2 id="our-model">Our Model</h2>
+<h3 id="architecture">Architecture</h3>
+<p>We used a standard transformer architecture. To ensure that it can in
+theory learn BFS, we ensured that the number of layers in our
+transformer exceeds the diameter of the input graphs.</p>
+<p>Since the order of the edges in the input doesn’t matter, we did not
+use positional encodings. Each edge <span
+class="math inline">(a,b)</span> is embedded to dimension <span
+class="math inline">d</span> where the first <span
+class="math inline">\frac{d}{2}</span> elements are the learned
+embedding of <span class="math inline">a</span> and the last <span
+class="math inline">\frac{d}{2}</span> elements are the learned
+embedding of <span class="math inline">b</span>. For the target vertex
+<span class="math inline">t</span>, we pair it with the special token
+<span class="math inline">TARGET</span> and embed <span
+class="math inline">(t,TARGET)</span> in the same way.</p>
+<!-- https://cocreate.csail.mit.edu/r/sxArTEXiAgJshznmm -->
+<p><img src="img/embeddings.svg" /></p>
+<h3 id="training">Training</h3>
+<p>To match the BFS transformer as closely as possible, we used a model
+dimension of <span class="math inline">64</span>, <span
+class="math inline">11</span> layers, and <span
+class="math inline">2</span> heads per layer, for a total of 550433
+parameters. In 32-bit float precision, that corresponds to around <span
+class="math inline">1.76\cdot10^6</span> bits. The number of possible
+graphs on 15 vertices generated using our procedure is approximately</p>
+<p><span class="math display">\frac{\binom{15}{2}^{15}}{15!} =
+1.59\cdot10^{18}.</span></p>
+<p>This is because there are <span
+class="math inline">\binom{15}{2}</span> choices for each of the 15
+edges and we don’t care about the order of the edges. This is only an
+approximation because some edges might be duplicated. Each graph has an
+answer between 1 and 15 which requires around 4 bits, so memorizing all
+the answers requires <span class="math inline">4\cdot1.59\cdot10^{18} =
+6.36\cdot10^{18}</span> bits, which is <span
+class="math inline">3.61\cdot10^{12}</span> times larger than our model
+size.</p>
+<p>To train the model, we used MSE loss, the Adam optimizer, a learning
+rate of <span class="math inline">3\cdot10^{-4}</span>, and a batch size
+of <span class="math inline">2^{15}</span> for one billion randomly
+generated graphs. A training run takes roughly eight hours to run on a
+Radeon 7900 XTX graphics card. Our final MSE loss was <span
+class="math inline">0.000555</span>.</p>
+<p>TODO: use https://mpld3.github.io/index.html to make interactive
+plots</p>
+<p><img src="training-loss.png" /></p>
+<p><img src="training-2d-histogram.png" /></p>
+<p>One pattern we consistently noticed during training is that the model
+often gets stuck and plateaus for many epochs before rapidly decreasing.
+For instance, this happened between epochs 100 and 300 in the graph
+above:</p>
+<p><img src="grokking.png" /></p>
+<p>“grokking” hypothesis: it’s memorizing all length 2 paths?</p>
+<p>TODO: cite Neel Nanda grokking modular addition</p>
+<p>TODO: CRAZY!!! training curves for 1, 2, 3 length paths</p>
+<p>One pitfall we encountered during training is that we initially used
+bfloat16 to save VRAM, but our huge batch size caused loss-of-precision
+problems and made training very difficult. It took us two weeks to debug
+this until we found that switching to float32 improved training
+significantly.</p>
+<h2 id="fine-tuning-results">Fine tuning results</h2>
+<p>After receiving our initial results, we fine-tuned with a learning
+rate of 1e-5, also with MSE and the same batch size. Our final results
+are shown in the images below.</p>
+<p><img src="fine-tuning-loss.png" /></p>
+<p><img src="fine-tuning-2d-histogram.png" /></p>
+<p><img src="test-2d-histogram.png" /></p>
+<p>TODO: get new graphs</p>
+<p>It’s pretty good!!!</p>
+<p>Can only generalize to target vertices from 2 to 7 since 8 through 15
+didn’t appear in the fine-tune data</p>
+<p>but this still means it</p>
 <h2 id="conclusion">Conclusion</h2>
+<p>however, a machine learning approach may do better in time through
+parallelism, although at the expense of using much more memory.
+<strong>TODO: ALEK: this is BS. If you want a parallel algorithm for
+BFS, here’s one
+https://en.wikipedia.org/wiki/Parallel_single-source_shortest_path_algorithm</strong></p>
 <p>just do bfs lol</p>
+<p><strong>Future Work</strong> There are a couple of other things that
+we could try to learn shortest paths better and maybe see more
+generalization. - Chain of thought - Train model to output a path, not
+just the distance. Give it partial points for outputting anything that
+is a legitimate path (i.e., consists of real edges) and more points for
+getting the distance correct.</p>
 <h2 class="unnumbered" id="references">References</h2>
 <div id="refs" class="references csl-bib-body hanging-indent"
 data-entry-spacing="0" role="list">
@@ -707,13 +711,6 @@ Exact Epidemiological Modeling of Pandemic Diseases.”</span> <em>IEEE
 Trans. Pattern Anal. Mach. Intell.</em> 45 (8): 9836–45. <a
 href="https://doi.org/10.1109/TPAMI.2023.3256421">https://doi.org/10.1109/TPAMI.2023.3256421</a>.
 </div>
-<div id="ref-10.5555/3666122.3666260" class="csl-entry" role="listitem">
-Zang, Xiao, Miao Yin, Jinqi Xiao, Saman Zonouz, and Bo Yuan. 2024.
-<span>“GraphMP: Graph Neural Network-Based Motion Planning with
-Efficient Graph Search.”</span> In <em>Proceedings of the 37th
-International Conference on Neural Information Processing Systems</em>.
-NIPS ’23. Red Hook, NY, USA: Curran Associates Inc.
-</div>
 </div>
 </body>
 </html>
diff --git a/insane-shortest-paths.ipynb b/insane-shortest-paths.ipynb
index e74974b..a3e58fb 100644
--- a/insane-shortest-paths.ipynb
+++ b/insane-shortest-paths.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 1,
    "execution_state": "idle",
    "id": "86ce5f44-94f6-43b0-a0d1-091b8134ffb6",
    "metadata": {},
@@ -22,8 +22,8 @@
     "from collections import deque\n",
     "\n",
     "# Set manual seeds for reproducibility\n",
-    "torch.manual_seed(33)\n",
-    "random.seed(33)\n",
+    "# torch.manual_seed(33)\n",
+    "# random.seed(33)\n",
     "\n",
     "# Configuration\n",
     "NVTXS = 16\n",
@@ -122,7 +122,6 @@
     "                Q = nn.Parameter(torch.zeros((2, HIDDENDIM), device=device))\n",
     "                Q[0, START_REACH - 1 + head] = SUPABIG\n",
     "                Q[1, NOTANS_FLAG_IDX] = 1\n",
-    "btrfs filesystem resize max\n",
     "                K = nn.Parameter(torch.zeros((2, HIDDENDIM), device=device))\n",
     "                K[0, head] = 1\n",
     "                K[1, ANS_FLAG_IDX] = BIG\n",
@@ -134,7 +133,6 @@
     "                self.mostKs.append(K)\n",
     "                self.mostQs.append(Q)\n",
     "                self.mostVs.append(V)\n",
-    "\n",
     "            self.weirdKs = nn.ParameterList()\n",
     "            self.weirdQs = nn.ParameterList()\n",
     "            self.weirdVs = nn.ParameterList()\n",
@@ -204,35 +202,440 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "execution_state": "idle",
    "id": "a9dd76f4-96f2-47b5-9bb9-a32a1b478dd4",
    "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
+     "name": "stderr",
      "output_type": "stream",
      "text": [
-      "Epoch [0/10000], Loss: 8.3387\n",
-      "Epoch [10/10000], Loss: 7.6416\n",
-      "Epoch [20/10000], Loss: 11.2689\n",
-      "Epoch [30/10000], Loss: 7.0312\n",
-      "Epoch [40/10000], Loss: 8.7287\n",
-      "Epoch [50/10000], Loss: 7.7182\n"
+      "/tmp/ipykernel_15454/381745885.py:148: UserWarning: Attempting to use hipBLASLt on an unsupported architecture! Overriding blas backend to hipblas (Triggered internally at ../aten/src/ATen/Context.cpp:296.)\n",
+      "  ksrc = torch.matmul(src, K.unsqueeze(0).transpose(-2, -1))\n"
      ]
     },
     {
-     "ename": "KeyboardInterrupt",
-     "evalue": "",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[6], line 11\u001b[0m\n\u001b[1;32m      9\u001b[0m loss \u001b[38;5;241m=\u001b[39m loss_fn(outputs, labels)\n\u001b[1;32m     10\u001b[0m optimizer\u001b[38;5;241m.\u001b[39mzero_grad()\n\u001b[0;32m---> 11\u001b[0m \u001b[43mloss\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbackward\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     12\u001b[0m optimizer\u001b[38;5;241m.\u001b[39mstep()\n\u001b[1;32m     13\u001b[0m train_err\u001b[38;5;241m.\u001b[39mappend(loss\u001b[38;5;241m.\u001b[39mitem())\n",
-      "File \u001b[0;32m~/.venv/lib64/python3.12/site-packages/torch/_tensor.py:581\u001b[0m, in \u001b[0;36mTensor.backward\u001b[0;34m(self, gradient, retain_graph, create_graph, inputs)\u001b[0m\n\u001b[1;32m    571\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m has_torch_function_unary(\u001b[38;5;28mself\u001b[39m):\n\u001b[1;32m    572\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m handle_torch_function(\n\u001b[1;32m    573\u001b[0m         Tensor\u001b[38;5;241m.\u001b[39mbackward,\n\u001b[1;32m    574\u001b[0m         (\u001b[38;5;28mself\u001b[39m,),\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    579\u001b[0m         inputs\u001b[38;5;241m=\u001b[39minputs,\n\u001b[1;32m    580\u001b[0m     )\n\u001b[0;32m--> 581\u001b[0m \u001b[43mtorch\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mautograd\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbackward\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    582\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mgradient\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mretain_graph\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcreate_graph\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43minputs\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43minputs\u001b[49m\n\u001b[1;32m    583\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.venv/lib64/python3.12/site-packages/torch/autograd/__init__.py:347\u001b[0m, in \u001b[0;36mbackward\u001b[0;34m(tensors, grad_tensors, retain_graph, create_graph, grad_variables, inputs)\u001b[0m\n\u001b[1;32m    342\u001b[0m     retain_graph \u001b[38;5;241m=\u001b[39m create_graph\n\u001b[1;32m    344\u001b[0m \u001b[38;5;66;03m# The reason we repeat the same comment below is that\u001b[39;00m\n\u001b[1;32m    345\u001b[0m \u001b[38;5;66;03m# some Python versions print out the first line of a multi-line function\u001b[39;00m\n\u001b[1;32m    346\u001b[0m \u001b[38;5;66;03m# calls in the traceback and some print out the last line\u001b[39;00m\n\u001b[0;32m--> 347\u001b[0m \u001b[43m_engine_run_backward\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    348\u001b[0m \u001b[43m    \u001b[49m\u001b[43mtensors\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    349\u001b[0m \u001b[43m    \u001b[49m\u001b[43mgrad_tensors_\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    350\u001b[0m \u001b[43m    \u001b[49m\u001b[43mretain_graph\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    351\u001b[0m \u001b[43m    \u001b[49m\u001b[43mcreate_graph\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    352\u001b[0m \u001b[43m    \u001b[49m\u001b[43minputs\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    353\u001b[0m \u001b[43m    \u001b[49m\u001b[43mallow_unreachable\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m,\u001b[49m\n\u001b[1;32m    354\u001b[0m \u001b[43m    \u001b[49m\u001b[43maccumulate_grad\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m,\u001b[49m\n\u001b[1;32m    355\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/.venv/lib64/python3.12/site-packages/torch/autograd/graph.py:825\u001b[0m, in \u001b[0;36m_engine_run_backward\u001b[0;34m(t_outputs, *args, **kwargs)\u001b[0m\n\u001b[1;32m    823\u001b[0m     unregister_hooks \u001b[38;5;241m=\u001b[39m _register_logging_hooks_on_whole_graph(t_outputs)\n\u001b[1;32m    824\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 825\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mVariable\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_execution_engine\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_backward\u001b[49m\u001b[43m(\u001b[49m\u001b[43m  \u001b[49m\u001b[38;5;66;43;03m# Calls into the C++ engine to run the backward pass\u001b[39;49;00m\n\u001b[1;32m    826\u001b[0m \u001b[43m        \u001b[49m\u001b[43mt_outputs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\n\u001b[1;32m    827\u001b[0m \u001b[43m    \u001b[49m\u001b[43m)\u001b[49m  \u001b[38;5;66;03m# Calls into the C++ engine to run the backward pass\u001b[39;00m\n\u001b[1;32m    828\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m    829\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m attach_logging_hooks:\n",
-      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch [0/10000], Loss: 0.0025\n",
+      "Epoch [10/10000], Loss: 6.4609\n",
+      "Epoch [20/10000], Loss: 11.0729\n",
+      "Epoch [30/10000], Loss: 10.3862\n",
+      "Epoch [40/10000], Loss: 8.3659\n",
+      "Epoch [50/10000], Loss: 8.4364\n",
+      "Epoch [60/10000], Loss: 7.0110\n",
+      "Epoch [70/10000], Loss: 6.2279\n",
+      "Epoch [80/10000], Loss: 14.5876\n",
+      "Epoch [90/10000], Loss: 13.5753\n",
+      "Epoch [100/10000], Loss: 15.5835\n",
+      "Epoch [110/10000], Loss: 14.3249\n",
+      "Epoch [120/10000], Loss: 11.1069\n",
+      "Epoch [130/10000], Loss: 11.6783\n",
+      "Epoch [140/10000], Loss: 10.2477\n",
+      "Epoch [150/10000], Loss: 10.8494\n",
+      "Epoch [160/10000], Loss: 8.3007\n",
+      "Epoch [170/10000], Loss: 6.8133\n",
+      "Epoch [180/10000], Loss: 5.5992\n",
+      "Epoch [190/10000], Loss: 6.9212\n",
+      "Epoch [200/10000], Loss: 5.9311\n",
+      "Epoch [210/10000], Loss: 6.0747\n",
+      "Epoch [220/10000], Loss: 4.9251\n",
+      "Epoch [230/10000], Loss: 3.9548\n",
+      "Epoch [240/10000], Loss: 5.9888\n",
+      "Epoch [250/10000], Loss: 4.9153\n",
+      "Epoch [260/10000], Loss: 6.6282\n",
+      "Epoch [270/10000], Loss: 4.7945\n",
+      "Epoch [280/10000], Loss: 6.8866\n",
+      "Epoch [290/10000], Loss: 5.7963\n",
+      "Epoch [300/10000], Loss: 4.1406\n",
+      "Epoch [310/10000], Loss: 5.8112\n",
+      "Epoch [320/10000], Loss: 6.3739\n",
+      "Epoch [330/10000], Loss: 4.7297\n",
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+      "Epoch [360/10000], Loss: 5.1536\n",
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+      "Epoch [380/10000], Loss: 4.8955\n",
+      "Epoch [390/10000], Loss: 5.0702\n",
+      "Epoch [400/10000], Loss: 5.5217\n",
+      "Epoch [410/10000], Loss: 4.0543\n",
+      "Epoch [420/10000], Loss: 3.8583\n",
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+      "Epoch [450/10000], Loss: 5.3544\n",
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+      "Epoch [500/10000], Loss: 3.4060\n",
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+      "Epoch [520/10000], Loss: 3.9425\n",
+      "Epoch [530/10000], Loss: 3.4496\n",
+      "Epoch [540/10000], Loss: 2.8899\n",
+      "Epoch [550/10000], Loss: 2.5607\n",
+      "Epoch [560/10000], Loss: 3.9549\n",
+      "Epoch [570/10000], Loss: 4.4588\n",
+      "Epoch [580/10000], Loss: 4.3738\n",
+      "Epoch [590/10000], Loss: 3.3019\n",
+      "Epoch [600/10000], Loss: 2.4798\n",
+      "Epoch [610/10000], Loss: 6.1956\n",
+      "Epoch [620/10000], Loss: 4.3365\n",
+      "Epoch [630/10000], Loss: 4.9766\n",
+      "Epoch [640/10000], Loss: 4.2719\n",
+      "Epoch [650/10000], Loss: 5.0380\n",
+      "Epoch [660/10000], Loss: 5.7970\n",
+      "Epoch [670/10000], Loss: 5.8626\n",
+      "Epoch [680/10000], Loss: 4.7593\n",
+      "Epoch [690/10000], Loss: 5.7902\n",
+      "Epoch [700/10000], Loss: 5.9829\n",
+      "Epoch [710/10000], Loss: 6.7365\n",
+      "Epoch [720/10000], Loss: 5.3005\n",
+      "Epoch [730/10000], Loss: 5.8437\n",
+      "Epoch [740/10000], Loss: 3.8711\n",
+      "Epoch [750/10000], Loss: 5.0535\n",
+      "Epoch [760/10000], Loss: 3.7943\n",
+      "Epoch [770/10000], Loss: 4.5757\n",
+      "Epoch [780/10000], Loss: 4.7215\n",
+      "Epoch [790/10000], Loss: 4.4653\n",
+      "Epoch [800/10000], Loss: 5.5769\n",
+      "Epoch [810/10000], Loss: 5.0396\n",
+      "Epoch [820/10000], Loss: 5.2878\n",
+      "Epoch [830/10000], Loss: 5.4599\n",
+      "Epoch [840/10000], Loss: 4.5172\n",
+      "Epoch [850/10000], Loss: 4.8925\n",
+      "Epoch [860/10000], Loss: 5.1588\n",
+      "Epoch [870/10000], Loss: 5.8972\n",
+      "Epoch [880/10000], Loss: 4.9056\n",
+      "Epoch [890/10000], Loss: 4.8735\n",
+      "Epoch [900/10000], Loss: 5.2677\n",
+      "Epoch [910/10000], Loss: 4.3955\n",
+      "Epoch [920/10000], Loss: 5.1297\n",
+      "Epoch [930/10000], Loss: 4.2394\n",
+      "Epoch [940/10000], Loss: 6.8890\n",
+      "Epoch [950/10000], Loss: 5.1845\n",
+      "Epoch [960/10000], Loss: 4.4620\n",
+      "Epoch [970/10000], Loss: 5.1748\n",
+      "Epoch [980/10000], Loss: 4.9878\n",
+      "Epoch [990/10000], Loss: 3.9090\n",
+      "Epoch [1000/10000], Loss: 3.6580\n",
+      "Epoch [1010/10000], Loss: 3.5537\n",
+      "Epoch [1020/10000], Loss: 4.5068\n",
+      "Epoch [1030/10000], Loss: 3.2602\n",
+      "Epoch [1040/10000], Loss: 3.7987\n",
+      "Epoch [1050/10000], Loss: 3.3821\n",
+      "Epoch [1060/10000], Loss: 3.9663\n",
+      "Epoch [1070/10000], Loss: 3.8562\n",
+      "Epoch [1080/10000], Loss: 3.7811\n",
+      "Epoch [1090/10000], Loss: 4.0012\n",
+      "Epoch [1100/10000], Loss: 4.2564\n",
+      "Epoch [1110/10000], Loss: 3.2248\n",
+      "Epoch [1120/10000], Loss: 3.7483\n",
+      "Epoch [1130/10000], Loss: 3.0315\n",
+      "Epoch [1140/10000], Loss: 3.3677\n",
+      "Epoch [1150/10000], Loss: 3.5367\n",
+      "Epoch [1160/10000], Loss: 2.7389\n",
+      "Epoch [1170/10000], Loss: 3.0337\n",
+      "Epoch [1180/10000], Loss: 2.2630\n",
+      "Epoch [1190/10000], Loss: 1.8084\n",
+      "Epoch [1200/10000], Loss: 3.3239\n",
+      "Epoch [1210/10000], Loss: 4.1555\n",
+      "Epoch [1220/10000], Loss: 2.8362\n",
+      "Epoch [1230/10000], Loss: 3.1269\n",
+      "Epoch [1240/10000], Loss: 2.2517\n",
+      "Epoch [1250/10000], Loss: 2.9400\n",
+      "Epoch [1260/10000], Loss: 2.5436\n",
+      "Epoch [1270/10000], Loss: 2.6504\n",
+      "Epoch [1280/10000], Loss: 2.9571\n",
+      "Epoch [1290/10000], Loss: 2.4060\n",
+      "Epoch [1300/10000], Loss: 2.6461\n",
+      "Epoch [1310/10000], Loss: 2.4692\n",
+      "Epoch [1320/10000], Loss: 2.0638\n",
+      "Epoch [1330/10000], Loss: 3.0852\n",
+      "Epoch [1340/10000], Loss: 2.3448\n",
+      "Epoch [1350/10000], Loss: 2.6796\n",
+      "Epoch [1360/10000], Loss: 2.0310\n",
+      "Epoch [1370/10000], Loss: 1.8680\n",
+      "Epoch [1380/10000], Loss: 2.1846\n",
+      "Epoch [1390/10000], Loss: 2.3017\n",
+      "Epoch [1400/10000], Loss: 1.6519\n",
+      "Epoch [1410/10000], Loss: 1.6228\n",
+      "Epoch [1420/10000], Loss: 1.4328\n",
+      "Epoch [1430/10000], Loss: 1.5642\n",
+      "Epoch [1440/10000], Loss: 1.8962\n",
+      "Epoch [1450/10000], Loss: 1.4433\n",
+      "Epoch [1460/10000], Loss: 2.1973\n",
+      "Epoch [1470/10000], Loss: 1.8118\n",
+      "Epoch [1480/10000], Loss: 1.7155\n",
+      "Epoch [1490/10000], Loss: 2.7671\n",
+      "Epoch [1500/10000], Loss: 2.4518\n",
+      "Epoch [1510/10000], Loss: 1.0202\n",
+      "Epoch [1520/10000], Loss: 2.2548\n",
+      "Epoch [1530/10000], Loss: 1.4305\n",
+      "Epoch [1540/10000], Loss: 2.1796\n",
+      "Epoch [1550/10000], Loss: 1.7766\n",
+      "Epoch [1560/10000], Loss: 2.0751\n",
+      "Epoch [1570/10000], Loss: 1.6544\n",
+      "Epoch [1580/10000], Loss: 2.8767\n",
+      "Epoch [1590/10000], Loss: 2.2069\n",
+      "Epoch [1600/10000], Loss: 1.5974\n",
+      "Epoch [1610/10000], Loss: 2.0101\n",
+      "Epoch [1620/10000], Loss: 1.9445\n",
+      "Epoch [1630/10000], Loss: 2.3080\n",
+      "Epoch [1640/10000], Loss: 1.2395\n",
+      "Epoch [1650/10000], Loss: 1.2486\n",
+      "Epoch [1660/10000], Loss: 1.3250\n",
+      "Epoch [1670/10000], Loss: 1.1839\n",
+      "Epoch [1680/10000], Loss: 2.0569\n",
+      "Epoch [1690/10000], Loss: 2.3591\n",
+      "Epoch [1700/10000], Loss: 1.4618\n",
+      "Epoch [1710/10000], Loss: 1.3663\n",
+      "Epoch [1720/10000], Loss: 0.7300\n",
+      "Epoch [1730/10000], Loss: 2.6778\n",
+      "Epoch [1740/10000], Loss: 2.2931\n",
+      "Epoch [1750/10000], Loss: 1.4289\n",
+      "Epoch [1760/10000], Loss: 1.1453\n",
+      "Epoch [1770/10000], Loss: 1.0400\n",
+      "Epoch [1780/10000], Loss: 1.3603\n",
+      "Epoch [1790/10000], Loss: 1.5058\n",
+      "Epoch [1800/10000], Loss: 1.2890\n",
+      "Epoch [1810/10000], Loss: 1.1259\n",
+      "Epoch [1820/10000], Loss: 1.3006\n",
+      "Epoch [1830/10000], Loss: 1.4118\n",
+      "Epoch [1840/10000], Loss: 1.6406\n",
+      "Epoch [1850/10000], Loss: 1.3513\n",
+      "Epoch [1860/10000], Loss: 1.2380\n",
+      "Epoch [1870/10000], Loss: 1.4618\n",
+      "Epoch [1880/10000], Loss: 2.8634\n",
+      "Epoch [1890/10000], Loss: 2.4145\n",
+      "Epoch [1900/10000], Loss: 2.1412\n",
+      "Epoch [1910/10000], Loss: 2.7974\n",
+      "Epoch [1920/10000], Loss: 2.3607\n",
+      "Epoch [1930/10000], Loss: 2.1780\n",
+      "Epoch [1940/10000], Loss: 2.1544\n",
+      "Epoch [1950/10000], Loss: 1.1798\n",
+      "Epoch [1960/10000], Loss: 2.0259\n",
+      "Epoch [1970/10000], Loss: 8.5005\n",
+      "Epoch [1980/10000], Loss: 7.2836\n",
+      "Epoch [1990/10000], Loss: 5.1658\n",
+      "Epoch [2000/10000], Loss: 4.4845\n",
+      "Epoch [2010/10000], Loss: 3.2873\n",
+      "Epoch [2020/10000], Loss: 3.9213\n",
+      "Epoch [2030/10000], Loss: 3.4896\n",
+      "Epoch [2040/10000], Loss: 4.8792\n",
+      "Epoch [2050/10000], Loss: 3.8883\n",
+      "Epoch [2060/10000], Loss: 4.8546\n",
+      "Epoch [2070/10000], Loss: 3.5432\n",
+      "Epoch [2080/10000], Loss: 4.3267\n",
+      "Epoch [2090/10000], Loss: 3.4671\n",
+      "Epoch [2100/10000], Loss: 5.4011\n",
+      "Epoch [2110/10000], Loss: 5.8443\n",
+      "Epoch [2120/10000], Loss: 2.8416\n",
+      "Epoch [2130/10000], Loss: 5.1449\n",
+      "Epoch [2140/10000], Loss: 5.6858\n",
+      "Epoch [2150/10000], Loss: 5.1926\n",
+      "Epoch [2160/10000], Loss: 4.5664\n",
+      "Epoch [2170/10000], Loss: 4.3358\n",
+      "Epoch [2180/10000], Loss: 4.5456\n",
+      "Epoch [2190/10000], Loss: 3.5273\n",
+      "Epoch [2200/10000], Loss: 6.8660\n",
+      "Epoch [2210/10000], Loss: 3.4792\n",
+      "Epoch [2220/10000], Loss: 3.4052\n",
+      "Epoch [2230/10000], Loss: 2.8651\n",
+      "Epoch [2240/10000], Loss: 2.1104\n",
+      "Epoch [2250/10000], Loss: 2.1549\n",
+      "Epoch [2260/10000], Loss: 1.8513\n",
+      "Epoch [2270/10000], Loss: 2.8559\n",
+      "Epoch [2280/10000], Loss: 1.3817\n",
+      "Epoch [2290/10000], Loss: 1.4976\n",
+      "Epoch [2300/10000], Loss: 1.7325\n",
+      "Epoch [2310/10000], Loss: 1.5967\n",
+      "Epoch [2320/10000], Loss: 0.8749\n",
+      "Epoch [2330/10000], Loss: 1.5636\n",
+      "Epoch [2340/10000], Loss: 1.5302\n",
+      "Epoch [2350/10000], Loss: 0.7900\n",
+      "Epoch [2360/10000], Loss: 1.0777\n",
+      "Epoch [2370/10000], Loss: 0.6089\n",
+      "Epoch [2380/10000], Loss: 1.2180\n",
+      "Epoch [2390/10000], Loss: 1.3731\n",
+      "Epoch [2400/10000], Loss: 1.1782\n",
+      "Epoch [2410/10000], Loss: 0.9826\n",
+      "Epoch [2420/10000], Loss: 1.8233\n",
+      "Epoch [2430/10000], Loss: 0.8246\n",
+      "Epoch [2440/10000], Loss: 0.7204\n",
+      "Epoch [2450/10000], Loss: 1.2327\n",
+      "Epoch [2460/10000], Loss: 1.2843\n",
+      "Epoch [2470/10000], Loss: 1.1326\n",
+      "Epoch [2480/10000], Loss: 1.1369\n",
+      "Epoch [2490/10000], Loss: 1.0106\n",
+      "Epoch [2500/10000], Loss: 1.4563\n",
+      "Epoch [2510/10000], Loss: 1.0163\n",
+      "Epoch [2520/10000], Loss: 0.3823\n",
+      "Epoch [2530/10000], Loss: 0.8872\n",
+      "Epoch [2540/10000], Loss: 0.4118\n",
+      "Epoch [2550/10000], Loss: 0.4925\n",
+      "Epoch [2560/10000], Loss: 0.1141\n",
+      "Epoch [2570/10000], Loss: 0.5785\n",
+      "Epoch [2580/10000], Loss: 0.5831\n",
+      "Epoch [2590/10000], Loss: 0.0845\n",
+      "Epoch [2600/10000], Loss: 0.5621\n",
+      "Epoch [2610/10000], Loss: 1.0745\n",
+      "Epoch [2620/10000], Loss: 0.2378\n",
+      "Epoch [2630/10000], Loss: 0.6215\n",
+      "Epoch [2640/10000], Loss: 0.7897\n",
+      "Epoch [2650/10000], Loss: 0.9359\n",
+      "Epoch [2660/10000], Loss: 0.5567\n",
+      "Epoch [2670/10000], Loss: 4.0690\n",
+      "Epoch [2680/10000], Loss: 3.3254\n",
+      "Epoch [2690/10000], Loss: 3.3888\n",
+      "Epoch [2700/10000], Loss: 3.7329\n",
+      "Epoch [2710/10000], Loss: 2.9879\n",
+      "Epoch [2720/10000], Loss: 2.6283\n",
+      "Epoch [2730/10000], Loss: 2.4366\n",
+      "Epoch [2740/10000], Loss: 2.8078\n",
+      "Epoch [2750/10000], Loss: 1.2757\n",
+      "Epoch [2760/10000], Loss: 1.0685\n",
+      "Epoch [2770/10000], Loss: 2.2750\n",
+      "Epoch [2780/10000], Loss: 1.9740\n",
+      "Epoch [2790/10000], Loss: 1.4824\n",
+      "Epoch [2800/10000], Loss: 1.1974\n",
+      "Epoch [2810/10000], Loss: 1.6074\n",
+      "Epoch [2820/10000], Loss: 1.2541\n",
+      "Epoch [2830/10000], Loss: 1.7665\n",
+      "Epoch [2840/10000], Loss: 1.9748\n",
+      "Epoch [2850/10000], Loss: 1.9842\n",
+      "Epoch [2860/10000], Loss: 2.5544\n",
+      "Epoch [2870/10000], Loss: 1.6564\n",
+      "Epoch [2880/10000], Loss: 1.0362\n",
+      "Epoch [2890/10000], Loss: 1.3166\n",
+      "Epoch [2900/10000], Loss: 2.4819\n",
+      "Epoch [2910/10000], Loss: 1.1353\n",
+      "Epoch [2920/10000], Loss: 1.6106\n",
+      "Epoch [2930/10000], Loss: 2.1840\n",
+      "Epoch [2940/10000], Loss: 1.4362\n",
+      "Epoch [2950/10000], Loss: 0.9568\n",
+      "Epoch [2960/10000], Loss: 1.8224\n",
+      "Epoch [2970/10000], Loss: 1.2919\n",
+      "Epoch [2980/10000], Loss: 1.1351\n",
+      "Epoch [2990/10000], Loss: 0.7588\n",
+      "Epoch [3000/10000], Loss: 1.2207\n",
+      "Epoch [3010/10000], Loss: 1.3446\n",
+      "Epoch [3020/10000], Loss: 1.1581\n",
+      "Epoch [3030/10000], Loss: 1.0448\n",
+      "Epoch [3040/10000], Loss: 2.0898\n",
+      "Epoch [3050/10000], Loss: 1.1978\n",
+      "Epoch [3060/10000], Loss: 1.2886\n",
+      "Epoch [3070/10000], Loss: 1.0066\n",
+      "Epoch [3080/10000], Loss: 1.5037\n",
+      "Epoch [3090/10000], Loss: 0.6185\n",
+      "Epoch [3100/10000], Loss: 0.9835\n",
+      "Epoch [3110/10000], Loss: 0.6671\n",
+      "Epoch [3120/10000], Loss: 0.6967\n",
+      "Epoch [3130/10000], Loss: 1.0013\n",
+      "Epoch [3140/10000], Loss: 1.4123\n",
+      "Epoch [3150/10000], Loss: 1.8096\n",
+      "Epoch [3160/10000], Loss: 1.1270\n",
+      "Epoch [3170/10000], Loss: 1.9781\n",
+      "Epoch [3180/10000], Loss: 1.0191\n",
+      "Epoch [3190/10000], Loss: 2.4403\n",
+      "Epoch [3200/10000], Loss: 0.8882\n",
+      "Epoch [3210/10000], Loss: 1.0005\n",
+      "Epoch [3220/10000], Loss: 0.5002\n",
+      "Epoch [3230/10000], Loss: 1.2351\n",
+      "Epoch [3240/10000], Loss: 0.8264\n",
+      "Epoch [3250/10000], Loss: 0.7881\n",
+      "Epoch [3260/10000], Loss: 1.4120\n",
+      "Epoch [3270/10000], Loss: 0.3342\n",
+      "Epoch [3280/10000], Loss: 1.3266\n",
+      "Epoch [3290/10000], Loss: 1.7115\n",
+      "Epoch [3300/10000], Loss: 1.0647\n",
+      "Epoch [3310/10000], Loss: 0.4623\n",
+      "Epoch [3320/10000], Loss: 1.2075\n",
+      "Epoch [3330/10000], Loss: 0.4555\n",
+      "Epoch [3340/10000], Loss: 0.8706\n",
+      "Epoch [3350/10000], Loss: 0.9383\n",
+      "Epoch [3360/10000], Loss: 0.7436\n",
+      "Epoch [3370/10000], Loss: 0.8466\n",
+      "Epoch [3380/10000], Loss: 0.8379\n",
+      "Epoch [3390/10000], Loss: 0.6832\n",
+      "Epoch [3400/10000], Loss: 1.0414\n",
+      "Epoch [3410/10000], Loss: 0.5256\n",
+      "Epoch [3420/10000], Loss: 1.2059\n",
+      "Epoch [3430/10000], Loss: 0.7949\n",
+      "Epoch [3440/10000], Loss: 0.5962\n",
+      "Epoch [3450/10000], Loss: 0.8650\n",
+      "Epoch [3460/10000], Loss: 0.8154\n",
+      "Epoch [3470/10000], Loss: 0.4271\n",
+      "Epoch [3480/10000], Loss: 0.5725\n",
+      "Epoch [3490/10000], Loss: 1.0792\n",
+      "Epoch [3500/10000], Loss: 0.5633\n",
+      "Epoch [3510/10000], Loss: 0.2986\n",
+      "Epoch [3520/10000], Loss: 0.3941\n",
+      "Epoch [3530/10000], Loss: 1.0033\n",
+      "Epoch [3540/10000], Loss: 0.1960\n",
+      "Epoch [3550/10000], Loss: 0.9863\n",
+      "Epoch [3560/10000], Loss: 0.4395\n",
+      "Epoch [3570/10000], Loss: 0.9612\n",
+      "Epoch [3580/10000], Loss: 2.4734\n",
+      "Epoch [3590/10000], Loss: 5.5539\n",
+      "Epoch [3600/10000], Loss: 3.7807\n",
+      "Epoch [3610/10000], Loss: 4.0435\n",
+      "Epoch [3620/10000], Loss: 4.1143\n",
+      "Epoch [3630/10000], Loss: 3.3714\n",
+      "Epoch [3640/10000], Loss: 3.3396\n",
+      "Epoch [3650/10000], Loss: 4.2713\n",
+      "Epoch [3660/10000], Loss: 2.2012\n",
+      "Epoch [3670/10000], Loss: 1.7168\n",
+      "Epoch [3680/10000], Loss: 2.2133\n",
+      "Epoch [3690/10000], Loss: 2.7070\n",
+      "Epoch [3700/10000], Loss: 3.3160\n",
+      "Epoch [3710/10000], Loss: 3.6073\n",
+      "Epoch [3720/10000], Loss: 2.2879\n",
+      "Epoch [3730/10000], Loss: 2.8893\n",
+      "Epoch [3740/10000], Loss: 2.7971\n",
+      "Epoch [3750/10000], Loss: 1.7426\n",
+      "Epoch [3760/10000], Loss: 2.7662\n",
+      "Epoch [3770/10000], Loss: 2.1203\n",
+      "Epoch [3780/10000], Loss: 3.8798\n",
+      "Epoch [3790/10000], Loss: 2.6662\n",
+      "Epoch [3800/10000], Loss: 1.8491\n",
+      "Epoch [3810/10000], Loss: 1.5527\n",
+      "Epoch [3820/10000], Loss: 4.1708\n",
+      "Epoch [3830/10000], Loss: 1.6162\n",
+      "Epoch [3840/10000], Loss: 2.6064\n",
+      "Epoch [3850/10000], Loss: 1.9516\n",
+      "Epoch [3860/10000], Loss: 2.1771\n",
+      "Epoch [3870/10000], Loss: 2.3933\n",
+      "Epoch [3880/10000], Loss: 1.8314\n",
+      "Epoch [3890/10000], Loss: 3.2097\n",
+      "Epoch [3900/10000], Loss: 1.8215\n",
+      "Epoch [3910/10000], Loss: 2.1805\n",
+      "Epoch [3920/10000], Loss: 1.6260\n",
+      "Epoch [3930/10000], Loss: 1.5388\n",
+      "Epoch [3940/10000], Loss: 1.4422\n",
+      "Epoch [3950/10000], Loss: 1.2274\n",
+      "Epoch [3960/10000], Loss: 2.1992\n",
+      "Epoch [3970/10000], Loss: 1.3654\n",
+      "Epoch [3980/10000], Loss: 1.5024\n",
+      "Epoch [3990/10000], Loss: 1.9630\n",
+      "Epoch [4000/10000], Loss: 1.7742\n",
+      "Epoch [4010/10000], Loss: 1.9968\n",
+      "Epoch [4020/10000], Loss: 2.2213\n",
+      "Epoch [4030/10000], Loss: 2.1302\n",
+      "Epoch [4040/10000], Loss: 2.3094\n",
+      "Epoch [4050/10000], Loss: 2.3253\n",
+      "Epoch [4060/10000], Loss: 2.2924\n",
+      "Epoch [4070/10000], Loss: 0.9917\n",
+      "Epoch [4080/10000], Loss: 1.8697\n",
+      "Epoch [4090/10000], Loss: 1.4888\n",
+      "Epoch [4100/10000], Loss: 0.6206\n",
+      "Epoch [4110/10000], Loss: 0.9877\n",
+      "Epoch [4120/10000], Loss: 1.2839\n",
+      "Epoch [4130/10000], Loss: 0.4944\n",
+      "Epoch [4140/10000], Loss: 0.6533\n",
+      "Epoch [4150/10000], Loss: 0.4354\n",
+      "Epoch [4160/10000], Loss: 0.4216\n"
      ]
     }
    ],
diff --git a/loss b/loss
index 1e0cc2f..08f0413 100644
--- a/loss
+++ b/loss
@@ -1,800 +1,7588 @@
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diff --git a/model.pth b/model.pth
index 4cd979c..c4b12cd 100644
Binary files a/model.pth and b/model.pth differ
diff --git a/test-2d-histogram.png b/test-2d-histogram.png
deleted file mode 100644
index 75f2f6e..0000000
Binary files a/test-2d-histogram.png and /dev/null differ
diff --git a/test.dot b/test.dot
new file mode 100644
index 0000000..664b30e
--- /dev/null
+++ b/test.dot
@@ -0,0 +1,18 @@
+graph G {
+  1 [color=blue];
+  2 [color=red];
+  3 [color=red];
+  5 [color=green];
+  11 [color=red];
+  1 -- 3 [color=red];
+  4 -- 3;
+  11 -- 2 [color=red];
+  9 -- 3;
+  6 -- 7
+  4 -- 5;
+  10 -- 8;
+  5 -- 3 [color=red];
+  3 -- 8;
+  5 -- 11 [color=red];
+  4 -- 9;
+}
diff --git a/train.dot b/train.dot
new file mode 100644
index 0000000..48d7d46
--- /dev/null
+++ b/train.dot
@@ -0,0 +1,18 @@
+graph G {
+  1 [color=blue];
+  2 [color=green];
+  3 [color=red];
+  5 [color=red];
+  11 [color=red];
+  1 -- 3 [color=red];
+  4 -- 3;
+  11 -- 2 [color=red];
+  9 -- 3;
+  6 -- 7
+  4 -- 5;
+  10 -- 8;
+  5 -- 3 [color=red];
+  3 -- 8;
+  5 -- 11 [color=red];
+  4 -- 9;
+}
diff --git a/training-2d-histogram.png b/training-2d-histogram.png
deleted file mode 100644
index 31c3340..0000000
Binary files a/training-2d-histogram.png and /dev/null differ
diff --git a/training-loss.png b/training-loss.png
deleted file mode 100644
index 9cdc225..0000000
Binary files a/training-loss.png and /dev/null differ
diff --git a/transformer_shortest_paths.ipynb b/transformer_shortest_paths.ipynb
index c2164ac..8a99b4b 100644
--- a/transformer_shortest_paths.ipynb
+++ b/transformer_shortest_paths.ipynb
@@ -230,7 +230,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "execution_state": "idle",
    "metadata": {},
    "outputs": [
@@ -270,7 +270,7 @@
        "          False]]))"
       ]
      },
-     "execution_count": 4,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -281,7 +281,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "execution_state": "idle",
    "metadata": {},
    "outputs": [
@@ -308,7 +308,7 @@
        " <BarContainer object of 64 artists>)"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -329,7 +329,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "execution_state": "idle",
    "metadata": {},
    "outputs": [
@@ -356,7 +356,7 @@
        " <BarContainer object of 64 artists>)"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -386,7 +386,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 8,
    "execution_state": "idle",
    "metadata": {
     "id": "tLOWhg_CeWzH"
@@ -423,7 +423,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 9,
    "execution_state": "idle",
    "metadata": {
     "colab": {
@@ -438,7 +438,7 @@
      "output_type": "stream",
      "text": [
       "Training data: 1048576K\n",
-      "Trainable parameters in the model: 500449\n"
+      "Trainable parameters in the model: 550433\n"
      ]
     }
    ],
@@ -449,7 +449,7 @@
     "NEPOCHS = 1000\n",
     "BSZ = 2**15 # Batch size\n",
     "NHEADS = 2\n",
-    "NLAYERS = 10\n",
+    "NLAYERS = 11\n",
     "DROPOUT = 0 # 0.2\n",
     "model = TransformerModel(input_dim=VOCAB_SIZE, model_dim=MODEL_DIM,\n",
     "                         output_dim=1, num_heads=NHEADS,\n",
@@ -474,7 +474,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 10,
    "execution_state": "idle",
    "metadata": {},
    "outputs": [],
@@ -486,7 +486,7 @@
     "# model = torch.compile(model)\n",
     "# model.load_state_dict(torch.load('model.pth', weights_only=True))\n",
     "\n",
-    "LR = 5e-4\n",
+    "LR = 3e-4\n",
     "\n",
     "criterion = nn.MSELoss()\n",
     "optimizer = torch.optim.Adam(model.parameters(), lr=LR)"
@@ -504,6 +504,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "execution_state": "running",
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
@@ -512,7 +513,3576 @@
     "id": "pvTfzGmCeXU4",
     "outputId": "0d3a20f3-23be-4c19-9eb6-46bfe11a48b1"
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/sipb/.venv/lib64/python3.12/site-packages/torch/nn/functional.py:6278: UserWarning: Memory Efficient attention on Navi31 GPU is still experimental. Enable it with TORCH_ROCM_AOTRITON_ENABLE_EXPERIMENTAL=1. (Triggered internally at ../aten/src/ATen/native/transformers/hip/sdp_utils.cpp:269.)\n",
+      "  attn_output = scaled_dot_product_attention(\n",
+      "/home/sipb/.venv/lib64/python3.12/site-packages/torch/_inductor/compile_fx.py:167: UserWarning: TensorFloat32 tensor cores for float32 matrix multiplication available but not enabled. Consider setting `torch.set_float32_matmul_precision('high')` for better performance.\n",
+      "  warnings.warn(\n",
+      "/tmp/torchinductor_sipb/lc/clcqc3ufbzrethiy77dmsu54kurxdmh4eji2f3msm347rhmfpf4j.py:1078: UserWarning: Attempting to use hipBLASLt on an unsupported architecture! Overriding blas backend to hipblas (Triggered internally at ../aten/src/ATen/Context.cpp:296.)\n",
+      "  extern_kernels.mm(reinterpret_tensor(buf1, (524288, 64), (64, 1), 0), reinterpret_tensor(primals_5, (64, 192), (1, 64), 0), out=buf2)\n",
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:53<00:00,  1.68s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 0/1000 \t Train Err: 44.25287628173828 15.68527889251709 8.788555145263672 3.8603785037994385 100.71075439453125\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 1/1000 \t Train Err: 42.749107360839844 19.990596771240234 12.096658706665039 6.1431379318237305 90.65858459472656\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 2/1000 \t Train Err: 35.17692565917969 0.05676012113690376 15.442191123962402 8.584199905395508 82.2193374633789\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 3/1000 \t Train Err: 32.94102478027344 0.0016151332529261708 21.24653434753418 13.028000831604004 70.40452575683594\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 4/1000 \t Train Err: 30.707416534423828 0.0012646751711145043 27.01055335998535 17.616626739501953 60.88502502441406\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 5/1000 \t Train Err: 29.5562801361084 0.0010397899895906448 32.37065124511719 21.991931915283203 53.443416595458984\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 6/1000 \t Train Err: 29.092647552490234 0.0007909027044661343 36.97315979003906 25.812442779541016 47.87839126586914\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 7/1000 \t Train Err: 28.649932861328125 0.0005968677578493953 40.76370620727539 28.99480438232422 43.76168441772461\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 8/1000 \t Train Err: 28.49782943725586 0.00046271493192762136 43.50001907348633 31.30975914001465 41.015228271484375\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 9/1000 \t Train Err: 28.43338394165039 0.00036097457632422447 45.3854866027832 32.91228103637695 39.220703125\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 10/1000 \t Train Err: 28.3504581451416 0.0002947713655885309 46.44082260131836 33.81328201293945 38.23492431640625\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 11/1000 \t Train Err: 28.3637638092041 0.00025288635515607893 44.81169509887695 32.499359130859375 39.33035659790039\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 12/1000 \t Train Err: 20.932743072509766 0.020399289205670357 9.31131649017334 9.292236328125 46.657718658447266\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 13/1000 \t Train Err: 15.104679107666016 0.004516741260886192 3.496262311935425 26.43575096130371 27.609149932861328\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 14/1000 \t Train Err: 11.633755683898926 0.006426772102713585 0.33657196164131165 12.253266334533691 24.989166259765625\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 15/1000 \t Train Err: 8.730537414550781 0.005749554373323917 0.4862631857395172 14.309078216552734 15.44126033782959\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 16/1000 \t Train Err: 7.443472385406494 0.006111220922321081 0.20445628464221954 5.455012321472168 16.42494773864746\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 17/1000 \t Train Err: 5.684250354766846 0.0027684608940035105 0.17002306878566742 7.258749961853027 9.979669570922852\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 18/1000 \t Train Err: 4.853455543518066 0.002522163325920701 0.1455077826976776 5.698103427886963 8.302152633666992\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 19/1000 \t Train Err: 4.262304306030273 0.008678397163748741 0.1446814388036728 6.152136325836182 6.787021636962891\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 20/1000 \t Train Err: 3.858119487762451 0.003093192121013999 0.06649590283632278 3.3348793983459473 7.0024285316467285\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 21/1000 \t Train Err: 3.4118576049804688 0.0032999212853610516 0.08424855768680573 4.119073390960693 5.404160976409912\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 22/1000 \t Train Err: 3.108879566192627 0.0038715973496437073 0.09217671304941177 3.321317434310913 4.763245582580566\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 23/1000 \t Train Err: 2.9745163917541504 0.0034261371474713087 0.042425476014614105 2.484790802001953 5.148287296295166\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 24/1000 \t Train Err: 2.8194165229797363 0.0035489683505147696 0.04434378817677498 2.200214385986328 4.857565879821777\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 25/1000 \t Train Err: 2.570242404937744 0.0033989306539297104 0.05114512890577316 1.687565565109253 4.485219478607178\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 26/1000 \t Train Err: 2.519033432006836 0.0032220594584941864 0.037310708314180374 1.374830961227417 4.5875935554504395\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 27/1000 \t Train Err: 2.4283571243286133 0.0033829077146947384 0.05773899331688881 1.9254313707351685 3.3634419441223145\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 28/1000 \t Train Err: 2.302886962890625 0.0026804266963154078 0.03176456317305565 1.1421442031860352 4.208995819091797\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 29/1000 \t Train Err: 2.1564438343048096 0.0029864327516406775 0.05358732491731644 1.2556946277618408 3.505455255508423\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 30/1000 \t Train Err: 2.1266884803771973 0.0027816162910312414 0.0484829805791378 1.4444752931594849 2.9733316898345947\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 31/1000 \t Train Err: 2.0390195846557617 0.0022390384692698717 0.03866223618388176 1.1827622652053833 2.866259813308716\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 32/1000 \t Train Err: 1.9310557842254639 0.007157730869948864 0.04426664113998413 1.3611301183700562 2.6592557430267334\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 33/1000 \t Train Err: 1.851065754890442 0.00836748257279396 0.02673536352813244 0.9250126481056213 2.746307373046875\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 34/1000 \t Train Err: 1.8189555406570435 0.002403518883511424 0.027730008587241173 0.7969512939453125 3.080704689025879\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 35/1000 \t Train Err: 1.7624272108078003 0.0018843680154532194 0.0399935357272625 1.2561802864074707 2.1936941146850586\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 36/1000 \t Train Err: 1.6249182224273682 0.004734295420348644 0.031796831637620926 0.9225327372550964 2.0132899284362793\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 37/1000 \t Train Err: 1.567882776260376 0.0021626888774335384 0.023232363164424896 0.6002436876296997 2.547755718231201\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 38/1000 \t Train Err: 1.5313199758529663 0.00217650830745697 0.026524055749177933 0.7098141312599182 2.2419848442077637\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 39/1000 \t Train Err: 1.4404828548431396 0.004386692773550749 0.02224084362387657 0.4259363114833832 2.4182753562927246\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 40/1000 \t Train Err: 1.2733204364776611 0.0018442481523379683 0.018874434754252434 0.42629194259643555 2.229574680328369\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 41/1000 \t Train Err: 1.259386658668518 0.003313510213047266 0.029421737417578697 0.5856508612632751 1.8896589279174805\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 42/1000 \t Train Err: 1.2521576881408691 0.004783857148140669 0.01938166655600071 0.3461814820766449 2.3111233711242676\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 43/1000 \t Train Err: 1.2292133569717407 0.002071063034236431 0.021942850202322006 0.4656696617603302 2.068932056427002\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 44/1000 \t Train Err: 1.128746747970581 0.003524728585034609 0.02287750504910946 0.45642775297164917 1.7306324243545532\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 45/1000 \t Train Err: 1.0967061519622803 0.01454948354512453 0.024551132693886757 0.54127436876297 1.5558075904846191\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 46/1000 \t Train Err: 1.0431199073791504 0.012847564183175564 0.04218384996056557 0.6190078258514404 1.189369559288025\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 47/1000 \t Train Err: 1.0133185386657715 0.0021092321258038282 0.013825979083776474 0.2770753800868988 1.6761137247085571\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 48/1000 \t Train Err: 0.9567054510116577 0.004586610943078995 0.014754511415958405 0.3456564247608185 1.453568696975708\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 49/1000 \t Train Err: 0.9407138228416443 0.0070776138454675674 0.02054545097053051 0.4561208486557007 1.220456838607788\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 50/1000 \t Train Err: 0.9202176332473755 0.0031614142935723066 0.011641060933470726 0.286685585975647 1.5036773681640625\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 51/1000 \t Train Err: 0.8502955436706543 0.004485825542360544 0.014037835411727428 0.261470228433609 1.4015151262283325\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 52/1000 \t Train Err: 0.8055517673492432 0.001586323487572372 0.01207085233181715 0.25895756483078003 1.2997738122940063\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 53/1000 \t Train Err: 0.745665431022644 0.0011599217541515827 0.011456611566245556 0.3580838143825531 1.1415109634399414\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 54/1000 \t Train Err: 0.7061874866485596 0.0031232465989887714 0.011377043090760708 0.3388000428676605 0.9392197728157043\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 55/1000 \t Train Err: 0.6648885607719421 0.0012688999995589256 0.00947241485118866 0.26360955834388733 1.1422845125198364\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 56/1000 \t Train Err: 0.7076109051704407 0.0024704698007553816 0.009398349560797215 0.3038281798362732 1.1086375713348389\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 57/1000 \t Train Err: 0.6785869598388672 0.0014807500410825014 0.01062911655753851 0.2191060185432434 1.1564222574234009\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 58/1000 \t Train Err: 0.6877794861793518 0.0014096886152401567 0.009400570765137672 0.30001187324523926 1.0206444263458252\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 59/1000 \t Train Err: 0.6211211681365967 0.0020437357015907764 0.007910181768238544 0.25007426738739014 0.9663841724395752\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 60/1000 \t Train Err: 0.6470574736595154 0.002864431357011199 0.009593289345502853 0.2109789252281189 1.1501246690750122\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 61/1000 \t Train Err: 0.5603711605072021 0.0008608726784586906 0.007078849244862795 0.20478710532188416 0.8139731884002686\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 62/1000 \t Train Err: 0.578612208366394 0.0032247111666947603 0.00902671180665493 0.42988908290863037 0.7487800717353821\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 63/1000 \t Train Err: 0.5186704397201538 0.00102539814542979 0.008104916661977768 0.2222120761871338 0.7046389579772949\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 64/1000 \t Train Err: 0.5231799483299255 0.002828507451340556 0.010938749648630619 0.2966611087322235 0.7127745747566223\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 65/1000 \t Train Err: 0.47884172201156616 0.0009621918434277177 0.006440795958042145 0.18400059640407562 0.704879105091095\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 66/1000 \t Train Err: 0.5025489926338196 0.0009218254708684981 0.010015169158577919 0.31187739968299866 0.6326962113380432\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 67/1000 \t Train Err: 0.43556588888168335 0.0009745100978761911 0.004804776981472969 0.18548405170440674 0.7211376428604126\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 68/1000 \t Train Err: 0.4796810746192932 0.0011300166370347142 0.00498929712921381 0.19455471634864807 0.7402910590171814\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 69/1000 \t Train Err: 0.4702203869819641 0.0010465772356837988 0.00821524765342474 0.19802263379096985 0.6487798094749451\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 70/1000 \t Train Err: 0.4697670042514801 0.0023691540118306875 0.01255676057189703 0.12256406992673874 0.7824207544326782\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 71/1000 \t Train Err: 0.45800718665122986 0.000834575854241848 0.006560661364346743 0.31839612126350403 0.5303618311882019\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 72/1000 \t Train Err: 0.4298030138015747 0.0008242715266533196 0.004054277669638395 0.12216580659151077 0.7027520537376404\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 73/1000 \t Train Err: 0.41886794567108154 0.003492131596431136 0.006118918769061565 0.13266974687576294 0.5819666981697083\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 74/1000 \t Train Err: 0.4155438542366028 0.005384758580476046 0.004661516286432743 0.18202976882457733 0.46242862939834595\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 75/1000 \t Train Err: 0.4029538929462433 0.0027740243822336197 0.004722914192825556 0.11864388734102249 0.6423448920249939\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 76/1000 \t Train Err: 0.40730276703834534 0.0007228117901831865 0.004857086110860109 0.19555920362472534 0.5367923974990845\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 77/1000 \t Train Err: 0.36605364084243774 0.0009539870661683381 0.004075151868164539 0.07661056518554688 0.6930822730064392\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 78/1000 \t Train Err: 0.35346490144729614 0.0008490128675475717 0.011079245246946812 0.2623752951622009 0.35006481409072876\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 79/1000 \t Train Err: 0.36204081773757935 0.0009433329687453806 0.00526107894256711 0.21243207156658173 0.48520198464393616\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 80/1000 \t Train Err: 0.37033170461654663 0.007113362662494183 0.025272028520703316 0.1579497754573822 0.509062647819519\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 81/1000 \t Train Err: 0.33435767889022827 0.0053968350403010845 0.009334199130535126 0.08819041401147842 0.5340674519538879\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 82/1000 \t Train Err: 0.33757588267326355 0.0005324012017808855 0.004930454771965742 0.17805498838424683 0.5068127512931824\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 83/1000 \t Train Err: 0.31310147047042847 0.0008425716659985483 0.002387900371104479 0.0860978364944458 0.5014434456825256\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 84/1000 \t Train Err: 0.2939777672290802 0.0005211451789364219 0.0028972462750971317 0.09632651507854462 0.32632964849472046\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 85/1000 \t Train Err: 0.299526184797287 0.0010479650227352977 0.0028079829644411802 0.21169798076152802 0.40237608551979065\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 86/1000 \t Train Err: 0.30821743607521057 0.0029116582591086626 0.0035962064284831285 0.12347913533449173 0.4878503084182739\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 87/1000 \t Train Err: 0.30215075612068176 0.0008221607422456145 0.002995165530592203 0.14785777032375336 0.37114524841308594\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 88/1000 \t Train Err: 0.28064608573913574 0.0016746899345889688 0.0033167945221066475 0.12754225730895996 0.36404597759246826\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 89/1000 \t Train Err: 0.3496437072753906 0.00890024658292532 0.004831824917346239 0.15963110327720642 0.61163729429245\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 90/1000 \t Train Err: 0.25926288962364197 0.0013453153660520911 0.003530274610966444 0.1070982962846756 0.3172129690647125\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 91/1000 \t Train Err: 0.27578499913215637 0.0030208230018615723 0.0031245634891092777 0.11023195832967758 0.3903992176055908\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 92/1000 \t Train Err: 0.2994685769081116 0.004197238944470882 0.0023698117583990097 0.1903829723596573 0.4574669599533081\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 93/1000 \t Train Err: 0.2922815680503845 0.0007029320695437491 0.002348515437915921 0.05019014701247215 0.5161943435668945\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 94/1000 \t Train Err: 0.2519854009151459 0.0017584029119461775 0.002146892249584198 0.09622428566217422 0.3795848488807678\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 95/1000 \t Train Err: 0.2682843506336212 0.0005638344446197152 0.002339219441637397 0.10693421214818954 0.41891878843307495\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 96/1000 \t Train Err: 0.23551344871520996 0.0013522340450435877 0.002122987760230899 0.07678966224193573 0.39242544770240784\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 97/1000 \t Train Err: 0.22959834337234497 0.0011262426851317286 0.005589182022958994 0.09626860916614532 0.3728175759315491\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 98/1000 \t Train Err: 0.25520408153533936 0.00047998130321502686 0.0021106365602463484 0.06091078370809555 0.46852487325668335\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 99/1000 \t Train Err: 0.2501460909843445 0.0004842414637096226 0.0019760928116738796 0.08570502698421478 0.2884354889392853\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 100/1000 \t Train Err: 0.20366686582565308 0.002971487818285823 0.00713342847302556 0.11135696619749069 0.31001028418540955\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 101/1000 \t Train Err: 0.24212954938411713 0.002736428752541542 0.006694257725030184 0.07518018037080765 0.4043455421924591\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 102/1000 \t Train Err: 0.21833863854408264 0.0023800276685506105 0.0043370905332267284 0.06609099358320236 0.32194095849990845\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 103/1000 \t Train Err: 0.17334935069084167 0.0016206795116886497 0.002039699349552393 0.07832205295562744 0.2227916121482849\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 104/1000 \t Train Err: 0.22861380875110626 0.00032782970811240375 0.0014689437812194228 0.04350364953279495 0.3887456953525543\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 105/1000 \t Train Err: 0.19524142146110535 0.0035212738439440727 0.006021957378834486 0.11795622110366821 0.25324639678001404\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 106/1000 \t Train Err: 0.15101337432861328 0.0010637118248268962 0.006495238747447729 0.07132977992296219 0.20919014513492584\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 107/1000 \t Train Err: 0.16016799211502075 0.0004500410286709666 0.0017898066435009241 0.05250254645943642 0.23433028161525726\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 108/1000 \t Train Err: 0.16674524545669556 0.0010276080574840307 0.004126560874283314 0.11649245023727417 0.1926332712173462\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 109/1000 \t Train Err: 0.1631726324558258 0.000415267248172313 0.0019610195886343718 0.047292474657297134 0.2021452933549881\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 110/1000 \t Train Err: 0.15775498747825623 0.000414436828577891 0.0015739103546366096 0.09467942267656326 0.19835522770881653\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 111/1000 \t Train Err: 0.1562364548444748 0.0061783152632415295 0.0036767187993973494 0.05223577097058296 0.2691049575805664\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 112/1000 \t Train Err: 0.12982504069805145 0.006277484819293022 0.0025301864370703697 0.0412493497133255 0.1602799892425537\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 113/1000 \t Train Err: 0.16289404034614563 0.0005659068119712174 0.0012484622420743108 0.056075569242239 0.21527709066867828\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 114/1000 \t Train Err: 0.1465548872947693 0.0014426918933168054 0.0027563830371946096 0.05711502209305763 0.18701669573783875\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 115/1000 \t Train Err: 0.14275527000427246 0.000653824012260884 0.0014178442070260644 0.0954805463552475 0.21085317432880402\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 116/1000 \t Train Err: 0.15016044676303864 0.000818660540971905 0.0016999151557683945 0.06580580770969391 0.1766045093536377\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 117/1000 \t Train Err: 0.12201909720897675 0.0015263869427144527 0.0018288405844941735 0.041804831475019455 0.1663890928030014\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 118/1000 \t Train Err: 0.12489122897386551 0.00029311463003978133 0.001244824263267219 0.025852475315332413 0.14584743976593018\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 119/1000 \t Train Err: 0.13460129499435425 0.010341204702854156 0.006242326460778713 0.04511499032378197 0.2327692061662674\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 120/1000 \t Train Err: 0.1339903473854065 0.0011800267966464162 0.0022739972919225693 0.032896753400564194 0.15254607796669006\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 121/1000 \t Train Err: 0.12022703886032104 0.00038554586353711784 0.004875303246080875 0.06586042791604996 0.1974797397851944\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 122/1000 \t Train Err: 0.11403584480285645 0.0008288199896924198 0.0015265692491084337 0.02858065813779831 0.17847180366516113\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 123/1000 \t Train Err: 0.10409620404243469 0.0009630229906179011 0.0013286847388371825 0.07061317563056946 0.12211479991674423\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 124/1000 \t Train Err: 0.09401391446590424 0.0007407785742543638 0.001438300940208137 0.04962582886219025 0.11180052161216736\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 125/1000 \t Train Err: 0.11572305113077164 0.0022304926533252 0.0015191843267530203 0.044924236834049225 0.16141481697559357\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 126/1000 \t Train Err: 0.09036736190319061 0.0019903378561139107 0.000955000170506537 0.041499681770801544 0.07043104618787766\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 127/1000 \t Train Err: 0.10687348991632462 0.0012028561905026436 0.0007425333024002612 0.03638176992535591 0.15492156147956848\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 128/1000 \t Train Err: 0.10416512191295624 0.00024147499061655253 0.0009293883922509849 0.028597401455044746 0.18022169172763824\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 129/1000 \t Train Err: 0.08835020661354065 0.003051575506106019 0.003711810801178217 0.05737682431936264 0.120809406042099\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 130/1000 \t Train Err: 0.09325292706489563 0.0029582607094198465 0.0012874709209427238 0.048724617809057236 0.09893109649419785\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 131/1000 \t Train Err: 0.0896429568529129 0.00045463963760994375 0.0013198753586038947 0.035679738968610764 0.10701773315668106\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 132/1000 \t Train Err: 0.08471657335758209 0.0019452492706477642 0.0034233005717396736 0.0296705961227417 0.06480914354324341\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 133/1000 \t Train Err: 0.09226851165294647 0.0015877934638410807 0.002174847759306431 0.02515079453587532 0.13485927879810333\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 134/1000 \t Train Err: 0.08039496093988419 0.0059851668775081635 0.003604266792535782 0.023677635937929153 0.10068632662296295\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 135/1000 \t Train Err: 0.07723499834537506 0.0029561370611190796 0.0013383673503994942 0.02225509285926819 0.07217926532030106\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 136/1000 \t Train Err: 0.08774624764919281 0.0015881237341091037 0.0009627199615351856 0.03728866204619408 0.1386537104845047\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 137/1000 \t Train Err: 0.09112915396690369 0.0011313623981550336 0.000519853550940752 0.02461346611380577 0.09449820965528488\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 138/1000 \t Train Err: 0.0764939934015274 0.0015739547088742256 0.002696078270673752 0.02539546601474285 0.07497072219848633\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 139/1000 \t Train Err: 0.08085883408784866 0.0021111860405653715 0.002203426556661725 0.038074932992458344 0.09940771758556366\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 140/1000 \t Train Err: 0.06707267463207245 0.00048505759332329035 0.0005829626461490989 0.023159010335803032 0.06615001708269119\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 141/1000 \t Train Err: 0.06301475316286087 0.0009192335419356823 0.0005843854160048068 0.03602571412920952 0.0841449722647667\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 142/1000 \t Train Err: 0.06407696008682251 0.004187325481325388 0.0031896685250103474 0.025413284078240395 0.0635743960738182\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 143/1000 \t Train Err: 0.056899648159742355 0.0012612127466127276 0.0010306687327101827 0.021679643541574478 0.05377352237701416\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 144/1000 \t Train Err: 0.07650666683912277 0.00024983700131997466 0.001161872292868793 0.03564540296792984 0.08232379704713821\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 145/1000 \t Train Err: 0.05720144882798195 0.0014120059786364436 0.0017668631626293063 0.03595374524593353 0.06960506737232208\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 146/1000 \t Train Err: 0.0696098804473877 0.00025453948182985187 0.0005893263150937855 0.018764346837997437 0.03399818018078804\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 147/1000 \t Train Err: 0.06046349182724953 0.000990899046882987 0.0004648214380722493 0.02092691697180271 0.02779306285083294\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 148/1000 \t Train Err: 0.059290580451488495 0.0022199612576514482 0.001315723406150937 0.023515846580266953 0.07406013458967209\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 149/1000 \t Train Err: 0.06473296880722046 0.0018222469370812178 0.001621031784452498 0.03560686111450195 0.06342668831348419\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 150/1000 \t Train Err: 0.053641099482774734 0.0003684388066176325 0.0008896152721717954 0.026580102741718292 0.07826311886310577\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 151/1000 \t Train Err: 0.05356581509113312 7.923251541797072e-05 0.00026825847453437746 0.018474940210580826 0.06338636577129364\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 152/1000 \t Train Err: 0.053509317338466644 0.000861925829667598 0.0006878876592963934 0.03851037099957466 0.045843761414289474\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 153/1000 \t Train Err: 0.053101420402526855 9.4662478659302e-05 0.0003207987465430051 0.020021196454763412 0.06933460384607315\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 154/1000 \t Train Err: 0.04212021827697754 0.00016945773677434772 0.0002675392315723002 0.01669382117688656 0.040745120495557785\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 155/1000 \t Train Err: 0.038299448788166046 0.0006350624025799334 0.0006876391125842929 0.021383486688137054 0.03851837292313576\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 156/1000 \t Train Err: 0.05666494742035866 0.0003512321272864938 0.00041459291242063046 0.02086237445473671 0.0636894553899765\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 157/1000 \t Train Err: 0.03654496371746063 7.953925523906946e-05 0.00024021716671995819 0.016982462257146835 0.03953758254647255\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 158/1000 \t Train Err: 0.04525972530245781 0.00030174560379236937 0.00044638325925916433 0.011691144667565823 0.041540782898664474\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 159/1000 \t Train Err: 0.039281442761421204 0.0004989005392417312 0.0007457975880242884 0.02650555409491062 0.03530228137969971\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 160/1000 \t Train Err: 0.04518686234951019 0.00017189154459629208 0.00015555098070763052 0.01069786585867405 0.0570724681019783\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 161/1000 \t Train Err: 0.050255514681339264 0.00024805148132145405 0.0007079236092977226 0.02650279738008976 0.06579962372779846\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 162/1000 \t Train Err: 0.044423386454582214 0.00031116121681407094 0.0003777859383262694 0.017297720536589622 0.051457729190588\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 163/1000 \t Train Err: 0.04354090988636017 0.0005877528456039727 0.00029637134866788983 0.013659253716468811 0.020231008529663086\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 164/1000 \t Train Err: 0.031157420948147774 9.798325481824577e-05 0.0003091402177233249 0.01797928847372532 0.023115914314985275\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 165/1000 \t Train Err: 0.04593996703624725 8.030498429434374e-05 0.0002926443121396005 0.013717164285480976 0.055002935230731964\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 166/1000 \t Train Err: 0.03411879763007164 0.0003377409011591226 0.0002743960649240762 0.01241423562169075 0.01924932189285755\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 167/1000 \t Train Err: 0.04760969430208206 0.00011350985732860863 0.00043987829121761024 0.014360723085701466 0.02648620493710041\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 168/1000 \t Train Err: 0.03372378274798393 0.0002949015761259943 0.00037480168975889683 0.014883959665894508 0.016884008422493935\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 169/1000 \t Train Err: 0.03702085092663765 0.00018087019270751625 0.0006288738804869354 0.024845065549016 0.04383993148803711\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 170/1000 \t Train Err: 0.02824767678976059 0.0003424994938541204 0.0004191694315522909 0.015994146466255188 0.014700128696858883\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 171/1000 \t Train Err: 0.03430527076125145 0.0009072513785213232 0.0003185459354426712 0.015698766335844994 0.011771176941692829\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 172/1000 \t Train Err: 0.03365296125411987 0.00030303309904411435 0.00022830757370684296 0.017944660037755966 0.02212398685514927\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 173/1000 \t Train Err: 0.041653022170066833 0.000587280432227999 0.0007374075939878821 0.015334094874560833 0.06751907616853714\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 174/1000 \t Train Err: 0.03477595001459122 0.0009183208458125591 0.00013558704813476652 0.013238264247775078 0.01334806066006422\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 175/1000 \t Train Err: 0.037530943751335144 0.00025187639403156936 0.00033183913910761476 0.01504728477448225 0.031140420585870743\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 176/1000 \t Train Err: 0.027848348021507263 0.0014607060002163053 0.001157138729467988 0.011170606128871441 0.01426300685852766\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 177/1000 \t Train Err: 0.03245190531015396 0.0002554329694248736 0.00015877540863584727 0.014040789566934109 0.04714728519320488\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 178/1000 \t Train Err: 0.041977256536483765 0.0001379920431645587 0.00021775254572276026 0.009346511214971542 0.01231997087597847\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 179/1000 \t Train Err: 0.03204528987407684 9.879021672531962e-05 0.0003249702858738601 0.01157579105347395 0.032357051968574524\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 180/1000 \t Train Err: 0.030494939535856247 5.318508192431182e-05 0.0001941232185345143 0.01810402423143387 0.03970681130886078\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 181/1000 \t Train Err: 0.03218014910817146 0.0006771694752387702 0.00016017410962376744 0.009343582205474377 0.03883388638496399\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 182/1000 \t Train Err: 0.03439633548259735 8.35641985759139e-05 0.0008245277567766607 0.026584787294268608 0.04398134723305702\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 183/1000 \t Train Err: 0.03437873348593712 0.0003609458508435637 0.0001779649028321728 0.011353005655109882 0.022845609113574028\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 184/1000 \t Train Err: 0.029747625812888145 0.0005436437204480171 0.0006577487220056355 0.02241024561226368 0.03428546339273453\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 185/1000 \t Train Err: 0.03702589124441147 0.001318416208960116 0.0003100436006207019 0.006715381983667612 0.012282946147024632\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 186/1000 \t Train Err: 0.022873839363455772 0.00014723198546562344 0.0011230326490476727 0.015240584500133991 0.020318059250712395\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 187/1000 \t Train Err: 0.02688605710864067 0.00014236278366297483 0.00022871489636600018 0.017673302441835403 0.029775310307741165\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 188/1000 \t Train Err: 0.026118462905287743 3.561102130333893e-05 0.00015905339387245476 0.010189777240157127 0.01750301755964756\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 189/1000 \t Train Err: 0.031032036989927292 6.626216054428369e-05 0.0001567322324262932 0.014112681150436401 0.03739028424024582\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 190/1000 \t Train Err: 0.02181524783372879 0.00023006339324638247 0.0005933582433499396 0.010394968092441559 0.00304942368529737\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 191/1000 \t Train Err: 0.027184132486581802 0.004482210148125887 0.0019434703281149268 0.010643635876476765 0.018308935686945915\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 192/1000 \t Train Err: 0.024762475863099098 0.00021026897593401372 0.00068919628392905 0.013836676254868507 0.00759515818208456\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 193/1000 \t Train Err: 0.027485240250825882 5.092989158583805e-05 0.00041440658969804645 0.007257797755300999 0.029338931664824486\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 194/1000 \t Train Err: 0.022330544888973236 0.0004199454269837588 0.0004707501211669296 0.019549088552594185 0.0023543694987893105\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 195/1000 \t Train Err: 0.022276023402810097 6.339305400615558e-05 0.00018617554451338947 0.012746947817504406 0.02517220377922058\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 196/1000 \t Train Err: 0.02131063863635063 6.503217446152121e-05 0.0001230579655384645 0.009538630954921246 0.010168644599616528\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 197/1000 \t Train Err: 0.021132078021764755 0.0002956095850095153 8.20207133074291e-05 0.006673957221210003 0.010186844505369663\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 198/1000 \t Train Err: 0.019411560148000717 0.00042201197356916964 0.0009095012792386115 0.013239831663668156 0.018353110179305077\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 199/1000 \t Train Err: 0.03216658905148506 4.9469184887129813e-05 0.0002943709841929376 0.01148073747754097 0.016176927834749222\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 200/1000 \t Train Err: 0.02571428008377552 0.0010263347066938877 0.0005481779226101935 0.016015449538826942 0.01978922262787819\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 201/1000 \t Train Err: 0.026272011920809746 3.759583705686964e-05 9.925611811922863e-05 0.008123734965920448 0.01331140287220478\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 202/1000 \t Train Err: 0.03202397748827934 6.046362250344828e-05 0.000284630514215678 0.011763068847358227 0.04103183373808861\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 203/1000 \t Train Err: 0.012851575389504433 0.00011363952944520861 0.00016413710545748472 0.010319913737475872 0.002792573068290949\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 204/1000 \t Train Err: 0.026115499436855316 0.0005245269276201725 0.00024940649745985866 0.011106887832283974 0.02185993455350399\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 205/1000 \t Train Err: 0.018948335200548172 2.8755090170307085e-05 8.58057028381154e-05 0.005748868454247713 0.015843190252780914\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 206/1000 \t Train Err: 0.018574167042970657 0.00015149133105296642 0.00048761311336420476 0.02577385865151882 0.013325332663953304\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 207/1000 \t Train Err: 0.02082146145403385 0.000238466338487342 0.00023394331219606102 0.006748242769390345 0.019078979268670082\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 208/1000 \t Train Err: 0.014403259381651878 6.994893192313612e-05 0.0008789921994321048 0.010097990743815899 0.00996581930667162\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 209/1000 \t Train Err: 0.020921753719449043 0.0004979136865586042 0.00010895056766457856 0.00956189725548029 0.015378139913082123\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 210/1000 \t Train Err: 0.022038539871573448 0.0001340815215371549 0.00015701379743404686 0.014402204193174839 0.02424498274922371\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 211/1000 \t Train Err: 0.01667097397148609 0.00011134350643260404 0.00014891373575665057 0.00600818358361721 0.009433449245989323\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 212/1000 \t Train Err: 0.01602860540151596 4.298926069168374e-05 7.710252975812182e-05 0.004729713778942823 0.005112841725349426\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 213/1000 \t Train Err: 0.01903412863612175 0.00030714491731487215 0.0001821738842409104 0.005955686792731285 0.022314537316560745\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 214/1000 \t Train Err: 0.015248223207890987 0.00026072614127770066 0.00019891293777618557 0.007477042265236378 0.0036678414326161146\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 215/1000 \t Train Err: 0.014912809245288372 0.00047885856474749744 0.0004725187609437853 0.00442067626863718 0.006714401766657829\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 216/1000 \t Train Err: 0.022600673139095306 5.488095121108927e-05 0.0005237676086835563 0.0061714984476566315 0.03166600689291954\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 217/1000 \t Train Err: 0.022118201479315758 8.072196214925498e-05 0.00010541417577769607 0.00999145582318306 0.022547846660017967\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 218/1000 \t Train Err: 0.01601581647992134 3.067262514377944e-05 0.00018664993694983423 0.004181408789008856 0.013367431238293648\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 219/1000 \t Train Err: 0.01162786316126585 5.145326576894149e-05 0.00015623572107870132 0.006794607732445002 0.001922846888191998\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 220/1000 \t Train Err: 0.012896351516246796 0.0003044742625206709 9.53769194893539e-05 0.006998015101999044 0.003260016907006502\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 221/1000 \t Train Err: 0.023554792627692223 0.00018602493219077587 0.0004451847053132951 0.011047394014894962 0.03432558849453926\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 222/1000 \t Train Err: 0.016859270632267 0.0002703650388866663 0.00010159210069105029 0.0054770237766206264 0.013049724511802197\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 223/1000 \t Train Err: 0.018101878464221954 5.2419105486478657e-05 6.96199931553565e-05 0.005247439723461866 0.011564591899514198\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 224/1000 \t Train Err: 0.015453542582690716 0.00010983451647916809 0.00022485408408101648 0.005099967587739229 0.012966718524694443\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 225/1000 \t Train Err: 0.018901851028203964 4.1673782106954604e-05 0.0015293046599254012 0.00927029736340046 0.015386526472866535\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 226/1000 \t Train Err: 0.019163722172379494 0.0016058672918006778 0.002710553817451 0.003990732133388519 0.013572349213063717\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 227/1000 \t Train Err: 0.0185165386646986 8.810655708657578e-05 0.0001792146940715611 0.007222854066640139 0.020297806710004807\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 228/1000 \t Train Err: 0.020369376987218857 0.0009141123155131936 0.001427489914931357 0.008912032470107079 0.02442525327205658\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 229/1000 \t Train Err: 0.01552458293735981 0.00011080846888944507 6.443277379730716e-05 0.004490815103054047 0.00922235008329153\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 230/1000 \t Train Err: 0.0195521991699934 2.673462404345628e-05 0.0002968674525618553 0.0058441669680178165 0.013992007821798325\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.02it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 231/1000 \t Train Err: 0.01986689493060112 4.5369306462816894e-05 4.316281047067605e-05 0.005999550223350525 0.015800679102540016\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 232/1000 \t Train Err: 0.019927091896533966 0.00010001207556342706 0.0014023327967152 0.0054413750767707825 0.027315480634570122\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.05it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 233/1000 \t Train Err: 0.014753343537449837 0.0003090432728640735 8.334611629834399e-05 0.004138716962188482 0.004037454724311829\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:31<00:00,  1.03it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 234/1000 \t Train Err: 0.012261731550097466 0.0003884017060045153 0.00043851000373251736 0.00813040230423212 0.007334974128752947\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 235/1000 \t Train Err: 0.011006608605384827 0.0003388413751963526 0.00021402201673481613 0.005710902623832226 0.008260917849838734\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "00%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 32/32 [00:30<00:00,  1.04it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 236/1000 \t Train Err: 0.00900082103908062 0.0020744148641824722 0.0004009941185358912 0.005855425260961056 0.000494154985062778\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "  6%|████████████▌                                                                                                                                                                                           | 2/32 [00:01<00:30,  1.00s/it]"
+     ]
+    }
+   ],
    "source": [
     "while epoch < NEPOCHS:\n",
     "    model.train()\n",
@@ -527,18 +4097,17 @@
     "        optimizer.zero_grad()\n",
     "        output = model(batch_src, batch_padding_mask)\n",
     "        loss = criterion(output.squeeze(1), batch_labels)\n",
-    "        train_loss = loss.item()\n",
     "        loss.backward()\n",
     "        optimizer.step()\n",
     "        \n",
-    "        train_err.append(train_loss)\n",
+    "        train_err.append(loss.item())\n",
     "        len1.append(criterion(output[batch_labels == 1].squeeze(1), batch_labels[batch_labels == 1]).item())\n",
     "        len2.append(criterion(output[batch_labels == 2].squeeze(1), batch_labels[batch_labels == 2]).item())\n",
     "        len3.append(criterion(output[batch_labels == 3].squeeze(1), batch_labels[batch_labels == 3]).item())\n",
     "        leninf.append(criterion(output[batch_labels == MAX_VTXS].squeeze(1), batch_labels[batch_labels == MAX_VTXS]).item())\n",
     "        \n",
     "        with open('loss', 'a') as f:\n",
-    "            f.write(f\"{train_loss} {len1[-1]} {len2[-1]} {len3[-1]} {leninf[-1]}\\n\")\n",
+    "            f.write(f\"{train_err[-1]} {len1[-1]} {len2[-1]} {len3[-1]} {leninf[-1]}\\n\")\n",
     "    print(f\"Epoch {epoch}/{NEPOCHS} \\t Train Err: {train_err[-1]} {len1[-1]} {len2[-1]} {len3[-1]} {leninf[-1]}\")\n",
     "\n",
     "    epoch += 1\n",
@@ -839,7 +4408,7 @@
     "    print(f\"Epoch {epoch}/{N_TUNE_EPOCHS} \\t Train Err: {train_loss:.4f}\")\n",
     "\n",
     "    if epoch % 10 == 9:\n",
-    "        torch.save(model.state_dict(), f\"tune_model_weights_{epoch + 1}.pth\")"
+    "        torch.save(model.state_dict(), f\"checkpoints/tune_model_weights_{epoch + 1}.pth\")"
    ]
   },
   {
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