path: root/transformer_shortest_paths.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LPphBnKR-aWF"
   },
   "source": [
    "# Step 0: Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "execution_state": "idle",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ge5QvElvhCOw",
    "outputId": "c7cdaefa-d6dc-44ad-c258-e4fb2aca97a5"
   },
   "outputs": [],
   "source": [
    "from collections import deque\n",
    "import pickle\n",
    "from tqdm import tqdm\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import pickle\n",
    "from math import sqrt\n",
    "from torch.utils.data import DataLoader, TensorDataset\n",
    "%matplotlib widget\n",
    "import matplotlib.pyplot as plt\n",
    "torch.manual_seed(42)\n",
    "\n",
    "import os\n",
    "from IPython.display import clear_output\n",
    "import ipdb\n",
    "\n",
    "import random\n",
    "random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "execution_state": "idle",
   "metadata": {
    "id": "lylOX2POPwFL"
   },
   "outputs": [],
   "source": [
    "SEQ_LEN = 65 # means 32 edges, final token is the target vertex\n",
    "PAD_TOKEN = 0\n",
    "AVG_DEG = 2\n",
    "MAX_VTXS = SEQ_LEN//AVG_DEG - 1 # 31\n",
    "MIN_VTXS = 8\n",
    "MAX_TUNE_VTXS = 16\n",
    "# vertices are labelled 1,2,...,63\n",
    "# we also have a padding token which is 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gKt-yIpDebF1"
   },
   "source": [
    "# Step 1: Generate synthetic data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "execution_state": "idle",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "1IbzGIWseK3E",
    "outputId": "a3cbc233-358c-4e17-ea6e-f4e9349d886b"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 23/23 [00:06<00:00,  3.52it/s]\n"
     ]
    }
   ],
   "source": [
    "# original task data\n",
    "NTRAIN1 = 300_000\n",
    "# the data will be edge lists\n",
    "# like this: [1 3 1 5 2 4 0 0 0 0 2]\n",
    "# this represents edges (1,3), (1,5) (2,4)\n",
    "# (the zeros are just padding tokens)\n",
    "# the final 2 means which vertex we're going to \n",
    "\n",
    "# the label is the shortest distance from vtx 1 to vtx 2\n",
    "# or \"number of vertices\" if no path exists\n",
    "\n",
    "def random_graph(n):\n",
    "    edge_list = []\n",
    "    adjacencies = [set() for _ in range(n+1)]\n",
    "    indices = [random.randint(1, n-1) for _ in range(AVG_DEG * (n-1))]\n",
    "    for i in range(0, len(indices), 2):\n",
    "        u = indices[i]\n",
    "        v = indices[i + 1]\n",
    "        if u != v:\n",
    "            edge_list += [u,v]\n",
    "            adjacencies[u].add(v)\n",
    "            adjacencies[v].add(u)\n",
    "\n",
    "    edge_list += [PAD_TOKEN]*(SEQ_LEN-len(edge_list))\n",
    "    return edge_list, adjacencies\n",
    "\n",
    "\"\"\"\n",
    "input: G, represented as an adjacency list\n",
    "output: [number of vertices]+[d(1,i) for i in range(n)] if target=None\n",
    "if target is set to some value, then we instead just output that specific distance\n",
    "\"\"\"\n",
    "def SSSP(n, G, target=2):\n",
    "    dist = [n for _ in G]\n",
    "    dist[1] = 0\n",
    "    frontier = deque()\n",
    "    frontier.append(1)\n",
    "    while len(frontier) > 0:\n",
    "        vtx = frontier.popleft()\n",
    "        for x in G[vtx]:\n",
    "            if dist[x] == n:\n",
    "                dist[x] = 1 + dist[vtx]\n",
    "                frontier.append(x)\n",
    "                if x == target:\n",
    "                    return dist[target]\n",
    "    if target is not None:\n",
    "        return dist[target]\n",
    "    else:\n",
    "        return dist\n",
    "\n",
    "graphs1 = []\n",
    "distance1 = []\n",
    "\n",
    "for n in tqdm(range(MIN_VTXS, MAX_VTXS)):\n",
    "    for _ in range(NTRAIN1//(MAX_VTXS - MIN_VTXS)):\n",
    "        edge_list, adj_list = random_graph(n)\n",
    "        dist = SSSP(n, adj_list)\n",
    "        edge_list[-1] = 2 # target token\n",
    "        graphs1.append(edge_list)\n",
    "        distance1.append(dist)\n",
    "\n",
    "data = {\n",
    "    \"data\": torch.tensor(graphs1),\n",
    "    \"labels\": torch.tensor(distance1, dtype=torch.float32)\n",
    "}\n",
    "\n",
    "with open('data.pkl', 'wb') as file:\n",
    "    pickle.dump(data, file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "execution_state": "idle",
   "metadata": {},
   "outputs": [],
   "source": [
    "def vertices_on_shortest_12_path(n, G, target=2):\n",
    "    dist = [n for _ in G]\n",
    "    parent = [-1 for _ in G]\n",
    "    dist[1] = 0\n",
    "    frontier = deque()\n",
    "    frontier.append(1)\n",
    "    while len(frontier) > 0:\n",
    "        vtx = frontier.popleft()\n",
    "        for x in G[vtx]:\n",
    "            if dist[x] == n:\n",
    "                parent[x] = vtx\n",
    "                dist[x] = 1 + dist[vtx]\n",
    "                frontier.append(x)\n",
    "                if x == target:\n",
    "                    path = [x]\n",
    "                    while parent[x] != -1:\n",
    "                        x = parent[x]\n",
    "                        path.append(x)\n",
    "                    return list(reversed(path))\n",
    "    return []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "execution_state": "idle",
   "metadata": {},
   "outputs": [],
   "source": [
    "# fine tuning data\n",
    "NTRAIN2 = 2000\n",
    "\n",
    "graphs2 = []\n",
    "distance2 = []\n",
    "\n",
    "for n in range(MIN_VTXS, MAX_TUNE_VTXS):\n",
    "    for _ in range(NTRAIN2//(MAX_TUNE_VTXS - MIN_VTXS)):\n",
    "        while True:\n",
    "            edge_list, adj_list = random_graph(n)\n",
    "            path = vertices_on_shortest_12_path(n, adj_list)\n",
    "            if len(path) > 1:\n",
    "                target_vtx_idx = random.randrange(1, len(path))\n",
    "                target_vtx = path[target_vtx_idx]\n",
    "                edge_list[-1] = target_vtx\n",
    "                graphs2.append(edge_list)\n",
    "                distance2.append(target_vtx_idx)\n",
    "                break\n",
    "\n",
    "tune_data = {\n",
    "    \"data\": torch.tensor(graphs2),\n",
    "    \"labels\": torch.tensor(distance2, dtype=torch.float32)\n",
    "}\n",
    "\n",
    "with open('tune_data.pkl', 'wb') as file:\n",
    "    pickle.dump(tune_data, file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "execution_state": "idle",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "EpDBxcgaIPpJ",
    "outputId": "37cf9577-8cd8-444c-ec1a-c6f4b6061b7f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pre-train dataset size = 149MB\n",
      "fine-tune dataset = 1MB\n"
     ]
    }
   ],
   "source": [
    "print(f\"pre-train dataset size = {os.path.getsize('data.pkl')//(1024*1024)}MB\")\n",
    "print(f\"fine-tune dataset = {os.path.getsize('tune_data.pkl')//(1024*1024)}MB\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "execution_state": "idle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f5d5ab87fe4145eb8728e6d950e749d8",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure 2\n",
       "                </div>\n",
       "                <img 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gAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAUptcDcNGiRbn44oszaNCgDB06NFdddVU2b97cY8yePXvS2tqaU089NSeffHKmTZuW7du39xizZcuWTJ06NSeeeGKGDh2aW265JW+++WaPMU899VQuuuii1NfX5+yzz86yZcveNp977rknZ511VgYOHJhJkyblueeeO0LvHACgb+j1AFy7dm1aW1vzk5/8JKtXr87+/ftz+eWXZ/fu3dUxc+fOzWOPPZaHH344a9euzbZt23L11VdX9x84cCBTp07Nvn378swzz+R73/teli1blgULFlTHvPLKK5k6dWouvfTSrF+/PnPmzMkXv/jFrFq1qjrmwQcfTFtbWxYuXJgXX3wx48aNS0tLS3bs2NGLKwIA0Lv6VSqVSi0nsHPnzgwdOjRr167NJZdcks7Ozpx++ulZvnx5rrnmmiTJpk2bct5556W9vT2TJ0/OE088kU9+8pPZtm1bhg0bliRZunRp5s2bl507d6auri7z5s3LihUrsnHjxuprXXvttdm1a1dWrlyZJJk0aVIuvvjiLFmyJEnS3d2dkSNHZvbs2bntttv+6Ny7urrS2NiYzs7ONDQ0vP+Lc0fjYfZ1Hv3PA4AaOOK/v48CNf8MYGfn/wbCkCFDkiTr1q3L/v37M2XKlOqYc889N6NGjUp7e3uSpL29PRdccEE1/pKkpaUlXV1deemll6pj3nqMg2MOHmPfvn1Zt25djzH9+/fPlClTqmMAAI5Fx9Xyxbu7uzNnzpx85CMfyfnnn58k6ejoSF1dXQYPHtxj7LBhw9LR0VEd89b4O7j/4L7Djenq6sobb7yR3/72tzlw4MAhx2zatOmQ8927d2/27t1b/bmrq+s9vHsAgNqo6RXA1tbWbNy4MQ888EAtp/EnW7RoURobG6uPkSNH1npKAADvWM0CcNasWXn88cfz4x//OCNGjKhub2pqyr59+7Jr164e47dv356mpqbqmD+8K/jgz39sTENDQ0444YScdtppGTBgwCHHHDzGH5o/f346Ozurj61bt76nNQAAqIVeD8BKpZJZs2blkUceyZNPPpnRo0f32D9+/Pgcf/zxWbNmTXXb5s2bs2XLljQ3NydJmpubs2HDhh53665evToNDQ0ZM2ZMdcxbj3FwzMFj1NXVZfz48T3GdHd3Z82aNdUxf6i+vj4NDQ09HgAAR5te/wxga2trli9fnh/+8IcZNGhQ9TN7jY2NOeGEE9LY2JiZM2emra0tQ4YMSUNDQ2bPnp3m5uZMnjw5SXL55ZdnzJgx+dznPpfFixeno6Mjt99+e1pbW1NfX58kuemmm7JkyZLceuutueGGG/Lkk0/moYceyooVK6pzaWtry4wZMzJhwoRMnDgxd911V3bv3p3rr7++t5cFAKDX9HoA3nfffUmSj33sYz22f/e7380XvvCFJMm3v/3t9O/fP9OmTcvevXvT0tKSe++9tzp2wIABefzxx3PzzTenubk5J510UmbMmJGvf/3r1TGjR4/OihUrMnfu3Nx9990ZMWJE7r///rS0tFTHTJ8+PTt37syCBQvS0dGRCy+8MCtXrnzbjSEAAMeSmn8P4NHM9wC+x+cBQA34HsA+8D2AAAD0LgEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUJjjaj0BCnZH42H2dfbmTACgKK4AAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFEYAAgAURgACABRGAAIAFKbXA/Dpp5/Opz71qQwfPjz9+vXLo48+2mN/pVLJggULcsYZZ+SEE07IlClT8vOf/7zHmN/85je57rrr0tDQkMGDB2fmzJl5/fXXe4z56U9/mo9+9KMZOHBgRo4cmcWLF79tLg8//HDOPffcDBw4MBdccEH+4z/+4wi9awCAvqPXA3D37t0ZN25c7rnnnkPuX7x4cb7zne9k6dKlefbZZ3PSSSelpaUle/bsqY657rrr8tJLL2X16tV5/PHH8/TTT+dLX/pSdX9XV1cuv/zynHnmmVm3bl2+9a1v5Y477sg///M/V8c888wz+cxnPpOZM2fmv//7v3PVVVflqquuysaNG4/wCgAA1Fa/SqVSqdmL9+uXRx55JFdddVXy+6t/w4cPz9/+7d/mK1/5SpKks7Mzw4YNy7Jly3LttdfmZz/7WcaMGZPnn38+EyZMSJKsXLkyn/jEJ/LLX/4yw4cPz3333Ze/+7u/S0dHR+rq6pIkt912Wx599NFs2rQpSTJ9+vTs3r07jz/+eHU+kydPzoUXXpilS5f+SfPv6upKY2NjOjs709DQ8L6vT+5oPMy+znKfBwDvwRH//X0U6FOfAXzllVfS0dGRKVOmVLc1NjZm0qRJaW9vT5K0t7dn8ODB1fhLkilTpqR///559tlnq2MuueSSavwlSUtLSzZv3pzf/va31TFvfZ2DYw6+DgDAseq4Wk/grTo6OpIkw4YN67F92LBh1X0dHR0ZOnRoj/3HHXdchgwZ0mPM6NGj33aMg/tOOeWUdHR0HPZ1DmXv3r3Zu3dv9eeurq53+U4BAGqnT10B7OsWLVqUxsbG6mPkyJG1nhIAwDvWpwKwqakpSbJ9+/Ye27dv317d19TUlB07dvTY/+abb+Y3v/lNjzGHOsZbX+P/GnNw/6HMnz8/nZ2d1cfWrVvfw7sFAKiNPhWAo0ePTlNTU9asWVPd1tXVlWeffTbNzc1Jkubm5uzatSvr1q2rjnnyySfT3d2dSZMmVcc8/fTT2b9/f3XM6tWrc8455+SUU06pjnnr6xwcc/B1DqW+vj4NDQ09HgAAR5teD8DXX38969evz/r165Pf3/ixfv36bNmyJf369cucOXPyjW98I//+7/+eDRs25POf/3yGDx9evVP4vPPOyxVXXJEbb7wxzz33XP7rv/4rs2bNyrXXXpvhw4cnST772c+mrq4uM2fOzEsvvZQHH3wwd999d9ra2qrz+PKXv5yVK1fm7//+77Np06bccccdeeGFFzJr1qzeXhIAgF7V6zeBvPDCC7n00kurPx+MshkzZmTZsmW59dZbs3v37nzpS1/Krl278pd/+ZdZuXJlBg4cWH3O97///cyaNSuXXXZZ+vfvn2nTpuU73/lOdX9jY2N+9KMfpbW1NePHj89pp52WBQsW9PiuwL/4i7/I8uXLc/vtt+erX/1qPvzhD+fRRx/N+eef32trAQBQCzX9HsCjne8BrNHzAOA98D2AfewzgAAAHHkCEACgMAIQAKAwAhAAoDACEACgMH3q3wKG98ydxQDwR7kCCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQmONqPQE4qt3ReJh9nb05EwD4k7kCCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBhfAwO14OtjAKghVwABAAojAAEACuNPwHA08adjAN4HrgACABTGFUDg3V9Z7O0rksfCFdCjZa1Ldyys97HwHjhiBCDQ+46FcDxafrn2teDs7fkcLf87Hc6x8P+XvvR6JAIQAN5HJcdMye/9KOQzgAAAhRGAAACFEYAAAIURgAAAhRGAAACFcRcwxN1rAJTFFUAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIUH4D33HNPzjrrrAwcODCTJk3Kc889V+spAQAcUUUH4IMPPpi2trYsXLgwL774YsaNG5eWlpbs2LGj1lMDADhiig7Af/iHf8iNN96Y66+/PmPGjMnSpUtz4okn5l/+5V9qPTUAgCPmuFpPoFb27duXdevWZf78+dVt/fv3z5QpU9Le3n7I5+zduzd79+6t/tzZ2Zkk6erqOjKT3Fv5v/cd7jWP9ecdztHyHvrSmtViPkfL8w7naHkPfWnNajGfo+V5h3O0vIe+tGZ/xMHf25XKYV77GNevUui737ZtWz7wgQ/kmWeeSXNzc3X7rbfemrVr1+bZZ59923PuuOOO3Hnnnb08UwDgSNi6dWtGjBhR62nURLFXAN+N+fPnp62trfpzd3d3fvOb3+TUU09Nv379eozt6urKyJEjs3Xr1jQ0NNRgtkcn6/bOWbN3x7q9O9bt3bFu79yRXLNKpZLXXnstw4cPf1+PezQpNgBPO+20DBgwINu3b++xffv27Wlqajrkc+rr61NfX99j2+DBgw/7Og0NDf7P/i5Yt3fOmr071u3dsW7vjnV7547UmjU2Nr7vxzyaFHsTSF1dXcaPH581a9ZUt3V3d2fNmjU9/iQMAHCsKfYKYJK0tbVlxowZmTBhQiZOnJi77roru3fvzvXXX1/rqQEAHDFFB+D06dOzc+fOLFiwIB0dHbnwwguzcuXKDBs27D0fu76+PgsXLnzbn4w5POv2zlmzd8e6vTvW7d2xbu+cNTuyir0LGACgVMV+BhAAoFQCEACgMAIQAKAwAhAAoDAC8Ai45557ctZZZ2XgwIGZNGlSnnvuuVpPqU+744470q9fvx6Pc889t9bT6nOefvrpfOpTn8rw4cPTr1+/PProoz32VyqVLFiwIGeccUZOOOGETJkyJT//+c9rNt++4o+t2xe+8IW3nX9XXHFFzebbFyxatCgXX3xxBg0alKFDh+aqq67K5s2be4zZs2dPWltbc+qpp+bkk0/OtGnT3vbF+qX5U9btYx/72NvOt5tuuqlmc+4L7rvvvowdO7b6hc/Nzc154oknqvuda0eGAHyfPfjgg2lra8vChQvz4osvZty4cWlpacmOHTtqPbU+7c///M/z6quvVh//+Z//Wesp9Tm7d+/OuHHjcs899xxy/+LFi/Od73wnS5cuzbPPPpuTTjopLS0t2bNnT6/PtS/5Y+uWJFdccUWP8+8HP/hBr86xr1m7dm1aW1vzk5/8JKtXr87+/ftz+eWXZ/fu3dUxc+fOzWOPPZaHH344a9euzbZt23L11VfXdN619qesW5LceOONPc63xYsX12zOfcGIESPyzW9+M+vWrcsLL7yQj3/84/n0pz+dl156KXGuHTkV3lcTJ06stLa2Vn8+cOBAZfjw4ZVFixbVdF592cKFCyvjxo2r9TSOKkkqjzzySPXn7u7uSlNTU+Vb3/pWdduuXbsq9fX1lR/84Ac1mmXf84frVqlUKjNmzKh8+tOfrtmcjgY7duyoJKmsXbu2Uvn9uXX88cdXHn744eqYn/3sZ5Uklfb29hrOtG/5w3WrVCqV//f//l/ly1/+ck3ndTQ45ZRTKvfff79z7QhyBfB9tG/fvqxbty5Tpkypbuvfv3+mTJmS9vb2ms6tr/v5z3+e4cOH54Mf/GCuu+66bNmypdZTOqq88sor6ejo6HHuNTY2ZtKkSc69P8FTTz2VoUOH5pxzzsnNN9+cX//617WeUp/S2dmZJBkyZEiSZN26ddm/f3+P8+3cc8/NqFGjnG9v8YfrdtD3v//9nHbaaTn//PMzf/78/O53v6vRDPueAwcO5IEHHsju3bvT3NzsXDuCiv6XQN5vv/rVr3LgwIG3/Usiw4YNy6ZNm2o2r75u0qRJWbZsWc4555y8+uqrufPOO/PRj340GzduzKBBg2o9vaNCR0dH8vtz7a2GDRtW3cehXXHFFbn66qszevTovPzyy/nqV7+aK6+8Mu3t7RkwYECtp1dz3d3dmTNnTj7ykY/k/PPPT35/vtXV1WXw4ME9xjrf/n+HWrck+exnP5szzzwzw4cPz09/+tPMmzcvmzdvzr/927/VdL61tmHDhjQ3N2fPnj05+eST88gjj2TMmDFZv369c+0IEYDU3JVXXln977Fjx2bSpEk588wz89BDD2XmzJk1nRvHvmuvvbb63xdccEHGjh2bD33oQ3nqqady2WWX1XRufUFra2s2btzoc7nv0P+1bl/60peq/33BBRfkjDPOyGWXXZaXX345H/rQh2ow077hnHPOyfr169PZ2Zl//dd/zYwZM7J27dpaT+uY5k/A76PTTjstAwYMeNvdSdu3b09TU1PN5nW0GTx4cP7sz/4sv/jFL2o9laPGwfPLuffeffCDH8xpp53m/Esya9asPP744/nxj3+cESNGVLc3NTVl37592bVrV4/xzrf/9X+t26FMmjQpSYo/3+rq6nL22Wdn/PjxWbRoUcaNG5e7777buXYECcD3UV1dXcaPH581a9ZUt3V3d2fNmjVpbm6u6dyOJq+//npefvnlnHHGGbWeylFj9OjRaWpq6nHudXV15dlnn3XuvUO//OUv8+tf/7ro869SqWTWrFl55JFH8uSTT2b06NE99o8fPz7HH398j/Nt8+bN2bJlS9Hn2x9bt0NZv359khR9vh1Kd3d39u7d61w7gvwJ+H3W1taWGTNmZMKECZk4cWLuuuuu7N69O9dff32tp9ZnfeUrX8mnPvWpnHnmmdm2bVsWLlyYAQMG5DOf+Uytp9anvP766z2uErzyyitZv359hgwZklGjRmXOnDn5xje+kQ9/+MMZPXp0vva1r2X48OG56qqrajrvWjvcug0ZMiR33nlnpk2blqamprz88su59dZbc/bZZ6elpaWm866l1tbWLF++PD/84Q8zaNCg6metGhsbc8IJJ6SxsTEzZ85MW1tbhgwZkoaGhsyePTvNzc2ZPHlyradfM39s3V5++eUsX748n/jEJ3Lqqafmpz/9aebOnZtLLrkkY8eOrfX0a2b+/Pm58sorM2rUqLz22mtZvnx5nnrqqaxatcq5diTV+jbkY9E//uM/VkaNGlWpq6urTJw4sfKTn/yk1lPq06ZPn14544wzKnV1dZUPfOADlenTp1d+8Ytf1Hpafc6Pf/zjSpK3PWbMmFGp/P6rYL72ta9Vhg0bVqmvr69cdtlllc2bN9d62jV3uHX73e9+V7n88ssrp59+euX444+vnHnmmZUbb7yx0tHRUetp19Sh1itJ5bvf/W51zBtvvFH5m7/5m8opp5xSOfHEEyt//dd/XXn11VdrOu9a+2PrtmXLlsoll1xSGTJkSKW+vr5y9tlnV2655ZZKZ2dnradeUzfccEPlzDPPrNTV1VVOP/30ymWXXVb50Y9+VN3vXDsy+lX+96QFAKAQPgMIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFCY/w8tmfmOTDaPEwAAAABJRU5ErkJggg==' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with plt.ioff():\n",
    "    plt.hist(data['labels'],bins=64)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "execution_state": "idle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "24b2976d050e43af8bad0e4080a224eb",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with plt.ioff():\n",
    "    plt.hist(tune_data['labels'],bins=64)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Q3Cg_8UQep8g"
   },
   "source": [
    "# Step 2: Define Transformer Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "execution_state": "idle",
   "metadata": {
    "id": "tLOWhg_CeWzH"
   },
   "outputs": [],
   "source": [
    "class TransformerModel(nn.Module):\n",
    "    def __init__(self, input_dim, model_dim, output_dim, num_heads, num_layers, seq_len, device, dropout):\n",
    "        super().__init__()\n",
    "        self.embedding = nn.Embedding(input_dim, model_dim//2)\n",
    "        # seq_len is odd\n",
    "        self.fancy_encoding = torch.repeat_interleave(torch.rand((1, seq_len // 2 + 1, model_dim // 2), device=device), 2, dim=1)\n",
    "        # cut off last element since the target vertex is not repeated\n",
    "        self.fancy_encoding = self.fancy_encoding[:, :seq_len, :]\n",
    "        \n",
    "        self.model_dim = model_dim\n",
    "        self.seq_len = seq_len\n",
    "        self.device = device\n",
    "\n",
    "        encoder_layer = nn.TransformerEncoderLayer(d_model=model_dim, nhead=num_heads,\n",
    "                                                   dim_feedforward=model_dim*4,\n",
    "                                                   dropout=dropout, batch_first=True)\n",
    "        self.transformer_encoder = nn.TransformerEncoder(encoder_layer, num_layers)\n",
    "\n",
    "        self.fc_out = nn.Linear(model_dim*seq_len, output_dim)\n",
    "\n",
    "    def forward(self, src, key_padding_mask):\n",
    "        batch_size, src_len = src.size(0), src.size(1)\n",
    "        embed = self.embedding(src)\n",
    "        src = torch.cat((embed * sqrt(self.model_dim), self.fancy_encoding.repeat((batch_size, 1, 1))), dim=2)\n",
    "\n",
    "        output = self.transformer_encoder(src, src_key_padding_mask=key_padding_mask)\n",
    "        output[key_padding_mask] = 0 # Hack to stop no_grad problem\n",
    "        flat_output = torch.flatten(output, start_dim=1, end_dim=2)\n",
    "        output = self.fc_out(flat_output)\n",
    "        return output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bpIeg86S-hBb"
   },
   "source": [
    "# Step 3: Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "execution_state": "idle",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "kWXvJRDYgFVP",
    "outputId": "c13adb9d-6565-43b5-8437-20cef3dc0d16"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trainable parameters in the model: 2390K\n"
     ]
    }
   ],
   "source": [
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "assert device.type == 'cuda', \"CUDA is not available. Please check your GPU setup.\"\n",
    "\n",
    "# PARAMS\n",
    "VOCAB_SIZE = 1 + MAX_VTXS # one more than the max number of vertices\n",
    "MODEL_DIM = 256 # Dimension of model (embedding and transformer)\n",
    "NEPOCHS = 1000\n",
    "BSZ = 3072\n",
    "LR = 0.003\n",
    "WD = 0.002\n",
    "NHEADS = 4\n",
    "NLAYERS = 3\n",
    "PAD_TOKEN = 0\n",
    "DROPOUT = 0.2\n",
    "model = TransformerModel(input_dim=VOCAB_SIZE, model_dim=MODEL_DIM,\n",
    "                         output_dim=1, num_heads=NHEADS,\n",
    "                         num_layers=NLAYERS, seq_len=SEQ_LEN,\n",
    "                         dropout=DROPOUT, device=device).to(device)\n",
    "\n",
    "with open(\"data.pkl\", \"rb\") as f:\n",
    "    pickled_stuff = pickle.load(f)\n",
    "\n",
    "data = pickled_stuff[\"data\"].to(device)\n",
    "label = pickled_stuff[\"labels\"].to(device)\n",
    "padding_mask = (data == PAD_TOKEN).bool().to(device)\n",
    "dataset = TensorDataset(data, label, padding_mask)\n",
    "train_dataset, test_dataset = torch.utils.data.random_split(dataset, [.8, .2])\n",
    "train_loader = DataLoader(train_dataset, batch_size=BSZ, shuffle=True)\n",
    "test_loader = DataLoader(test_dataset, batch_size=BSZ, shuffle=True)\n",
    "\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=LR, weight_decay=WD)\n",
    "\n",
    "trainable_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
    "print(f\"Trainable parameters in the model: {trainable_params//1000}K\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "execution_state": "idle",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(141.4637, device='cuda:0')\n"
     ]
    }
   ],
   "source": [
    "baseline_error = criterion(label, torch.tensor(1.5, dtype=torch.float32, device=device))\n",
    "print(baseline_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "f8Zn33m7CxL5"
   },
   "source": [
    "# Step 4: Train the Model for the first task"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "execution_state": "idle",
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate():\n",
    "    model.eval()\n",
    "    test_loss = 0\n",
    "    with torch.no_grad():\n",
    "        for batch_src, batch_labels, batch_padding_mask in test_loader:\n",
    "            output = model(batch_src, batch_padding_mask)\n",
    "            loss = criterion(output.squeeze(1), batch_labels)\n",
    "            test_loss += loss.item()/len(test_loader)\n",
    "    return test_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "execution_state": "idle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "329425e6ee6d4189aefee350eba741c7",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This has to be in a separate cell for some weird event loop reasons\n",
    "fig,ax = plt.subplots()\n",
    "fig.suptitle('MSE vs Epochs')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "execution_state": "running",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 486
    },
    "id": "pvTfzGmCeXU4",
    "outputId": "0d3a20f3-23be-4c19-9eb6-46bfe11a48b1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/1000 \t Train Err: 88.4438 \t Test Err: 72.6466 \t baseline err: 141.4637\n",
      "Epoch 2/1000 \t Train Err: 72.6060 \t Test Err: 75.4987 \t baseline err: 141.4637\n",
      "Epoch 3/1000 \t Train Err: 72.6729 \t Test Err: 73.9506 \t baseline err: 141.4637\n",
      "Epoch 6/1000 \t Train Err: 72.7866 \t Test Err: 72.4612 \t baseline err: 141.4637\n",
      "Epoch 7/1000 \t Train Err: 73.0815 \t Test Err: 74.9404 \t baseline err: 141.4637\n",
      "Epoch 8/1000 \t Train Err: 72.8054 \t Test Err: 73.7412 \t baseline err: 141.4637\n",
      "Epoch 9/1000 \t Train Err: 73.0514 \t Test Err: 82.7393 \t baseline err: 141.4637\n",
      "Epoch 10/1000 \t Train Err: 73.0291 \t Test Err: 72.2577 \t baseline err: 141.4637\n",
      "Epoch 11/1000 \t Train Err: 73.0081 \t Test Err: 72.4944 \t baseline err: 141.4637\n",
      "Epoch 12/1000 \t Train Err: 72.6500 \t Test Err: 75.2036 \t baseline err: 141.4637\n",
      "Epoch 13/1000 \t Train Err: 72.6255 \t Test Err: 73.4970 \t baseline err: 141.4637\n",
      "Epoch 14/1000 \t Train Err: 72.6803 \t Test Err: 74.0005 \t baseline err: 141.4637\n",
      "Epoch 15/1000 \t Train Err: 72.7032 \t Test Err: 73.0177 \t baseline err: 141.4637\n",
      "Epoch 16/1000 \t Train Err: 72.7891 \t Test Err: 75.1899 \t baseline err: 141.4637\n",
      "Epoch 17/1000 \t Train Err: 74.0133 \t Test Err: 71.7237 \t baseline err: 141.4637\n",
      "Epoch 18/1000 \t Train Err: 72.7520 \t Test Err: 75.8566 \t baseline err: 141.4637\n",
      "Epoch 19/1000 \t Train Err: 72.5771 \t Test Err: 74.9531 \t baseline err: 141.4637\n",
      "Epoch 20/1000 \t Train Err: 72.6114 \t Test Err: 73.3918 \t baseline err: 141.4637\n",
      "Epoch 21/1000 \t Train Err: 71.5844 \t Test Err: 57.3829 \t baseline err: 141.4637\n",
      "Epoch 22/1000 \t Train Err: 56.8166 \t Test Err: 60.2253 \t baseline err: 141.4637\n",
      "Epoch 23/1000 \t Train Err: 58.2172 \t Test Err: 56.7333 \t baseline err: 141.4637\n",
      "Epoch 24/1000 \t Train Err: 56.1189 \t Test Err: 55.7485 \t baseline err: 141.4637\n",
      "Epoch 25/1000 \t Train Err: 55.5304 \t Test Err: 56.2083 \t baseline err: 141.4637\n",
      "Epoch 26/1000 \t Train Err: 68.7059 \t Test Err: 72.6976 \t baseline err: 141.4637\n",
      "Epoch 27/1000 \t Train Err: 72.7020 \t Test Err: 73.1029 \t baseline err: 141.4637\n",
      "Epoch 28/1000 \t Train Err: 72.4459 \t Test Err: 73.5617 \t baseline err: 141.4637\n",
      "Epoch 29/1000 \t Train Err: 72.5310 \t Test Err: 75.8304 \t baseline err: 141.4637\n",
      "Epoch 30/1000 \t Train Err: 72.5256 \t Test Err: 73.0845 \t baseline err: 141.4637\n",
      "Epoch 31/1000 \t Train Err: 72.4667 \t Test Err: 72.9080 \t baseline err: 141.4637\n",
      "Epoch 32/1000 \t Train Err: 72.5369 \t Test Err: 72.6703 \t baseline err: 141.4637\n",
      "Epoch 33/1000 \t Train Err: 72.4685 \t Test Err: 74.7614 \t baseline err: 141.4637\n",
      "Epoch 34/1000 \t Train Err: 72.4926 \t Test Err: 74.0886 \t baseline err: 141.4637\n",
      "Epoch 35/1000 \t Train Err: 71.3339 \t Test Err: 55.4380 \t baseline err: 141.4637\n",
      "Epoch 36/1000 \t Train Err: 60.7870 \t Test Err: 59.4468 \t baseline err: 141.4637\n",
      "Epoch 37/1000 \t Train Err: 55.6557 \t Test Err: 56.7001 \t baseline err: 141.4637\n",
      "Epoch 38/1000 \t Train Err: 55.4896 \t Test Err: 55.8308 \t baseline err: 141.4637\n",
      "Epoch 39/1000 \t Train Err: 55.6962 \t Test Err: 58.9664 \t baseline err: 141.4637\n",
      "Epoch 40/1000 \t Train Err: 55.5519 \t Test Err: 57.7560 \t baseline err: 141.4637\n",
      "Epoch 41/1000 \t Train Err: 55.5370 \t Test Err: 56.6866 \t baseline err: 141.4637\n",
      "Epoch 42/1000 \t Train Err: 55.4300 \t Test Err: 56.3424 \t baseline err: 141.4637\n",
      "Epoch 43/1000 \t Train Err: 55.4922 \t Test Err: 56.3748 \t baseline err: 141.4637\n",
      "Epoch 44/1000 \t Train Err: 55.6073 \t Test Err: 59.0728 \t baseline err: 141.4637\n",
      "Epoch 45/1000 \t Train Err: 55.5497 \t Test Err: 58.5533 \t baseline err: 141.4637\n",
      "Epoch 46/1000 \t Train Err: 55.4837 \t Test Err: 57.2847 \t baseline err: 141.4637\n",
      "Epoch 47/1000 \t Train Err: 55.4173 \t Test Err: 57.1441 \t baseline err: 141.4637\n",
      "Epoch 48/1000 \t Train Err: 55.4576 \t Test Err: 55.7806 \t baseline err: 141.4637\n",
      "Epoch 49/1000 \t Train Err: 55.5678 \t Test Err: 56.6457 \t baseline err: 141.4637\n",
      "Epoch 50/1000 \t Train Err: 55.5537 \t Test Err: 60.0365 \t baseline err: 141.4637\n",
      "Epoch 51/1000 \t Train Err: 55.5123 \t Test Err: 55.6848 \t baseline err: 141.4637\n",
      "Epoch 52/1000 \t Train Err: 55.5872 \t Test Err: 55.8084 \t baseline err: 141.4637\n",
      "Epoch 53/1000 \t Train Err: 55.4548 \t Test Err: 56.5655 \t baseline err: 141.4637\n",
      "Epoch 54/1000 \t Train Err: 55.5124 \t Test Err: 56.3470 \t baseline err: 141.4637\n",
      "Epoch 55/1000 \t Train Err: 55.4518 \t Test Err: 57.6169 \t baseline err: 141.4637\n",
      "Epoch 56/1000 \t Train Err: 55.4073 \t Test Err: 55.6467 \t baseline err: 141.4637\n",
      "Epoch 57/1000 \t Train Err: 55.4745 \t Test Err: 56.3436 \t baseline err: 141.4637\n",
      "Epoch 58/1000 \t Train Err: 55.4862 \t Test Err: 56.2289 \t baseline err: 141.4637\n",
      "Epoch 59/1000 \t Train Err: 55.5221 \t Test Err: 55.3599 \t baseline err: 141.4637\n",
      "Epoch 60/1000 \t Train Err: 55.4843 \t Test Err: 55.3953 \t baseline err: 141.4637\n",
      "Epoch 61/1000 \t Train Err: 55.5095 \t Test Err: 56.4781 \t baseline err: 141.4637\n",
      "Epoch 62/1000 \t Train Err: 55.6532 \t Test Err: 56.4005 \t baseline err: 141.4637\n",
      "Epoch 63/1000 \t Train Err: 55.5240 \t Test Err: 57.4780 \t baseline err: 141.4637\n",
      "Epoch 64/1000 \t Train Err: 55.4915 \t Test Err: 55.8880 \t baseline err: 141.4637\n",
      "Epoch 65/1000 \t Train Err: 55.4006 \t Test Err: 56.1770 \t baseline err: 141.4637\n",
      "Epoch 66/1000 \t Train Err: 55.3153 \t Test Err: 56.3041 \t baseline err: 141.4637\n",
      "Epoch 67/1000 \t Train Err: 55.3105 \t Test Err: 55.7897 \t baseline err: 141.4637\n",
      "Epoch 68/1000 \t Train Err: 55.9038 \t Test Err: 54.9242 \t baseline err: 141.4637\n",
      "Epoch 69/1000 \t Train Err: 55.4002 \t Test Err: 55.2162 \t baseline err: 141.4637\n",
      "Epoch 70/1000 \t Train Err: 55.5265 \t Test Err: 54.4618 \t baseline err: 141.4637\n",
      "Epoch 71/1000 \t Train Err: 55.4598 \t Test Err: 56.2988 \t baseline err: 141.4637\n",
      "Epoch 72/1000 \t Train Err: 55.4995 \t Test Err: 55.1318 \t baseline err: 141.4637\n",
      "Epoch 73/1000 \t Train Err: 55.5224 \t Test Err: 55.6233 \t baseline err: 141.4637\n",
      "Epoch 74/1000 \t Train Err: 55.2633 \t Test Err: 55.0628 \t baseline err: 141.4637\n",
      "Epoch 75/1000 \t Train Err: 55.3569 \t Test Err: 54.9321 \t baseline err: 141.4637\n",
      "Epoch 76/1000 \t Train Err: 55.4845 \t Test Err: 55.7232 \t baseline err: 141.4637\n",
      "Epoch 77/1000 \t Train Err: 55.3814 \t Test Err: 54.6657 \t baseline err: 141.4637\n",
      "Epoch 78/1000 \t Train Err: 55.4396 \t Test Err: 55.2952 \t baseline err: 141.4637\n",
      "Epoch 79/1000 \t Train Err: 55.4018 \t Test Err: 55.4081 \t baseline err: 141.4637\n",
      "Epoch 80/1000 \t Train Err: 55.5015 \t Test Err: 56.3544 \t baseline err: 141.4637\n",
      "Epoch 81/1000 \t Train Err: 55.5352 \t Test Err: 55.8122 \t baseline err: 141.4637\n",
      "Epoch 82/1000 \t Train Err: 55.4454 \t Test Err: 54.7959 \t baseline err: 141.4637\n",
      "Epoch 83/1000 \t Train Err: 55.4375 \t Test Err: 55.1435 \t baseline err: 141.4637\n",
      "Epoch 84/1000 \t Train Err: 55.4614 \t Test Err: 54.7396 \t baseline err: 141.4637\n",
      "Epoch 85/1000 \t Train Err: 55.4046 \t Test Err: 55.3768 \t baseline err: 141.4637\n",
      "Epoch 86/1000 \t Train Err: 55.3655 \t Test Err: 54.7487 \t baseline err: 141.4637\n",
      "Epoch 87/1000 \t Train Err: 55.4036 \t Test Err: 55.0165 \t baseline err: 141.4637\n",
      "Epoch 88/1000 \t Train Err: 55.4548 \t Test Err: 55.5787 \t baseline err: 141.4637\n",
      "Epoch 89/1000 \t Train Err: 55.3973 \t Test Err: 54.7695 \t baseline err: 141.4637\n",
      "Epoch 90/1000 \t Train Err: 55.4891 \t Test Err: 56.6628 \t baseline err: 141.4637\n",
      "Epoch 91/1000 \t Train Err: 55.5870 \t Test Err: 56.8348 \t baseline err: 141.4637\n",
      "Epoch 92/1000 \t Train Err: 55.4630 \t Test Err: 55.4178 \t baseline err: 141.4637\n",
      "Epoch 93/1000 \t Train Err: 55.5218 \t Test Err: 55.8851 \t baseline err: 141.4637\n",
      "Epoch 94/1000 \t Train Err: 55.4550 \t Test Err: 55.9211 \t baseline err: 141.4637\n",
      "Epoch 95/1000 \t Train Err: 55.4727 \t Test Err: 56.5819 \t baseline err: 141.4637\n",
      "Epoch 96/1000 \t Train Err: 55.4301 \t Test Err: 57.2222 \t baseline err: 141.4637\n",
      "Epoch 97/1000 \t Train Err: 55.4108 \t Test Err: 55.3496 \t baseline err: 141.4637\n",
      "Epoch 98/1000 \t Train Err: 55.4733 \t Test Err: 55.8675 \t baseline err: 141.4637\n",
      "Epoch 99/1000 \t Train Err: 55.3536 \t Test Err: 56.2623 \t baseline err: 141.4637\n",
      "Epoch 100/1000 \t Train Err: 55.2286 \t Test Err: 54.2883 \t baseline err: 141.4637\n",
      "Epoch 101/1000 \t Train Err: 54.6294 \t Test Err: 54.3795 \t baseline err: 141.4637\n",
      "Epoch 102/1000 \t Train Err: 54.0334 \t Test Err: 52.9438 \t baseline err: 141.4637\n",
      "Epoch 103/1000 \t Train Err: 55.8557 \t Test Err: 55.9887 \t baseline err: 141.4637\n",
      "Epoch 104/1000 \t Train Err: 55.3523 \t Test Err: 55.6809 \t baseline err: 141.4637\n",
      "Epoch 105/1000 \t Train Err: 54.8650 \t Test Err: 54.1854 \t baseline err: 141.4637\n",
      "Epoch 106/1000 \t Train Err: 54.8108 \t Test Err: 54.9449 \t baseline err: 141.4637\n",
      "Epoch 107/1000 \t Train Err: 54.4932 \t Test Err: 53.3353 \t baseline err: 141.4637\n",
      "Epoch 108/1000 \t Train Err: 54.0328 \t Test Err: 54.7242 \t baseline err: 141.4637\n",
      "Epoch 109/1000 \t Train Err: 52.3047 \t Test Err: 50.1951 \t baseline err: 141.4637\n",
      "Epoch 110/1000 \t Train Err: 46.5255 \t Test Err: 36.4212 \t baseline err: 141.4637\n",
      "Epoch 111/1000 \t Train Err: 35.6437 \t Test Err: 36.2409 \t baseline err: 141.4637\n",
      "Epoch 112/1000 \t Train Err: 35.5794 \t Test Err: 36.0152 \t baseline err: 141.4637\n",
      "Epoch 113/1000 \t Train Err: 49.8337 \t Test Err: 56.2286 \t baseline err: 141.4637\n",
      "Epoch 114/1000 \t Train Err: 55.4618 \t Test Err: 55.5159 \t baseline err: 141.4637\n",
      "Epoch 115/1000 \t Train Err: 48.2926 \t Test Err: 37.0193 \t baseline err: 141.4637\n",
      "Epoch 116/1000 \t Train Err: 43.0000 \t Test Err: 42.3349 \t baseline err: 141.4637\n",
      "Epoch 117/1000 \t Train Err: 36.4887 \t Test Err: 38.2387 \t baseline err: 141.4637\n",
      "Epoch 118/1000 \t Train Err: 35.7809 \t Test Err: 37.3943 \t baseline err: 141.4637\n",
      "Epoch 119/1000 \t Train Err: 35.7078 \t Test Err: 37.0414 \t baseline err: 141.4637\n",
      "Epoch 120/1000 \t Train Err: 35.7773 \t Test Err: 37.2562 \t baseline err: 141.4637\n",
      "Epoch 121/1000 \t Train Err: 36.1376 \t Test Err: 38.1538 \t baseline err: 141.4637\n",
      "Epoch 122/1000 \t Train Err: 38.3734 \t Test Err: 38.6760 \t baseline err: 141.4637\n",
      "Epoch 123/1000 \t Train Err: 36.6591 \t Test Err: 38.0746 \t baseline err: 141.4637\n",
      "Epoch 124/1000 \t Train Err: 37.1041 \t Test Err: 38.8434 \t baseline err: 141.4637\n",
      "Epoch 125/1000 \t Train Err: 37.0860 \t Test Err: 37.3192 \t baseline err: 141.4637\n",
      "Epoch 126/1000 \t Train Err: 35.8674 \t Test Err: 36.7553 \t baseline err: 141.4637\n",
      "Epoch 127/1000 \t Train Err: 35.8025 \t Test Err: 36.0833 \t baseline err: 141.4637\n",
      "Epoch 128/1000 \t Train Err: 35.6595 \t Test Err: 36.1782 \t baseline err: 141.4637\n",
      "Epoch 129/1000 \t Train Err: 35.6861 \t Test Err: 36.1815 \t baseline err: 141.4637\n",
      "Epoch 130/1000 \t Train Err: 35.5056 \t Test Err: 36.4077 \t baseline err: 141.4637\n",
      "Epoch 131/1000 \t Train Err: 35.5161 \t Test Err: 36.6100 \t baseline err: 141.4637\n",
      "Epoch 132/1000 \t Train Err: 35.4981 \t Test Err: 36.1938 \t baseline err: 141.4637\n",
      "Epoch 133/1000 \t Train Err: 35.4577 \t Test Err: 36.2723 \t baseline err: 141.4637\n",
      "Epoch 134/1000 \t Train Err: 35.5685 \t Test Err: 36.0326 \t baseline err: 141.4637\n",
      "Epoch 135/1000 \t Train Err: 35.4790 \t Test Err: 36.0421 \t baseline err: 141.4637\n",
      "Epoch 136/1000 \t Train Err: 35.5135 \t Test Err: 35.9383 \t baseline err: 141.4637\n",
      "Epoch 137/1000 \t Train Err: 35.4027 \t Test Err: 35.5105 \t baseline err: 141.4637\n",
      "Epoch 138/1000 \t Train Err: 35.4036 \t Test Err: 35.1535 \t baseline err: 141.4637\n",
      "Epoch 139/1000 \t Train Err: 35.5047 \t Test Err: 35.7687 \t baseline err: 141.4637\n",
      "Epoch 140/1000 \t Train Err: 35.3858 \t Test Err: 35.5093 \t baseline err: 141.4637\n",
      "Epoch 141/1000 \t Train Err: 35.3629 \t Test Err: 35.1772 \t baseline err: 141.4637\n",
      "Epoch 142/1000 \t Train Err: 35.3714 \t Test Err: 35.0682 \t baseline err: 141.4637\n",
      "Epoch 143/1000 \t Train Err: 35.3976 \t Test Err: 35.6668 \t baseline err: 141.4637\n",
      "Epoch 144/1000 \t Train Err: 35.4523 \t Test Err: 35.2633 \t baseline err: 141.4637\n",
      "Epoch 145/1000 \t Train Err: 35.3763 \t Test Err: 35.5053 \t baseline err: 141.4637\n",
      "Epoch 146/1000 \t Train Err: 35.3906 \t Test Err: 35.1866 \t baseline err: 141.4637\n",
      "Epoch 147/1000 \t Train Err: 35.4717 \t Test Err: 35.2663 \t baseline err: 141.4637\n",
      "Epoch 148/1000 \t Train Err: 49.5998 \t Test Err: 54.9490 \t baseline err: 141.4637\n",
      "Epoch 149/1000 \t Train Err: 56.0901 \t Test Err: 55.1923 \t baseline err: 141.4637\n",
      "Epoch 150/1000 \t Train Err: 55.4467 \t Test Err: 54.8896 \t baseline err: 141.4637\n",
      "Epoch 151/1000 \t Train Err: 55.4050 \t Test Err: 55.0999 \t baseline err: 141.4637\n",
      "Epoch 152/1000 \t Train Err: 55.3775 \t Test Err: 55.0012 \t baseline err: 141.4637\n",
      "Epoch 153/1000 \t Train Err: 55.3564 \t Test Err: 55.1625 \t baseline err: 141.4637\n",
      "Epoch 154/1000 \t Train Err: 55.4071 \t Test Err: 55.5768 \t baseline err: 141.4637\n",
      "Epoch 155/1000 \t Train Err: 55.1633 \t Test Err: 55.3753 \t baseline err: 141.4637\n",
      "Epoch 156/1000 \t Train Err: 45.2929 \t Test Err: 37.6036 \t baseline err: 141.4637\n",
      "Epoch 157/1000 \t Train Err: 36.1442 \t Test Err: 35.6718 \t baseline err: 141.4637\n",
      "Epoch 158/1000 \t Train Err: 35.5764 \t Test Err: 35.4595 \t baseline err: 141.4637\n",
      "Epoch 159/1000 \t Train Err: 35.3944 \t Test Err: 35.3251 \t baseline err: 141.4637\n"
     ]
    }
   ],
   "source": [
    "train_err = []\n",
    "test_err = []\n",
    "\n",
    "for epoch in range(NEPOCHS):\n",
    "    model.train()\n",
    "    train_loss = 0\n",
    "    for batch_src, batch_labels, batch_padding_mask in train_loader:\n",
    "        optimizer.zero_grad()\n",
    "        output = model(batch_src, batch_padding_mask)\n",
    "        loss = criterion(output.squeeze(1), batch_labels)\n",
    "        train_loss += loss.item()/len(train_loader)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "\n",
    "    test_loss = evaluate()\n",
    "            \n",
    "    test_err.append(test_loss)\n",
    "    train_err.append(train_loss)\n",
    "    ax.plot(train_err, label='Train', color='blue')\n",
    "    ax.plot(test_err, label='Test', color='red')\n",
    "    ax.set_xlabel('Epochs')\n",
    "    ax.set_ylabel('MSE')\n",
    "    fig.canvas.draw()\n",
    "    print(f\"Epoch {epoch + 1}/{NEPOCHS} \\t Train Err: {train_loss:.4f} \\t Test Err: {test_loss:.4f} \\t baseline err: {baseline_error:.4f}\")\n",
    "\n",
    "    if epoch % 100 == 99:\n",
    "        torch.save(model.state_dict(), f\"model_weights_{epoch}.pth\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "execution_state": "idle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55.06520214080811"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "execution_state": "running",
   "metadata": {
    "id": "LoGEmM5lH7_A"
   },
   "outputs": [],
   "source": [
    "batch_src, batch_labels, batch_padding_mask = next(iter(train_loader))\n",
    "output = model(batch_src, batch_padding_mask)\n",
    "batch_src[0], batch_labels[0], output[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "execution_state": "running",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.hist(output.detach().cpu().numpy().flatten(),bins=32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "execution_state": "running",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.hist(label.detach().cpu().numpy().flatten(),bins=32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "execution_state": "running",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.scatter(batch_labels.detach().cpu().numpy().flatten(),output.detach().cpu().numpy().flatten())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "execution_state": "running",
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_src2, batch_labels2, batch_padding_mask2 = next(iter(test_loader))\n",
    "output2 = model(batch_src2, batch_padding_mask2)\n",
    "loss = criterion(output2.squeeze(1), batch_labels2)\n",
    "batch_src2[0], batch_labels2[0], output2[0], loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "execution_state": "running",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.scatter(batch_labels2.detach().cpu().numpy().flatten(),output2.detach().cpu().numpy().flatten())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LC6Xv3YfC0Rm"
   },
   "source": [
    "# Step 5: Fine Tune"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "execution_state": "running",
   "metadata": {},
   "outputs": [],
   "source": [
    "N_TUNE_EPOCHS = 100\n",
    "TUNE_BSZ = 1024\n",
    "TUNE_LR = 0.003\n",
    "TUNE_WD = 0.002\n",
    "\n",
    "with open(\"tune_data.pkl\", \"rb\") as f:\n",
    "    pickled_tune_stuff = pickle.load(f)\n",
    "\n",
    "tune_data = pickled_tune_stuff[\"data\"].to(device)\n",
    "tune_label = pickled_tune_stuff[\"labels\"].to(device)\n",
    "tune_padding_mask = (tune_data == PAD_TOKEN).bool().to(device)\n",
    "tune_dataset = TensorDataset(tune_data, tune_label, tune_padding_mask)\n",
    "tune_train_dataset, tune_test_dataset = torch.utils.data.random_split(tune_dataset, [.8, .2])\n",
    "tune_train_loader = DataLoader(tune_train_dataset, batch_size=TUNE_BSZ, shuffle=True)\n",
    "tune_test_loader = DataLoader(tune_test_dataset, batch_size=TUNE_BSZ, shuffle=True)\n",
    "\n",
    "tune_criterion = nn.MSELoss()\n",
    "tune_optimizer = torch.optim.Adam(model.parameters(), lr=TUNE_LR, weight_decay=TUNE_WD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "execution_state": "running",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This has to be in a separate cell for some weird event loop reasons\n",
    "%matplotlib widget\n",
    "fig,ax = plt.subplots()\n",
    "fig.suptitle('MSE vs Epochs')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "execution_state": "running",
   "metadata": {},
   "outputs": [],
   "source": [
    "ax.clear()\n",
    "\n",
    "tune_train_err = []\n",
    "tune_test_err = []\n",
    "\n",
    "for epoch in range(N_TUNE_EPOCHS):\n",
    "    model.train()\n",
    "    tune_train_loss = 0\n",
    "    for batch_src, batch_labels, batch_padding_mask in tune_train_loader:\n",
    "        optimizer.zero_grad()\n",
    "        output = model(batch_src, batch_padding_mask)\n",
    "        loss = criterion(output.squeeze(1), batch_labels)\n",
    "        tune_train_loss += loss.item()/len(tune_train_loader)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "\n",
    "    model.eval()\n",
    "    tune_test_loss = 0\n",
    "    with torch.no_grad():\n",
    "        for batch_src, batch_labels, batch_padding_mask in tune_test_loader:\n",
    "            output = model(batch_src, batch_padding_mask)\n",
    "            loss = criterion(output.squeeze(1), batch_labels)\n",
    "            tune_test_loss += loss.item()/len(tune_test_loader)\n",
    "            \n",
    "    tune_test_err.append(tune_test_loss)\n",
    "    tune_train_err.append(tune_train_loss)\n",
    "    ax.plot(tune_train_err, label='Train', color='blue')\n",
    "    ax.plot(tune_test_err, label='Test', color='red')\n",
    "    ax.set_xlabel('Epochs')\n",
    "    ax.set_ylabel('MSE')\n",
    "    fig.canvas.draw()\n",
    "    print(f\"Epoch {epoch + 1}/{NEPOCHS} \\t Train Err: {train_loss:.4f} \\t Test Err: {test_loss:.4f} \\t baseline err: {baseline_error:.4f}\")\n",
    "\n",
    "    if epoch % 100 == 9:\n",
    "        torch.save(model.state_dict(), f\"tune_model_weights_{epoch}.pth\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JtTLXn4zC1z_"
   },
   "source": [
    "# Step 6: Test generalization"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "gpuType": "T4",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
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