Untitled.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "974e9cc9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.environ[\"CUDA_VISIBLE_DEVICES\"] = \"7\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "f74abd27",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from datasets import load_dataset\n",
    "\n",
    "from tokenizers import Tokenizer\n",
    "from tokenizers.models import WordLevel\n",
    "from tokenizers.trainers import WordLevelTrainer\n",
    "from tokenizers.pre_tokenizers import Whitespace\n",
    "import os\n",
    "from dataloader.dataloader import NMTDataset\n",
    "from torch.utils.data import DataLoader\n",
    "from models.transformer import Transformer\n",
    "from torchsummary import torchsummary\n",
    "from tqdm import tqdm\n",
    "import matplotlib.pyplot as plt\n",
    "from torchmetrics import ExactMatch, Accuracy\n",
    "\n",
    "device = torch.device(\"cuda\")\n",
    "cpu_device = torch.device(\"cpu\")\n",
    "\n",
    "%reload_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "46078432",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Repo card metadata block was not found. Setting CardData to empty.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Repo card metadata block was not found. Setting CardData to empty.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2507\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Repo card metadata block was not found. Setting CardData to empty.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "520\n"
     ]
    }
   ],
   "source": [
    "n_train = 40000\n",
    "train_dataset = load_dataset('cfilt/iitb-english-hindi', split=f\"train[:{n_train}]\")\n",
    "print(len(train_dataset))\n",
    "\n",
    "test_dataset = load_dataset('cfilt/iitb-english-hindi', split=\"test\")\n",
    "print(len(test_dataset))\n",
    "\n",
    "val_dataset = load_dataset('cfilt/iitb-english-hindi', split=\"validation\")\n",
    "print(len(val_dataset))\n",
    "\n",
    "train_dataloader = torch.utils.data.DataLoader(train_dataset, batch_size=len(train_dataset))\n",
    "val_dataloader = torch.utils.data.DataLoader(val_dataset, batch_size=len(val_dataset))\n",
    "test_dataloader = torch.utils.data.DataLoader(test_dataset, batch_size=len(test_dataset))\n",
    "\n",
    "tr = next(iter(train_dataloader))\n",
    "vl = next(iter(val_dataloader))\n",
    "tt = next(iter(test_dataloader))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "378921ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(124, 122)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find max length\n",
    "x = next(iter(train_dataloader))\n",
    "mx_src, mx_tar = 0, 0\n",
    "for src, tar in zip(x[\"translation\"][\"en\"], x[\"translation\"][\"hi\"]):\n",
    "    mx_src = max(mx_src, len(tokenizer_src.encode(src).ids))\n",
    "    mx_tar = max(mx_tar, len(tokenizer_tar.encode(tar).ids))\n",
    "mx_src, mx_tar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b621ca3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tokenizers.Tokenizer at 0xa7d7cf0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for lang in [\"hi\", \"en\"]:\n",
    "    tokenizer_path = f\"dataset/vocab_{lang}_{n_train}.json\"\n",
    "    if os.path.exists(tokenizer_path):\n",
    "        # load tokenizer\n",
    "        tokenizer = Tokenizer.from_file(tokenizer_path)\n",
    "    else:\n",
    "        tokenizer = Tokenizer(WordLevel(unk_token=\"<unk>\"))\n",
    "        tokenizer.pre_tokenizer = Whitespace()\n",
    "        trainer = WordLevelTrainer(special_tokens=['<unk>', '<pad>', '<sos>', '<eos>'], min_frequency=2)\n",
    "        tokenizer.train_from_iterator(tr['translation'][lang] + vl['translation'][lang]+ tt['translation'][lang], trainer=trainer)\n",
    "\n",
    "        # save tokenizer\n",
    "        tokenizer.save(tokenizer_path)\n",
    "\n",
    "\n",
    "tokenizer_src = Tokenizer.from_file(f\"dataset/vocab_en_{n_train}.json\")\n",
    "tokenizer_tar = Tokenizer.from_file(f\"dataset/vocab_hi_{n_train}.json\")\n",
    "tokenizer_tar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "47efb16a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "36000 520\n"
     ]
    }
   ],
   "source": [
    "train_ds = NMTDataset(tokenizer_src, tokenizer_tar, train_dataloader)\n",
    "val_ds = NMTDataset(tokenizer_src, tokenizer_tar, val_dataloader)\n",
    "print(len(train_ds), len(val_ds))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a7909854",
   "metadata": {},
   "outputs": [],
   "source": [
    "B = 512\n",
    "train_dl = DataLoader(train_ds, batch_size=B, shuffle=True)\n",
    "val_dl = DataLoader(val_ds, batch_size=len(val_ds), shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5b629c23",
   "metadata": {},
   "outputs": [],
   "source": [
    "seq_len = 100\n",
    "d_model = 512\n",
    "drop_prob = 0.1\n",
    "n_h = 8\n",
    "d_ff = 2048\n",
    "d_k = d_model/n_h\n",
    "n_layers = 6\n",
    "\n",
    "transformer = Transformer(tokenizer_src.get_vocab_size(), tokenizer_tar.get_vocab_size(), d_model, n_h, n_layers , d_ff, seq_len, drop_prob, tokenizer_src.token_to_id(\"<pad>\"), tokenizer_tar.token_to_id(\"<pad>\")).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "64f71be6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# torchsummary.summary(transformer, [(1, 100), (1, 100)], device=\"cpu\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "943beb31",
   "metadata": {},
   "source": [
    "### Train loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1089f7b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.nn.functional as F\n",
    "import torch.nn as nn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6ab4b068",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 1e-4\n",
    "optim = torch.optim.Adam(transformer.parameters(),lr=lr)\n",
    "loss_fn = torch.nn.CrossEntropyLoss(ignore_index=tokenizer_src.token_to_id('<pad>'))\n",
    "EM = ExactMatch(task=\"multiclass\", num_classes=tokenizer_tar.get_vocab_size(), \n",
    "                ignore_index=tokenizer_tar.token_to_id(\"<pad>\")).to(device)\n",
    "Acc = Accuracy(task=\"multiclass\", num_classes=tokenizer_tar.get_vocab_size(), \n",
    "                ignore_index=tokenizer_tar.token_to_id(\"<pad>\")).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "54e891a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 1/3 train loss - 4.440422058105469: 100%|██████████████████████████████████████| 12/12 [00:20<00:00,  1.71s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving Model - Val loss: 6.654748916625977 Val acc 0.25666874647140503 Val EM 0.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 2/3 train loss - 2.7716526985168457: 100%|█████████████████████████████████████| 12/12 [00:19<00:00,  1.66s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving Model - Val loss: 5.752293109893799 Val acc 0.3809438943862915 Val EM 0.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 3/3 train loss - 1.879019021987915: 100%|██████████████████████████████████████| 12/12 [00:14<00:00,  1.19s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving Model - Val loss: 5.184224605560303 Val acc 0.4507092535495758 Val EM 0.0\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 3\n",
    "\n",
    "train_losses, val_losses = [], []\n",
    "val_ems, val_accs = [], []\n",
    "prev_loss = 1e4\n",
    "for i in range(n_epochs):\n",
    "    transformer.train()\n",
    "    tqdm_obj = tqdm(train_dl)\n",
    "    for src, tar in tqdm_obj:\n",
    "        src, tar = src.to(device), tar.to(device)\n",
    "        optim.zero_grad()\n",
    "        logits = transformer(src, tar)\n",
    "        y_pred = torch.argmax(logits, dim=-1)\n",
    "        loss = loss_fn(logits.permute(0,2,1), tar)\n",
    "        loss.backward()\n",
    "        optim.step()\n",
    "        train_losses.append(loss.detach().to(cpu_device))\n",
    "        tqdm_obj.set_description_str(f\"Epoch {i+1}/{n_epochs} train loss - {loss.detach().to(cpu_device)}\")\n",
    "    \n",
    "    \n",
    "    with torch.no_grad():\n",
    "        transformer.eval()\n",
    "        src, tar = next(iter(val_dl))\n",
    "        src, tar = src.to(device), tar.to(device)\n",
    "        val_logits = transformer(src, tar)\n",
    "        val_y_pred = torch.argmax(val_logits, dim=-1)\n",
    "        val_loss = loss_fn(val_logits.permute(0,2,1), tar)\n",
    "        val_losses.append(val_loss.detach().to(cpu_device))\n",
    "        \n",
    "        val_acc, val_em = Acc(val_y_pred, tar).to(cpu_device), EM(val_y_pred, tar).to(cpu_device)\n",
    "        val_accs.append(val_acc)\n",
    "        val_ems.append(val_em)\n",
    "        if val_loss < prev_loss:\n",
    "            print(\"Saving Model -\", end=\" \")\n",
    "            torch.save(transformer.state_dict(), f\"ckpts/test_transformer_{n_train}_{lr}\")            \n",
    "        prev_loss = val_loss\n",
    "        \n",
    "    print(f\"Val loss: {val_loss.detach().to(cpu_device)} Val acc {val_acc} Val EM {val_em}\") "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "dd23fad8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(val_losses, label=\"val\")\n",
    "plt.legend()\n",
    "plt.savefig(f\"plots/val_loss_{n_train}\")\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(train_losses, label=\"train\")\n",
    "plt.legend()\n",
    "plt.savefig(f\"plots/train_loss_{n_train}.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b5a69a19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WLUpMTCxzfSNHjtTw4cM1bNgwde3aVc2aNXPstbli4cKFGjZsmJ544gndfPPNio2N1RdffKGIiAi3vz8AAKqDavPZUlXFarUqODi4XJ9NYWY2m01r1qxxnOgMoGzMGcAYd88ZI7+/2XMDAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMxePhZt68eYqKipK/v7+io6O1ffv2Mutnz56tm2++WQEBAYqIiNCECRN08eLFKuoWAABUdx4NN0uXLlV8fLymT5+uXbt2qW3bturVq5dOnjxZYv2iRYs0efJkTZ8+Xfv27dPbb7+tpUuX6umnn67izgEAQHXl0XAza9YsjRo1SiNGjNCtt96q5ORkBQYGasGCBSXWb9myRV26dNFDDz2kqKgo9ezZU4MHD77q3h4AAFBz1PLUCxcUFGjnzp1KSEhwjHl5eal79+7aunVric/p3Lmz/vWvf2n79u3q1KmTDh06pDVr1mjo0KGlvk5+fr7y8/Mdy1arVZJks9lks9nc9G6uPVfee03+HgBGMGcAY9w9Z4ysx2PhJjs7W4WFhQoNDXUaDw0N1f79+0t8zkMPPaTs7Gz99re/ld1u16VLlzR69OgyD0slJSVpxowZxcbXrVunwMDAir0JE0hNTfV0C8A1hTkDGOOuOZOXl1fuWo+FG1ekp6frhRde0Pz58xUdHa0ffvhB48aN01//+lclJiaW+JyEhATFx8c7lq1WqyIiItSzZ08FBQVVVevVjs1mU2pqqnr06CEfHx9PtwNUe8wZwBh3z5krR17Kw2PhJiQkRN7e3srKynIaz8rKUlhYWInPSUxM1NChQ/XII49Iklq3bq3c3Fz9+c9/1pQpU+TlVfwUIj8/P/n5+RUb9/HxYQMlvg+AUcwZwBh3zRkj6/DYCcW+vr7q0KGD0tLSHGNFRUVKS0tTTExMic/Jy8srFmC8vb0lSXa7vfKaBQAA1wyPHpaKj4/X8OHD1bFjR3Xq1EmzZ89Wbm6uRowYIUkaNmyYwsPDlZSUJEnq16+fZs2apfbt2zsOSyUmJqpfv36OkAMAAGo2j4abgQMH6tSpU5o2bZoyMzPVrl07rV271nGScUZGhtOemqlTp8pisWjq1Kk6duyYGjZsqH79+un555/31FsAAADVjMdPKI6Li1NcXFyJj6Wnpzst16pVS9OnT9f06dOroDMAAHAt8vjHLwAAALgT4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJgK4QYAAJhKLVef+P333+vTTz/VyZMnVVRU5PTYtGnTKtwYAACAK1wKN2+++abGjBmjkJAQhYWFyWKxOB6zWCyEGwAA4DEuhZvnnntOzz//vCZNmuTufgAAACrEpXNuzpw5owEDBri7FwAAgApzKdwMGDBA69atc3cvAAAAFVbuw1Jz5sxxfH3TTTcpMTFR27ZtU+vWreXj4+NU+/jjj7uvQwAAAAPKHW5effVVp+XatWtrw4YN2rBhg9O4xWIh3AAAAI8pd7g5fPhwZfYBAADgFtzEDwAAmIpL4eb+++/XzJkzi42/+OKLXEUFAAA8yqVws3HjRvXp06fYeO/evbVx48YKNwUAAOAql8LN+fPn5evrW2zcx8dHVqu1wk0BAAC4yqVw07p1ay1durTY+JIlS3TrrbdWuCkAAABXufTxC4mJierfv78OHjyobt26SZLS0tK0ePFiLVu2zK0NAgAAGOFSuOnXr59WrlypF154QcuXL1dAQIDatGmjTz75RF27dnV3jwAAAOXmUriRpL59+6pv377u7AUAAKDCXDrnplmzZjp9+nSx8bNnz6pZs2YVbgoAAMBVLoWbI0eOqLCwsNh4fn6+jh07VuGmAAAAXGXosNSqVascX3/88ccKDg52LBcWFiotLU1RUVFuaw4AAMAoQ+EmNjZW0uUPxxw+fLjTYz4+PoqKitIrr7zituYAAACMMhRuioqKJEk33HCDvvjiC4WEhFRKUwAAAK5y6WopPiEcAABUVy5fCp6bm6sNGzYoIyNDBQUFTo89/vjjFW4MAADAFS6Fm927d6tPnz7Ky8tTbm6u6tevr+zsbAUGBqpRo0aEGwAA4DEuXQo+YcIE9evXT2fOnFFAQIC2bdumH3/8UR06dNDLL7/s7h4BAADKzaVw8+WXX+qJJ56Ql5eXvL29lZ+fr4iICL344ot6+umn3d0jAABAubkUbnx8fOTldfmpjRo1UkZGhiQpODhYR48edV93AAAABrl0zk379u31xRdfqHnz5urataumTZum7Oxs/fOf/1SrVq3c3SMAAEC5ubTn5oUXXlDjxo0lSc8//7zq1aunMWPG6NSpU3rjjTfc2iAAAIARLu256dixo+PrRo0aae3atW5rCAAAoCJc2nMDAABQXRnac9OtW7dy1a1fv96lZgAAACrKULhJT09XZGSk+vbtKx8fn8rqCQAAwGWGws3MmTO1cOFCLVu2TEOGDNHIkSO5OgoAAFQrhs65eeqpp7R3716tXLlS586dU5cuXdSpUyclJyfLarVWVo8AAADl5tIJxTExMXrzzTd14sQJjR07VgsWLFCTJk0IOAAAwOMqdLXUrl27tGHDBu3bt0+tWrVy6TycefPmKSoqSv7+/oqOjtb27dvLrD979qzGjh2rxo0by8/PTy1atNCaNWtcfQsAAMBkDN/n5vjx40pJSVFKSoqsVqv++Mc/6vPPP9ett95q+MWXLl2q+Ph4JScnKzo6WrNnz1avXr303XffqVGjRsXqCwoK1KNHDzVq1EjLly9XeHi4fvzxR9WtW9fwawMAAHMyFG769OmjTz/9VD179tRLL72kvn37qlYtl+4DKEmaNWuWRo0apREjRkiSkpOTtXr1ai1YsECTJ08uVr9gwQL9/PPP2rJli2MvUVRUVJmvkZ+fr/z8fMfylUNnNptNNpvN5d6vdVfee03+HgBGMGcAY9w9Z4ysx2K32+3lLfby8lLjxo3VqFEjWSyWUut27dp11XUVFBQoMDBQy5cvV2xsrGN8+PDhOnv2rD788MNiz+nTp4/q16+vwMBAffjhh2rYsKEeeughTZo0Sd7e3iW+zjPPPKMZM2YUG1+0aJECAwOv2icAAPC8vLw8PfTQQ8rJyVFQUFCZtYZ2u0yfPr1Cjf1adna2CgsLFRoa6jQeGhqq/fv3l/icQ4cOaf369RoyZIjWrFmjH374QY8++qhsNlupvSUkJCg+Pt6xbLVaFRERoZ49e171m2NmNptNqamp6tGjB/csAsqBOQMY4+45Y+SiJY+FG1cUFRWpUaNGeuONN+Tt7a0OHTro2LFjeumll0rtzc/PT35+fsXGfXx82ECJ7wNgFHMGMMZdc8bIOly6Wqpbt246e/ZssXGr1Vruj2gICQmRt7e3srKynMazsrIUFhZW4nMaN26sFi1aOB2CuuWWW5SZmamCgoLyvwEAAGBaLoWb9PT0EsPExYsXtWnTpnKtw9fXVx06dFBaWppjrKioSGlpaYqJiSnxOV26dNEPP/ygoqIix9iBAwfUuHFj+fr6GnwXAADAjAwdlvrqq68cX+/du1eZmZmO5cLCQq1du1bh4eHlXl98fLyGDx+ujh07qlOnTpo9e7Zyc3MdV08NGzZM4eHhSkpKkiSNGTNGc+fO1bhx4/TYY4/p+++/1wsvvKDHH3/cyNsAAAAmZijctGvXThaLRRaLpcTDTwEBAfr73/9e7vUNHDhQp06d0rRp05SZmal27dpp7dq1jpOMMzIy5OX1y86liIgIffzxx5owYYLatGmj8PBwjRs3TpMmTTLyNgAAgIkZCjeHDx+W3W5Xs2bNtH37djVs2NDxmK+vrxo1alTqJdmliYuLU1xcXImPpaenFxuLiYnRtm3bDL0GAACoOQyFm8jISElyOucFAACgOnHphOKkpCQtWLCg2PiCBQs0c+bMCjcFAADgKpfCzeuvv66WLVsWG7/tttuUnJxc4aYAAABc5VK4yczMVOPGjYuNN2zYUCdOnKhwUwAAAK5yKdxERERo8+bNxcY3b96sJk2aVLgpAAAAV7n0kd6jRo3S+PHjZbPZHJeEp6WlaeLEiXriiSfc2iAAAIARLoWbp556SqdPn9ajjz7quFOxv7+/Jk2apISEBLc2CAAAYIRL4cZisWjmzJlKTEzUvn37FBAQoObNm5f4AZUAAABVyaVwc0Xt2rV1xx13uKsXAACACnM53OzYsUPvvfeeMjIyin2I5gcffFDhxgAAAFzh0tVSS5YsUefOnbVv3z6tWLFCNptN3377rdavX6/g4GB39wgAAFBuLoWbF154Qa+++qr+/e9/y9fXV6+99pr279+vBx98UE2bNnV3jwAAAOXmUrg5ePCg+vbtK+nyB2bm5ubKYrFowoQJeuONN9zaIAAAgBEuhZt69erp3LlzkqTw8HB98803kqSzZ88qLy/Pfd0BAAAY5NIJxXfddZdSU1PVunVrDRgwQOPGjdP69euVmpqq3//+9+7uEQAAoNxcCjdz587VxYsXJUlTpkyRj4+PtmzZovvvv19Tp051a4MAAABGuBRu6tev7/jay8tLkydPdltDAAAAFeHSOTcpKSkljl+6dImPXwAAAB7lUrh5/PHHNWDAAJ05c8Yx9t133yk6OlqLFy92W3MAAABGuRRudu/erZ9++kmtW7dWamqq5s2bp9tvv10tW7bUnj173N0jAABAubl0zs2NN96ozZs3a/z48brnnnvk7e2td955R4MHD3Z3fwAAAIa4tOdGklavXq0lS5YoJiZGdevW1dtvv63jx4+7szcAAADDXAo3f/nLXzRgwABNmjRJmzZt0ldffSVfX1+1bt1a7733nrt7BAAAKDeXDktt3rxZn3/+udq2bStJCgsL05o1azRv3jyNHDlSDz74oFubBAAAKC+Xws3OnTvl5+dXbHzs2LHq3r17hZsCAABwlaHDUidPnpSkEoONdPk+Nzk5ORXvCgAAwEWGwk3jxo0dAUeSWrduraNHjzqWT58+rZiYGPd1BwAAYJChcGO3252Wjxw5IpvNVmYNAABAVXL5UvDSWCwWd68SAACg3NwebgAAADzJ0NVSFotF586dk7+/v+x2uywWi86fPy+r1SpJjv8DAAB4iqFwY7fb1aJFC6fl9u3bOy1zWAoAAHiSoXDz6aefVlYfAAAAbmEo3HTt2rWy+gAAAHALl04o3rVrl77++mvH8ocffqjY2Fg9/fTTKigocFtzAAAARrn8wZkHDhyQJB06dEiDBg1SYGCgli1bpokTJ7q1QQAAACNcCjcHDhxQu3btJEnLli3TXXfdpUWLFiklJUXvv/++O/sDAAAwxKVwY7fbVVRUJEn65JNP1KdPH0lSRESEsrOz3dcdAACAQS6Fm44dO+q5557TP//5T23YsEF9+/aVJB0+fFihoaFubRAAAMAIl8LN7NmztWvXLsXFxWnKlCm66aabJEnLly9X586d3dogAACAEYYuBb+iTZs2TldLXfHSSy/J29u7wk0BAAC4yqU9N0ePHtVPP/3kWN6+fbvGjx+v//3f/5WPj4/bmgMAADDKpXDz0EMPOe5WnJmZqR49emj79u2aMmWKnn32Wbc2CAAAYIRL4eabb75Rp06dJEnvvfeeWrVqpS1btujdd99VSkqKO/sDAAAwxKVwY7PZ5OfnJ+nypeD33XefJKlly5Y6ceKE+7oDAAAwyKVwc9tttyk5OVmbNm1Samqq7rnnHknS8ePH1aBBA7c2CAAAYIRL4WbmzJl6/fXXdffdd2vw4MFq27atJGnVqlWOw1UAAACe4NKl4Hfffbeys7NltVpVr149x/if//xnBQYGuq05AAAAo1wKN5Lk7e3tFGwkKSoqqqL9AAAAVIjL4Wb58uV67733lJGRoYKCAqfHdu3aVeHGAAAAXOHSOTdz5szRiBEjFBoaqt27d6tTp05q0KCBDh06pN69exte37x58xQVFSV/f39FR0dr+/bt5XrekiVLZLFYFBsba/g1AQCAObkUbubPn6833nhDf//73+Xr66uJEycqNTVVjz/+uHJycgyta+nSpYqPj9f06dO1a9cutW3bVr169dLJkyfLfN6RI0f05JNP6s4773TlLQAAAJNyKdxkZGQ4PiAzICBA586dkyQNHTpUixcvNrSuWbNmadSoURoxYoRuvfVWJScnKzAwUAsWLCj1OYWFhRoyZIhmzJihZs2aufIWAACASbl0zk1YWJh+/vlnRUZGqmnTptq2bZvatm2rw4cPy263l3s9BQUF2rlzpxISEhxjXl5e6t69u7Zu3Vrq85599lk1atRIf/rTn7Rp06YyXyM/P1/5+fmOZavVKunyjQhtNlu5ezWbK++9Jn8PACOYM4Ax7p4zRtbjUrjp1q2bVq1apfbt22vEiBGaMGGCli9frh07dqh///7lXk92drYKCwsVGhrqNB4aGqr9+/eX+JzPPvtMb7/9tr788styvUZSUpJmzJhRbHzdunVcti4pNTXV0y0A1xTmDGCMu+ZMXl5euWtdCjdvvPGGioqKJEljx45VgwYNtGXLFt133336y1/+4soqy+XcuXMaOnSo3nzzTYWEhJTrOQkJCYqPj3csW61WRUREqGfPngoKCqqsVqs9m82m1NRU9ejRg09yB8qBOQMY4+45c+XIS3m4FG68vLzk5fXL6TqDBg3SoEGDDK8nJCRE3t7eysrKchrPyspSWFhYsfqDBw/qyJEj6tevn2PsSsiqVauWvvvuO914441Oz/Hz83N8Dtav+fj4sIES3wfAKOYMYIy75oyRdZQ73Hz11VflXmmbNm3KVefr66sOHTooLS3NcTl3UVGR0tLSFBcXV6y+ZcuW+vrrr53Gpk6dqnPnzum1115TREREuXsEAADmVO5w065dO1kslqueMGyxWFRYWFjuBuLj4zV8+HB17NhRnTp10uzZs5Wbm6sRI0ZIkoYNG6bw8HAlJSXJ399frVq1cnp+3bp1JanYOAAAqJnKHW4OHz5cKQ0MHDhQp06d0rRp05SZmal27dpp7dq1jpOMMzIynA6BAQAAlKXc4SYyMrLSmoiLiyvxMJQkpaenl/nclJQU9zcEAACuWS7tEklKSirxJnsLFizQzJkzK9wUAACAq1wKN6+//rpatmxZbPy2225TcnJyhZsCAABwlUvhJjMzU40bNy423rBhQ504caLCTQEAALjKpXATERGhzZs3FxvfvHmzmjRpUuGmAAAAXOXSTfxGjRql8ePHy2azqVu3bpKktLQ0TZw4UU888YRbGwQAADDCpXDz1FNP6fTp03r00UdVUFAgSfL399ekSZOcPgQTAACgqrkUbiwWi2bOnKnExETt27dPAQEBat68eYkfcwAAAFCVXAo3V9SuXVt33HGHu3oBAACosHKHm/79+yslJUVBQUHq379/mbUffPBBhRsDAABwRbnDTXBwsCwWiyQpKCjI8TUAAEB1Uu5ws3DhQsfXfOQBAACorly6z023bt109uzZYuNWq9VxaTgAAIAnuBRu0tPTHZeA/9rFixe1adOmCjcFAADgKkNXS3311VeOr/fu3avMzEzHcmFhodauXavw8HD3dQcAAGCQoXDTrl07WSwWWSyWEg8/BQQE6O9//7vbmgMAADDKULg5fPiw7Ha7mjVrpu3bt6thw4aOx3x9fdWoUSN5e3u7vUkAAIDyMhRuIiMjJUlFRUWV0gwAAEBFlTvcrFq1qtwrve+++1xqBgAAoKLKHW5iY2PLVWexWFRYWOhqPwAAABVS7nDDoSgAAHAtcOk+NwAAANWVS58K/uyzz5b5+LRp01xqBgAAoKJcCjcrVqxwWrbZbDp8+LBq1aqlG2+8kXADAAA8xqVws3v37mJjVqtVDz/8sP7whz9UuCkAAABXue2cm6CgIM2YMUOJiYnuWiUAAIBhbj2hOCcnRzk5Oe5cJQAAgCEuHZaaM2eO07LdbteJEyf0z3/+U71793ZLYwAAAK5wKdy8+uqrTsteXl5q2LChhg8froSEBLc0BgAA4AqXws3hw4fd3QcAAIBbGAo3I0eOLFfdggULXGoGAACgogyFm5SUFEVGRqp9+/ay2+2V1RMAAIDLDIWbMWPGaPHixTp8+LBGjBihP/7xj6pfv35l9QYAAGCYoUvB582bpxMnTmjixIn697//rYiICD344IP6+OOP2ZMDAACqBcP3ufHz89PgwYOVmpqqvXv36rbbbtOjjz6qqKgonT9/vjJ6BAAAKLcK3cTPy8tLFotFdrtdhYWF7uoJAADAZYbDTX5+vhYvXqwePXqoRYsW+vrrrzV37lxlZGSodu3aldEjAABAuRk6ofjRRx/VkiVLFBERoZEjR2rx4sUKCQmprN4AAAAMMxRukpOT1bRpUzVr1kwbNmzQhg0bSqz74IMP3NIcAACAUYbCzbBhw2SxWCqrFwAAgAozfBM/AACA6qxCV0sBAABUN4QbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKtUi3MybN09RUVHy9/dXdHS0tm/fXmrtm2++qTvvvFP16tVTvXr11L179zLrAQBAzeLxcLN06VLFx8dr+vTp2rVrl9q2batevXrp5MmTJdanp6dr8ODB+vTTT7V161ZFRESoZ8+eOnbsWBV3DgAAqiNDnwpeGWbNmqVRo0ZpxIgRkqTk5GStXr1aCxYs0OTJk4vVv/vuu07Lb731lt5//32lpaVp2LBhxerz8/OVn5/vWLZarZIkm80mm83mzrdyTbny3mvy9wAwgjkDGOPuOWNkPR4NNwUFBdq5c6cSEhIcY15eXurevbu2bt1arnXk5eXJZrOpfv36JT6elJSkGTNmFBtft26dAgMDXWvcRFJTUz3dAnBNYc4AxrhrzuTl5ZW71qPhJjs7W4WFhQoNDXUaDw0N1f79+8u1jkmTJqlJkybq3r17iY8nJCQoPj7esWy1Wh2HsoKCglxv/hpns9mUmpqqHj16yMfHx9PtANUecwYwxt1z5sqRl/Lw+GGpivjb3/6mJUuWKD09Xf7+/iXW+Pn5yc/Pr9i4j48PGyjxfQCMYs4AxrhrzhhZh0fDTUhIiLy9vZWVleU0npWVpbCwsDKf+/LLL+tvf/ubPvnkE7Vp06Yy2wQAANcQj14t5evrqw4dOigtLc0xVlRUpLS0NMXExJT6vBdffFF//etftXbtWnXs2LEqWgUAANcIjx+Wio+P1/Dhw9WxY0d16tRJs2fPVm5uruPqqWHDhik8PFxJSUmSpJkzZ2ratGlatGiRoqKilJmZKUmqXbu2ateu7bH3AQAAqgePh5uBAwfq1KlTmjZtmjIzM9WuXTutXbvWcZJxRkaGvLx+2cH0j3/8QwUFBXrggQec1jN9+nQ988wzVdk6AACohjwebiQpLi5OcXFxJT6Wnp7utHzkyJHKbwgAAFyzPH6HYgAAAHci3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3AAAAFMh3NRAdrtdP+cW6PRF6efcAtntdk+3BFRrzBnAGE/PGYu9hs1Sq9Wq4OBg5eTkKCgoyNPtVKmcCza9v/MnvbPliH78Oc8xHlk/UMM7R+n+DtcrOMDHgx0C1QtzBjCmMueMkd/fhJsaYsOBUxrzr526UFAoSfr1P7rl//8f4Outf/yxg7q2aFjl/QHVDXMGMKay54yR398clqoBNhw4pRELt+uCrVB2Of/A6f+X7ZIu2Ao1YuF2bThwquqbBKoR5gxgTHWbM9Ui3MybN09RUVHy9/dXdHS0tm/fXmb9smXL1LJlS/n7+6t169Zas2ZNFXV67cm5YNOYf+28/IN1lX10dvvlH74x/9qpnAu2qmgPqHaYM4Ax1XHOeDzcLF26VPHx8Zo+fbp27dqltm3bqlevXjp58mSJ9Vu2bNHgwYP1pz/9Sbt371ZsbKxiY2P1zTffVHHn14b3d/6kCwWFV/2Bu8July4UFOqDXT9VbmNANcWcAYypjnPG4+fcREdH64477tDcuXMlSUVFRYqIiNBjjz2myZMnF6sfOHCgcnNz9dFHHznGfvOb36hdu3ZKTk6+6utdq+fc5ObmlvqYt7e3/P39i9Xa7XbdM3ujjv584ZddhBaLvHz8HLVFBReLrc8iKby+v1bF3anAwEDHeF5eXqlnvFssFpdrL1y4oKKiolLf33XXXedS7cWLF1VYWOiW2sDAQFksl48a5+fn69KlS26pDQgIkJfX5b8xCgoKZLOV/peMkVp/f395e3sbrrXZbCooKCi11s/PT7Vq1TJce+nSJeXn55da6+vrKx8fH8O1hYWFunix+M/wFT4+PvL19S13rY+Pj+55bZOOns5Vka3092bx9pbF+3IPdnuRZCtQeH1/rXy0i+Pf/opatWrJz8/v/2vtysvLK7Y+V2pLm/cVrfXy8lJAQIBLtWwjat42wm63K3b+Zh37+aLskiy1fGTxulxrL7wke2HJ780iKbJhsDZM/r0sFku55v2FCxfK/fu7VpmPVrKCggLt3LlTCQkJjjEvLy91795dW7duLfE5W7duVXx8vNNYr169tHLlyhLr8/Pznb5hVqtV0uV/oLL+Maub2rVrl/pY79699eGHHzqWGzVqVOpG0S+ilcIe+ptj+VjySBVdsBary5AUPq+5Gg9/1TH20z9GqtBa8h41nwZN1eSR+Y7l4289KtvpjBJrvYMa6foxCxzLJ96ZoILM70us9QoIUsTjixzLmYsmK/9oyXvpLD5+ahr/vmP55LJndOHQjhJrJSly0i8B+dTKJOV9t7nU2ogJy+Xle/mXQ/bqV5X7TVqptdc/9q68A4MlSafX/UPnd68utTZ89NuqFRwqSTrz6QJZt39Qam3jkfPk2zBSknT2s3eVs3lxqbVhw2bJr3ELSVLO5+/rbPrCUmtDB78g/6ZtJEnndn2kn1NL/yOh4QPTFXjjHZKk819/otNrZpdaG/I/k3Vdy99KknL3f6bsD/9Wam2DPuNVu3V3SVLewS90avmMUmvr9xitOrffK0m6mPGVshY/XWpt3btHKDj6fklS/okDyvzf+FJrg7sMVt3fDpEkFWQf1YkFY0utDerUX/V+N1KSVGg9pWPJf1KGpNDE4rW12/dVg55jLtfm5einvw8pdb3Xtfq9QvpOkHT5D4+jrz5Qam3gzV3UMPaXbeePM+8ttTagWUc1GvCMYzlj1v2y20r+RfLf24ijcx4qcRshSb5hbCOuYBtx2a+3Ebl708vcRuT9z2SdssaoXqCvli9froceeqjU2rfeekuxsbGlPv7fPBpusrOzVVhYqNDQUKfx0NBQ7d+/v8TnZGZmllifmZlZYn1SUpJmzCi+oVy3bp3TXwbXspMnTzqdd1TWXxcAAFQXH639RA38pd27d5dZt2fPHkO/sz16WOr48eMKDw/Xli1bFBMT4xifOHGiNmzYoM8//7zYc3x9ffXOO+9o8ODBjrH58+drxowZysrKKlZf0p6biIgIZWdnm/6w1M+5Bbr7lU3OxeU4LHVF6vjfKqzBL98jdjnXvF3O/83sh6VyL0l3v/KZ7PYi2Q0clrpS+/HjnRUc6HwPDw5LXcY2wrXa6r6NOJtXoHvm/HKkpbyHpa7UfjHl96oX6Fvuw1IhISHV/7BUSEiIvL29i4WSrKwshYWFlficsLAwQ/V+fn6OjcWvXTm+fq2oW7eu4drgYLtuCKuvjJ/zil2Wd8WV3ai/ZpHUtH6gWkQ0cjp/IPi6gGK1pTFzrcxcq8qqlaQ6lVMbVPohW6O1IXa7IusHXp4zJcyNklgsXvLy9VfT+oFqGRlW7Jyb/1a3dvn/+jRSWx3mBrX/z8y1/zXvG9tL/z1j8a4li3fJMePK75mGQZeDno+Pj1NQLklZIfC/efRqKV9fX3Xo0EFpab8cmywqKlJaWprTnpxfi4mJcaqXpNTU1FLrazKLxaLhnaNceu7DXaKuupEGzIY5AxhTXeeMxy8Fj4+P15tvvql33nlH+/bt05gxY5Sbm6sRI0ZIkoYNG+Z0wvG4ceO0du1avfLKK9q/f7+eeeYZ7dixQ3FxcZ56C9Xa/R2uV4Cvt8r78+NluXwHyf63X1+5jQHVFHMGMKY6zhmPh5uBAwfq5Zdf1rRp09SuXTt9+eWXWrt2reOk4YyMDJ04ccJR37lzZy1atEhvvPGG2rZtq+XLl2vlypVq1aqVp95CtRYc4KN//LGDLNJVf/CuPJ78xw58Xg5qLOYMYEx1nDMev89NVbtW73NTUeX9zI/kP3bQXXxODsCcAQyq7DnDB2eWoaaGG+nyLbI/2PWTUjYX/7TWh7tc/rTWIH/++gSuYM4AxlTmnCHclKEmh5sr7Ha7Tlnz9NHaT3TvPd0dZ6sDKBlzBjCmMuYMnwqOMlksFtUL9FUDf6leoC8baeAqmDOAMZ6eM4QbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKoQbAABgKrU83UBVs9vtkiSr1erhTjzLZrMpLy9PVqtVPj4+nm4HqPaYM4Ax7p4zV35vX/k9XpYaF27OnTsnSYqIiPBwJwAAwKhz584pODi4zBqLvTwRyESKiop0/Phx1alTRxaLxdPteIzValVERISOHj2qoKAgT7cDVHvMGcAYd88Zu92uc+fOqUmTJvLyKvusmhq358bLy0vXX3+9p9uoNoKCgthQAwYwZwBj3DlnrrbH5gpOKAYAAKZCuAEAAKZCuKmh/Pz8NH36dPn5+Xm6FeCawJwBjPHknKlxJxQDAABzY88NAAAwFcINAAAwFcINAAAwFcINAAAwFcJNDTRv3jxFRUXJ399f0dHR2r59u6dbAqqtjRs3ql+/fmrSpIksFotWrlzp6ZaAaispKUl33HGH6tSpo0aNGik2NlbfffddlfdBuKlhli5dqvj4eE2fPl27du1S27Zt1atXL508edLTrQHVUm5urtq2bat58+Z5uhWg2tuwYYPGjh2rbdu2KTU1VTabTT179lRubm6V9sGl4DVMdHS07rjjDs2dO1fS5c/aioiI0GOPPabJkyd7uDugerNYLFqxYoViY2M93QpwTTh16pQaNWqkDRs26K677qqy12XPTQ1SUFCgnTt3qnv37o4xLy8vde/eXVu3bvVgZwAAM8rJyZEk1a9fv0pfl3BTg2RnZ6uwsFChoaFO46GhocrMzPRQVwAAMyoqKtL48ePVpUsXtWrVqkpfu8Z9KjgAAKh8Y8eO1TfffKPPPvusyl+bcFODhISEyNvbW1lZWU7jWVlZCgsL81BXAACziYuL00cffaSNGzfq+uuvr/LX57BUDeLr66sOHTooLS3NMVZUVKS0tDTFxMR4sDMAgBnY7XbFxcVpxYoVWr9+vW644QaP9MGemxomPj5ew4cPV8eOHdWpUyfNnj1bubm5GjFihKdbA6ql8+fP64cffnAsHz58WF9++aXq16+vpk2berAzoPoZO3asFi1apA8//FB16tRxnM8ZHBysgICAKuuDS8FroLlz5+qll15SZmam2rVrpzlz5ig6OtrTbQHVUnp6un73u98VGx8+fLhSUlKqviGgGrNYLCWOL1y4UA8//HDV9UG4AQAAZsI5NwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwCqpVOnTmnMmDFq2rSp/Pz8FBYWpl69emnz5s2SLt/mfeXKlZ5tEkC1xAdnAqiW7r//fhUUFOidd95Rs2bNlJWVpbS0NJ0+fdrTrQGo5vhsKQDVztmzZ1WvXj2lp6era9euxR6PiorSjz/+6FiOjIzUkSNHJEkffvihZsyYob1796pJkyYaPny4pkyZolq1Lv8tZ7FYNH/+fK1atUrp6elq3LixXnzxRT3wwANV8t4AVD4OSwGodmrXrq3atWtr5cqVys/PL/b4F198IenyJw2fOHHCsbxp0yYNGzZM48aN0969e/X6668rJSVFzz//vNPzExMTdf/992vPnj0aMmSIBg0apH379lX+GwNQJdhzA6Baev/99zVq1ChduHBBt99+u7p27apBgwapTZs2ki7vgVmxYoViY2Mdz+nevbt+//vfKyEhwTH2r3/9SxMnTtTx48cdzxs9erT+8Y9/OGp+85vf6Pbbb9f8+fOr5s0BqFTsuQFQLd1///06fvy4Vq1apXvuuUfp6em6/fbblZKSUupz9uzZo2effdax56d27doaNWqUTpw4oby8PEddTEyM0/NiYmLYcwOYCCcUA6i2/P391aNHD/Xo0UOJiYl65JFHNH36dD388MMl1p8/f14zZsxQ//79S1wXgJqBPTcArhm33nqrcnNzJUk+Pj4qLCx0evz222/Xd999p5tuuqnYf15ev2zutm3b5vS8bdu26ZZbbqn8NwCgSrDnBkC1c/r0aQ0YMEAjR45UmzZtVKdOHe3YsUMvvvii/ud//kfS5Sum0tLS1KVLF/n5+alevXqaNm2a7r33XjVt2lQPPPCAvLy8tGfPHn3zzTd67rnnHOtftmyZOnbsqN/+9rd69913tX37dr399tueersA3IwTigFUO/n5+XrmmWe0bt06HTx4UDabTRERERowYICefvppBQQE6N///rfi4+N15MgRhYeHOy4F//jjj/Xss89q9+7d8vHxUcuWLfXII49o1KhRki6fUDxv3jytXLlSGzduVOPGjTVz5kw9+OCDHnzHANyJcAOgRinpKisA5sI5NwAAwFQINwAAwFQ4oRhAjcKReMD82HMDAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABM5f8AtDhcVi3q4pcAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = EM.plot(val_ems)\n",
    "fig.savefig(f\"plots/EM_{n_train}.pdf\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2ffb405d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = Acc.plot(val_accs)\n",
    "fig.savefig(f\"plots/Acc_{n_train}.pdf\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a759204",
   "metadata": {},
   "source": [
    "### Inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "8e4448d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "transformer = Transformer(tokenizer_src.get_vocab_size(), tokenizer_tar.get_vocab_size(), d_model, n_h, n_layers , d_ff, seq_len, drop_prob, tokenizer_src.token_to_id(\"<pad>\"), tokenizer_tar.token_to_id(\"<pad>\")).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "d9b80fa8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<All keys matched successfully>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transformer.load_state_dict(torch.load(\"ckpts/test_transformer_36000_0.0001\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "e844c63e",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    transformer.eval()\n",
    "    src, tar = next(iter(val_dl))\n",
    "    src, tar = src.to(device), tar.to(device)\n",
    "    val_logits = transformer(src, tar)\n",
    "    val_y_pred = torch.argmax(val_logits, dim=-1)\n",
    "    val_loss = loss_fn(val_logits.permute(0,2,1), tar)\n",
    "    val_losses.append(val_loss.detach().to(cpu_device))\n",
    "\n",
    "    val_acc, val_em = Acc(val_y_pred, tar).to(cpu_device), EM(val_y_pred, tar).to(cpu_device)\n",
    "#     val_accs.append(val_acc)\n",
    "    val_ems.append(val_em)\n",
    "#     if val_loss < prev_loss:\n",
    "#         print(\"Saving Model -\", end=\" \")\n",
    "#         torch.save(transformer.state_dict(), f\"ckpts/test_transformer_{n_train}_{lr}\")            \n",
    "#     prev_loss = val_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "baff4c0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(0.7066), tensor(0.0096), tensor(2.9209, device='cuda:0'))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val_acc, val_em, val_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c719d6bb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "848b8400",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([512, 100, 7127])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "src = next(iter(train_dl))[0]\n",
    "tar = next(iter(train_dl))[1]\n",
    "logits = transformer(src, tar)\n",
    "logits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "1446062e",
   "metadata": {},
   "outputs": [],
   "source": [
    "log_probs = F.log_softmax(logits, dim=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "9a12b137",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([512, 100]),\n",
       " tensor([5064, 4260, 4499,  606, 6286,  397, 2506,  133, 6286, 3653, 1399,  181,\n",
       "          133,  397,   66, 6286,  397,  397,  397,  397,  397,  397, 6286,  133,\n",
       "          181,  397,  133, 6286, 6286, 6286,  397,  397, 2979,  397,  397, 3603,\n",
       "          397,  181, 3603, 6286, 3603, 6286, 5191,  133,  133, 5191,  397,  397,\n",
       "          397, 3129,  397, 6327, 6286, 1399,  397, 6286, 6286,  181,  133, 6286,\n",
       "         4614,  397,  397,  397, 2506,  133, 6760, 3129,  397,  397,  145, 6866,\n",
       "          181,  133,  181, 3603,  181,  181,  181,  515,  181, 5191, 2884,  133,\n",
       "         5191,  397, 1916,  133, 5191,  133, 5527, 6327,  133,  133, 5527,  133,\n",
       "          397, 5527, 6743, 5191]))"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = torch.argmax(logits, dim=-1)\n",
    "y_pred.shape, y_pred[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "05c36cd3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(8.9751, grad_fn=<NllLoss2DBackward0>)"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss_fn(logits.permute(0,2,1), tar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f875abab",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "codemirror_mode": {
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