digits.ipynb

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    "# Goal\n",
    "The goal of this program is to train a model to recognize hand-written digits 0-9.\n",
    "\n",
    "# Strategy\n",
    "- Download the MNIST data of labeled images of digits. \n",
    "- Create data loaders with training and validation data.\n",
    "- Define a model with linear and ReLU layers.\n",
    "- Define a loss function suitable for classification task.\n",
    "- Define a metric function to measure the performance of the model.\n",
    "- Run training epochs and print metrics after each epoch.\n",
    "- Export the trained model so that it can be used to create an app with Gradio + HF Spaces."
   ]
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    "from fastai.vision.all import *\n",
    "\n",
    "def load_and_label(p):\n",
    "    dirs = p.ls().sorted()\n",
    "    images_by_category = [ [tensor(Image.open(file)) for file in dir.ls().sorted() if file.is_file()] for dir in dirs] \n",
    "    labels = torch.cat( [ torch.full( (len(images_by_category[i]),), i) for i in range(len(images_by_category))])  \n",
    "    # labels = labels.unsqueeze(1).float()\n",
    "    images = torch.cat([torch.stack(l) for l in images_by_category])\n",
    "    images = images.view(-1, 28*28).float()\n",
    "    return (images, labels)\n",
    "    \n",
    "def to_dataset(images, labels):\n",
    "    return list(zip(images, labels))\n",
    "\n",
    "def init_params(size, std=1.0):\n",
    "    return (torch.randn(size)*std).requires_grad_()\n",
    "\n",
    "def init():\n",
    "    # Create the datasets\n",
    "    path = untar_data(URLs.MNIST)\n",
    "    train_path = path/\"training\"\n",
    "    valid_path = path/\"testing\"\n",
    "    \n",
    "    (train_xs, train_ys) = load_and_label(train_path) \n",
    "    (valid_xs, valid_ys) = load_and_label(valid_path) \n",
    "    \n",
    "    train_dset = to_dataset(train_xs, train_ys)\n",
    "    valid_dset = to_dataset(valid_xs, valid_ys)\n",
    "    \n",
    "    train_dl = DataLoader(train_dset, batch_size=256)\n",
    "    valid_dl = DataLoader(valid_dset, batch_size=256) \n",
    "    \n",
    "    return (train_xs, train_ys, valid_xs, valid_ys, train_dl, valid_dl)\n",
    "    \n",
    "#def mnist_loss(predictions, targets):\n",
    "#    # Use cross_entropy for classification tasks.\n",
    "#    # predictions.size() should be [batch_size, num_classes]\n",
    "#    # targets.size() should be [batch_size]\n",
    "#    return F.cross_entropy(predictions, targets)\n",
    "\n",
    "# def calc_grad(xb, yb, model):\n",
    "#     preds = model(xb)\n",
    "#     loss = mnist_loss(preds, yb)\n",
    "#     loss.backward()\n",
    "# \n",
    "# def train_epoch(model, lr, params):\n",
    "#     for xb, yb in train_dl:\n",
    "#         calc_grad(xb, yb, model)\n",
    "#         for p in params:\n",
    "#             p.data -= p.grad*lr\n",
    "#             p.grad.zero_()\n",
    "\n",
    "def batch_accuracy(xb, yb):\n",
    "    preds = torch.argmax(xb, dim=1)\n",
    "    correct = (preds == yb)\n",
    "    return correct.float().mean()\n",
    "\n",
    "def validate_epoch(model):\n",
    "    accs = [batch_accuracy(model(xb), yb) for xb,yb in valid_dl]\n",
    "    return round(torch.stack(accs).mean().item(), 4)"
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    "(train_xs, \n",
    " train_ys, \n",
    " valid_xs, \n",
    " valid_ys, \n",
    " train_dl, \n",
    " valid_dl) = init()"
   ]
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       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>batch_accuracy</th>\n",
       "      <th>time</th>\n",
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       "      <td>1.904833</td>\n",
       "      <td>0.334900</td>\n",
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       "      <td>00:01</td>\n",
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       "      <td>0.870865</td>\n",
       "      <td>1.864434</td>\n",
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       "      <td>00:00</td>\n",
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       "      <td>00:00</td>\n",
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       "      <td>1.402944</td>\n",
       "      <td>0.496100</td>\n",
       "      <td>00:00</td>\n",
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       "      <td>12</td>\n",
       "      <td>0.537203</td>\n",
       "      <td>1.341192</td>\n",
       "      <td>0.514600</td>\n",
       "      <td>00:00</td>\n",
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       "      <td>1.190640</td>\n",
       "      <td>0.565600</td>\n",
       "      <td>00:00</td>\n",
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       "      <td>1.150586</td>\n",
       "      <td>0.579600</td>\n",
       "      <td>00:00</td>\n",
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       "      <td>1.114411</td>\n",
       "      <td>0.592400</td>\n",
       "      <td>00:00</td>\n",
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = nn.Sequential(\n",
    "    nn.Linear(28*28, 64),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(64, 64),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(64, 64),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(64, 64),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(64, 10)\n",
    ")\n",
    "dls = DataLoaders(train_dl, valid_dl)\n",
    "learn = Learner(dls, model, opt_func=SGD,\n",
    "                loss_func=F.cross_entropy, metrics=batch_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b51f954f-22be-4cab-b9d4-fd592d32b9f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "learn.model.train()\n",
    "learn.fit(20, lr=1e-4)\n",
    "plt.plot(L(learn.recorder.values).itemgot(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "5ece5c0f-7c59-448f-a741-62f00088abe6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Object `learn.lr_find()` not found.\n"
     ]
    }
   ],
   "source": [
    "??learn.lr_find()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "50476694-0473-4aff-a375-0d204e10d012",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<fastai.learner.Learner at 0x7f7557d28850>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn.load(\"digit_classifier_94\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "c8bde148-d331-43a1-bf17-50eb29ed9e07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Path('models/digit_classifier_95.pth')"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Save the current model\n",
    "learn.save(\"digit_classifier_95\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "60c65c02-63fb-4429-8b34-6cc8efe800be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0002"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1e-4 + 1e-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "c17e4d1a-90b0-4d03-a623-fa4756c2af3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>batch_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.162387</td>\n",
       "      <td>0.154575</td>\n",
       "      <td>0.954300</td>\n",
       "      <td>00:01</td>\n",
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       "      <td>0.953900</td>\n",
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       "    <tr>\n",
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       "      <td>0.165545</td>\n",
       "      <td>0.154101</td>\n",
       "      <td>0.953800</td>\n",
       "      <td>00:01</td>\n",
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       "    <tr>\n",
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       "      <td>0.166283</td>\n",
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       "      <td>0.953900</td>\n",
       "      <td>00:01</td>\n",
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       "    <tr>\n",
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       "      <td>0.166729</td>\n",
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       "      <td>0.953900</td>\n",
       "      <td>00:01</td>\n",
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       "      <td>0.153876</td>\n",
       "      <td>0.954000</td>\n",
       "      <td>00:01</td>\n",
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       "      <td>0.954000</td>\n",
       "      <td>00:01</td>\n",
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       "      <td>0.954100</td>\n",
       "      <td>00:01</td>\n",
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       "      <td>00:01</td>\n",
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       "      <td>0.954100</td>\n",
       "      <td>00:01</td>\n",
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    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fda8d933df0>]"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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XTE1NRVxcHIYPHw6DwYCMjAzodDpkZmYCADQaDSIjIzvk8PDwgI+Pj3V7a2sr7r33XhQWFuLTTz+F2Wy2Hpny9vaGUqnsxrdHPEq5FMMGeuKo3oCjegOCvN3FjkREROTwbC4+c+bMQVVVFVauXAm9Xo/IyEjs2rULwcHBAAC9Xt/hnj5msxlr1qzBiRMnoFAoMHXqVOTl5WHIkCHWfWpqavDII4+grKwMWq0WUVFR2Lt3L8aPH3/Nuc6ePYudO3cCAMaOHdvha1999RVuvvlmWz+q6CICvNqKz3kDpo+88qX+REREdHUSgQMkVgaDAVqtFrW1tXZx2mvzN6ew8tOjSIjwQ/YDsWLHISIisku2/P7mWl12rH3AmVd2ERER9QwWHzsWPqit+JytbkJtk+kqexMREdHVsPjYMa27Ajf0UwPggqVEREQ9gcXHznGldiIiop7D4mPnwrlmFxERUY9h8bFzXLOLiIio57D42LmRv5zqKimvh8lsETkNERGRY2PxsXOB/dXQuMnRYrbgpwv1YschIiJyaCw+dk4ikXDOh4iIqIew+DgA640MWXyIiIiuC4uPA2gfcD5WxuJDRER0PVh8HMClp7q4tBoREVH3sfg4gOF+npBJJahuNKHM0Cx2HCIiIofF4uMAVAoZhg3wBMA7OBMREV0PFh8HwQFnIiKi68fi4yDC/TUAeAdnIiKi68Hi4yAi/LUAeMSHiIjoerD4OIj2Iz4/X2xEvbFV5DRERESOicXHQfh4usHPyw2CAJzg/XyIiIi6hcXHgURw6QoiIqLrwuLjQKxXdunrRE5CRETkmFh8HIj1Ds68souIiKhbWHwcSPupruN6A1rNFpHTEBEROR4WHwcS7OMBd6UMxlYLTlc1iB2HiIjI4bD4OBCZVIKwQe03MuScDxERka1YfBxMOK/sIiIi6jYWHwfz65VdLD5ERES2YvFxMO0DzlylnYiIyHYsPg4mdJAGEglwoc6IirpmseMQERE5FBYfB+OulCPE1wMAcIwDzkRERDZh8XFAPN1FRETUPSw+Dsg64Mwru4iIiGzC4uOAuHQFERFR97D4OKCRvxSfkxfq0Wwyi5yGiIjIcbD4OKABGjf4eiphEYATZRxwJiIiulYsPg5IIpHwdBcREVE3sPg4qAguXUFERGQzFh8H1X5lFy9pJyIiunYsPg7q0nv5WCyCyGmIiIgcA4uPgwrx9YBSLkVDixmlFxvFjkNEROQQWHwclFwmRdggDQAOOBMREV0rFh8HxqUriIiIbMPi48DCeWUXERGRTVh8HJh1zS4e8SEiIromLD4OrH3GR1/bjOqGFpHTEBER2T8WHwemUSkw2NsdAOd8iIiIrgWLj4OL4NIVRERE14zFx8FZ53w44ExERHRVLD4Ojkd8iIiIrh2Lj4ML/+WIz48V9TC2mkVOQ0REZN9YfBxcgFYFrVqBVouAkvJ6seMQERHZNRYfByeRSHgHZyIiomvE4uMEwjnnQ0REdE1YfJwAr+wiIiK6Niw+TuDSU12CIIichoiIyH6x+DiBYQM9oZBJYGhuxbmaJrHjEBER2S0WHyeglEsxbGDbul083UVERHR53So+GzZsQEhICFQqFWJiYrBv374r7p+ZmYnw8HCo1WqEhobi7bff7vD1LVu2QCKRdHo0Nzd3+XppaWmQSCRISkrqsP3DDz/E9OnT4evrC4lEAp1O152P55B4I0MiIqKrs7n47NixA0lJSXjuuedQVFSEKVOmYMaMGSgtLe1y/6ysLKSkpGDFihU4cuQIUlNTkZiYiE8++aTDfl5eXtDr9R0eKpWq0+vt378f2dnZGD16dKevNTQ0ID4+Hi+//LKtH8vhtQ8485J2IiKiy5Pb+oT09HQ89NBDePjhhwEAb7zxBr744gtkZWUhLS2t0/7vvPMOHn30UcyZMwcAMHToUHz33Xd45ZVXcOedd1r3k0gkGDRo0BXfu76+HgsWLMCbb76JF154odPXFy5cCAA4ffq0rR/L4YX7/3Kqi8WHiMjqYkMLLtQZxY5Bl5BIgBF+GtHe36bi09LSgoKCAixbtqzD9oSEBOTl5XX5HKPR2OnIjVqtRn5+PkwmExQKBYC2UhMcHAyz2YyxY8di1apViIqK6vC8xMREzJw5E9OmTeuy+NjKaDTCaPz1PwiDwXFLQ/uprjMXm2BoNsFLpRA5ERGRuL48Wo7EbYUwtlrEjkKXUMqlKH5hhmjvb1PxqayshNlshp+fX4ftfn5+KCsr6/I506dPx6ZNmzB79mxER0ejoKAAmzdvhslkQmVlJfz9/REWFoYtW7Zg1KhRMBgMWLt2LeLj43Hw4EEMHz4cAJCTk4PCwkLs37+/mx+1s7S0NKSmpvbY64mpn7sSN/RT41xNE47r6zA+xFvsSEREojlb3Yg/vH8QxlYLtGoFFDKJ2JHoF0qZuNdV2XyqC2g7LXUpQRA6bWu3fPlylJWVIS4uDoIgwM/PD4sWLcLq1ashk8kAAHFxcYiLi7M+Jz4+HtHR0Vi3bh0yMjJw5swZLF26FLt37+5y7qe7UlJSkJycbP2zwWBAUFBQj71+Xwv398K5miYcPV/L4kNELstktuDx7UWobTJhTFA/vP/oRCjlvIiZ2tj0N8HX1xcymazT0Z2KiopOR4HaqdVqbN68GY2NjTh9+jRKS0sxZMgQaDQa+Pr6dh1KKsW4ceNQUlICACgoKEBFRQViYmIgl8shl8uxZ88eZGRkQC6Xw2zu3qrkbm5u8PLy6vBwZBGc8yEiwmtfnEBRaQ00KjnWz4ti6aEObPrboFQqERMTg9zc3A7bc3NzMWnSpCs+V6FQIDAwEDKZDDk5OZg1axak0q7fXhAE6HQ6+Pv7AwBuvfVWHDp0CDqdzvqIjY3FggULoNPprEeOXJ116QoWHyJyUf8+Xo6Ne08CAF69dwyCvN1FTkT2xuZTXcnJyVi4cCFiY2MxceJEZGdno7S0FIsXLwbQdvro3Llz1nv1FBcXIz8/HxMmTEB1dTXS09Nx+PBhbN261fqaqampiIuLw/Dhw2EwGJCRkQGdTofMzEwAgEajQWRkZIccHh4e8PHx6bD94sWLKC0txfnz5wEAJ06cAAAMGjToqleMOYMIfy0AoLi8HiazBQqRz6MSEfUlfW0T/vDeQQDAoklDcHuk8/+7T7azufjMmTMHVVVVWLlyJfR6PSIjI7Fr1y4EBwcDAPR6fYd7+pjNZqxZswYnTpyAQqHA1KlTkZeXhyFDhlj3qampwSOPPIKysjJotVpERUVh7969GD9+vE3Zdu7cif/5n/+x/nnu3LkAgOeffx4rVqyw9aM6nMD+ani6yVFvbMXJCw0IHSTe5YJERH2p1WzBE9uLUN1owqgbtEi5I0zsSGSnJAJXtbQyGAzQarWora112Hmf+/6Sh/2nq/H6nDH4bVSg2HGIiPrEq18cR+ZXP0HjJsenT0xGsI+H2JGoD9ny+5vnQpzMryu114mchIiob+wtvoANX/8EAEi7ZxRLD10Ri4+TCW9fs4uLlRKRCyg3NOPJHToIArBgwmDMGh0gdiSycyw+TubSK7t4FpOInJnZImBpThGqGloQ7u+F5bMixI5EDoDFx8mM8NNAJpXgYkMLyg1cn4aInFfGv0rw3cmL8FDKkDk/CioFb21CV8fi42RUChluHNB2fpsrtRORs8r7sRIZ/267ye1LvxuFoQM8RU5EjoLFxwlZ53xYfIjICV2oM2LpL3M9c8cF4e6xN4gdiRwIi48TiuCAMxE5KbNFwJM7dLhQZ0SonwbP3zlS7EjkYFh8nFD7gDNPdRGRs9nw1Y/45sdKqBUyZC6IglrJuR6yDYuPE2o/1XWqqgENxlaR0xAR9YzvT1bh9S+LAQCrZkdi2EDenZ5sx+LjhHw93TBQ4wZBAI6X8UaGROT4quqNeCKnCBYBuCc6EPfG8M701D0sPk6KK7UTkbOwWAQkv3cQ5QYjhg30xKrZnOuh7mPxcVK/Ll3B4kNEjm3j3pPYU3wBbnIpMudHw11p8/raRFYsPk6KS1cQkTM4cPoiXtt9AgCQetdIhA7iXA9dHxYfJ9V+qut4mQFmC5euICLHU93Qgse3F8FsEXD32ADMGRckdiRyAiw+TmqIjwfUChmaTRacrmoQOw4RkU0EQcBT7x+EvrYZQ3098OJvR0EikYgdi5wAi4+Tkkkl1kPCPN1FRI7mrW9O4V/HK6CUS7F+fjQ83TjXQz2DxceJ8couInJERaXVePmz4wCAP8+KsP5bRtQTWHycGK/sIiJHU9towpJtRWi1CJg5yh8LJgwWOxI5GRYfJ2Y94sNTXUTkAARBwNN/P4hzNU0Y7O2OtHs410M9j8XHiYUN0kAiASrqjLhQZxQ7DhHRFW3NO43dR8uhlLXdr8dLpRA7EjkhFh8n5q6UI8THAwBPdxGRfTt0thYv7Wqb63n2jjCMCtSKnIicFYuPkwvnSu1EZOcMzSYkbitEi9mC20cOwoOThogdiZwYi4+Tax9w5pVdRGSPBEFAygeHUHqxEYH91Xjl3tGc66FexeLj5CK4dAUR2bF3vy/FPw/pIZdKsG5eFLRqzvVQ72LxcXLtV3adrGxAs8kschoiol8dOV+LVZ8eBQAsmxGGqMH9RU5EroDFx8kN1LjB20MJs0VAcXmd2HGIiAAA9cZWLNlWhJZWC6aFD8RDk0PEjkQugsXHyUkkEp7uIiK7IggCnvvoEE5VNiBAq8Jr943hXA/1GRYfF8ClK4jInuzYfwYf685DJpVg3fwo9HNXih2JXAiLjwvg0hVEZC+Olxnw/M4jAICnEkIRE+wtciJyNSw+LiDcWnzqYLEIIqchIlfVYGxF4t8KYWy14ObQAXj0pqFiRyIXxOLjAoYO8IBSLkW9sRVnqhvFjkNELurPHx/BTxca4OflhjX3jYFUyrke6nssPi5AIZMi1E8DgKe7iEgcfy84iw8Kz0IqATLmRsHH003sSOSiWHxcRLh/W/HhlV1E1NdKyuuw/B+HAQDJt43AhKE+IiciV8bi4yK4dAURiaGpxYzEbYVoMpkxZbgvHrt5mNiRyMWx+LiIiIC2lY55xIeI+tKKnUdQXF6PARo3pN8/lnM9JDoWHxcR9suprvO1zahpbBE5DRG5gn8UncOOA2cgkQBr54zFAA3nekh8LD4uwkulQJC3GgBPdxFR7zt5oR7PfnQIAPDELcMxaZivyImI2rD4uBAuXUFEfaHZZEbitiI0tpgxcagPnrh1uNiRiKxYfFxIhH/bnM8xPRcrJaLes+rTozimN8DHQ4m1c8dCxrkesiMsPi7Eekk7T3URUS/59Ifz+Nv3pZBIgNfnjMVAL5XYkYg6YPFxIe2Llf5YUYeWVovIaYjI2ZyubMCyD9rmeh67+UbcNGKAyImIOmPxcSE39FPDSyWHySzgx4p6seMQkRMxtpqxZHsh6o2tGD/EG09OGyF2JKIusfi4EIlEYj3qw9NdRNST0nYdx+FzBvR3V2DtvLGQy/jrhewT/2a6mHBe2UVEPezzw3psyTsNAEifMxb+WrW4gYiugMXHxfy6dEWtyEmIyBmcudiIp//+AwDg0d8MxdTQgSInIroyFh8X036q65i+DoIgiJyGiBxZS6sFS7YVoq65FdGD++GphFCxIxFdFYuPixk20BNyqQS1TSacr20WOw4RObDVnx/HwbO10KoVWDc/GgrO9ZAD4N9SF+Mml2HYQE8AnPMhou778mg5Nn1zCgDw2n1jcEM/zvWQY2DxcUG/nu5i8SEi252racIf3j8IAHhocghui/ATORHRtWPxcUFcs4uIustktuDxbYWobTJhTKAWz9weJnYkIpuw+LigX6/sYvEhItu8tvsECktroFHJsX5+NJRy/hohx8K/sS6o/V4+pRcbUddsEjkNETmKr45XYOOekwCAV+8djSBvd5ETEdmOxccF9fdQIkDbtnDg8TKu1E5EV6evbULyezoAwIMTg3F7pL+4gYi6icXHRfEOzkR0rVrNFizdrkN1owmRN3jh2ZnhYkci6jYWHxdlXbOLxYeIruKNL0uQf/oiPN3kWD8vGm5ymdiRiLqNxcdFtQ84Hytj8SGiy9tXcgGZX/8IAEj73SgM8fUQORHR9elW8dmwYQNCQkKgUqkQExODffv2XXH/zMxMhIeHQ61WIzQ0FG+//XaHr2/ZsgUSiaTTo7m56zsLp6WlQSKRICkpqcN2QRCwYsUKBAQEQK1W4+abb8aRI0e68xGdXvupruNldWg1W0ROQ0T2qMLQjKQcHQQBmD9hMO4cEyB2JKLrZnPx2bFjB5KSkvDcc8+hqKgIU6ZMwYwZM1BaWtrl/llZWUhJScGKFStw5MgRpKamIjExEZ988kmH/by8vKDX6zs8VCpVp9fbv38/srOzMXr06E5fW716NdLT07F+/Xrs378fgwYNwm233Ya6Og7w/rfB3u7wUMrQ0mrBycoGseMQkZ0xWwQszdGhqqEFYYM0+POsCLEjEfUIm4tPeno6HnroITz88MMIDw/HG2+8gaCgIGRlZXW5/zvvvINHH30Uc+bMwdChQzF37lw89NBDeOWVVzrsJ5FIMGjQoA6P/1ZfX48FCxbgzTffRP/+/Tt8TRAEvPHGG3juuefwu9/9DpGRkdi6dSsaGxuxbds2Wz+m05NKJRxwJqLLWvfvEvznZBXclTJkLoiGSsG5HnIOclt2bmlpQUFBAZYtW9Zhe0JCAvLy8rp8jtFo7HTkRq1WIz8/HyaTCQqFAkBbqQkODobZbMbYsWOxatUqREVFdXheYmIiZs6ciWnTpuGFF17o8LVTp06hrKwMCQkJ1m1ubm74zW9+g7y8PDz66KNdZjMajdY/GwyuVQAiArxw4OdqHNMbMDvqBrHjEDm8L4+W40//OIzaJse/P1aTyQwAeOm3o3DjAE+R0xD1HJuKT2VlJcxmM/z8Oq7L4ufnh7Kysi6fM336dGzatAmzZ89GdHQ0CgoKsHnzZphMJlRWVsLf3x9hYWHYsmULRo0aBYPBgLVr1yI+Ph4HDx7E8OHDAQA5OTkoLCzE/v37u3yf9vfvKtvPP//c5XPS0tKQmppqy7fAqYTzDs5EPeZUZQOW5hShocUsdpQe8z/xQ/g/ReR0bCo+7SQSSYc/C4LQaVu75cuXo6ysDHFxcRAEAX5+fli0aBFWr14Nmazt0GlcXBzi4uKsz4mPj0d0dDTWrVuHjIwMnDlzBkuXLsXu3bu7nPvpbraUlBQkJydb/2wwGBAUFHTF13cml67ZdaXvExFdWbPJjCXbCtHQYsb4Id547b4xcPT/nNzkUgz0uvK/t0SOyKbi4+vrC5lM1unoTkVFRacjLe3UajU2b96MjRs3ory8HP7+/sjOzoZGo4Gvr2+Xz5FKpRg3bhxKSkoAAAUFBaioqEBMTIx1H7PZjL1792L9+vUwGo3WmaCysjL4+/96R9ErZXNzc4Obm9u1fwOcTOggDaQSoKqhBRfqjPxHjqibXtp1DEfOG+DtoUTGvCgM0vK/JSJ7ZdNws1KpRExMDHJzcztsz83NxaRJk674XIVCgcDAQMhkMuTk5GDWrFmQSrt+e0EQoNPprAXm1ltvxaFDh6DT6ayP2NhYLFiwADqdDjKZDCEhIRg0aFCHbC0tLdizZ89Vs7kqlUKGob+cuz/C011E3bLrkB5v/6ftdPqa+8ew9BDZOZtPdSUnJ2PhwoWIjY3FxIkTkZ2djdLSUixevBhA2+mjc+fOWe/VU1xcjPz8fEyYMAHV1dVIT0/H4cOHsXXrVutrpqamIi4uDsOHD4fBYEBGRgZ0Oh0yMzMBABqNBpGRkR1yeHh4wMfHx7q9/b4+L730EoYPH47hw4fjpZdegru7O+bPn9+9744LiPD3wo8V9Th63oCpoQPFjkPkUEqrGvHM338AADz6m6H8b4jIAdhcfObMmYOqqiqsXLkSer0ekZGR2LVrF4KDgwEAer2+wz19zGYz1qxZgxMnTkChUGDq1KnIy8vDkCFDrPvU1NTgkUceQVlZGbRaLaKiorB3716MHz/epmx//OMf0dTUhMceewzV1dWYMGECdu/eDY1GY+vHdBkRAV7YefA8B5yJbGRsNWPJ9kLUGVsRE9wfTyWEih2JiK6BRBAEQewQ9sJgMECr1aK2thZeXl5ix+kTe4sv4IHN+Rg6wAP//sPNYschchgrPzmKzd+eglatwK6lU3BDP7XYkYhcli2/v7lWl4trv6T9VGUDGltaRU5D5Bh2HynD5m9PAQDW3DeGpYfIgbD4uLgBGjcM0LhBENrW7SKiKztb3Yin3j8IAHh4cgimRXR91SgR2ScWH/p1pXbO+RBdkclswePbi2BobsWYoH744+1hYkciIhux+BDX7CK6Rq9+cQJFpTXQqORYPy8KSjn/CSVyNPyvlhARwKUriK7m38fLkb33JADg1XvHIMjbXeRERNQdLD5kPdV1oqwOZgsv8iP6b/raJvzhvba5nkWThuD2yEEiJyKi7mLxIYT4ekClkKKxxYyfqxrEjkNkV1rNFjyxvQjVjSaMukGLlDs410PkyFh8CDKpBKGDeLqLqCvpucXYf7oanm5yrJ8fBTe5TOxIRHQdWHwIQMeV2omozZ7iC9jw9U8AgJfvGYVgHw+RExHR9WLxIQC/DjjzknaiNuWGZiTv0AEAFkwYjFmjA8QNREQ9gsWHAAAR/m3rmfFUFxFgtgh4YnsRqhpaEO7vheWzIsSOREQ9hMWHAAChg7wgkQDlBiOq6o1ixyES1dp/leD7UxfhoZQhc34UVArO9RA5CxYfAgB4uskx5Jf5hWN6Ll1BruvbHyux7t8lAICXfjcKQwd4ipyIiHoSiw9ZhVtPd9WKnIRIHBV1zViao4MgAHNig3D32BvEjkREPYzFh6x4ZRe5MrNFwJM7dKisNyLUT4MVd40UOxIR9QIWH7Li0hXkyjZ89SO+/bEKaoUMmQuioFZyrofIGbH4kFWEvxYA8NOFBjSbzCKnIeo7352swutfFgMAVs2OxLCBGpETEVFvYfEhKz8vN/R3V8BsEVBSXi92HKI+UVVvxNKcIlgE4J7oQNwbEyh2JCLqRSw+ZCWRSC453cUBZ3J+FouAJ987iHKDETcO8MCq2ZzrIXJ2LD7UQfuAMy9pJ1fwl70/YW/xBbjJpchcEA13pVzsSETUy1h8qINwXtlFLmL/6YtYs7ttrif1rpEI+2WhXiJybiw+1MGlV3ZZLILIaYh6R3VDC57YXgSzRcDdYwMwZ1yQ2JGIqI+w+FAHNw7whFImRb2xFWerm8SOQ9TjBEHAU+8fhL62GUN9PfDib0dBIpGIHYuI+giLD3WgkEkxYlDbLfp5Px9yRpv2ncK/jldAKZdi3fwoeLpxrofIlbD4UCfhg3gjQ3JOhaXVeOXz4wCA5bMiMDJAK3IiIuprLD7UiXXOhwPO5ERqG014fFsRWi0CZo7yx+8nDBY7EhGJgMWHOvn1knYWH3IOgiDg6b8fxLmaJgz2dkfaPZzrIXJVLD7USdgvxedcTRNqG00ipyG6flvyTmP30XIoZVJkzo+Gl0ohdiQiEgmLD3WiVSsQ2F8NgHM+5Ph+OFuDl3YdAwA8e0cYRgVyrofIlbH4UJd4uoucgaHZhCXbimAyC5g+0g8PThoidiQiEhmLD3XJegdnFh9yUIIgYNkHP6D0YiMC+6ux+p4xnOshIhYf6hqv7CJH9+73pdh1qAxyqQTr5kVB6865HiJi8aHLaD/VVVJRh5ZWi8hpiGxz5HwtVn16FACwbEYYogb3FzkREdkLFh/qUmB/NTQqOUxmAT9dqBc7DtE1qze2Ysm2IrS0WjAtfCAemhwidiQisiMsPtQliUTCldrJ4QiCgGc/PIRTlQ0I0Krw2n2c6yGijlh86LIiOOBMDiZn/xnsPHgeMqkE6+ZHoZ+7UuxIRGRnWHzostoHnHlJOzmCY3oDVuw8AgB4KiEUMcHeIiciInvE4kOXdekRH0EQRE5DdHkNxlYs2VYIY6sFN4cOwKM3DRU7EhHZKRYfuqxhAz0hl0pQ02iCvrZZ7DhEl7X848P46UID/LzcsOa+MZBKOddDRF1j8aHLUilkGDbQEwAHnMl+vX/gDD4sPAepBMiYGwUfTzexIxGRHWPxoSvi0hVkz0rK6/Dnj9vmep6cNgIThvqInIiI7B2LD10Rl64ge9XUYkbitkI0mcyYPMwXj00dJnYkInIALD50RdalK1h8yM6s2HkExeX1GKBxw+tzxkLGuR4iugYsPnRF7Ud8fq5qRL2xVeQ0RG3+UXQOOw6cgUQCrJ0zFgM0nOshomvD4kNX5O2hxCAvFQDgOI/6kB346UI9nv3oEADgiVuGY9IwX5ETEZEjYfGhq+LpLrIXzSYzEv9WiMYWM+KGeuOJW4eLHYmIHAyLD11VBNfsIjux8tOjOF5WBx8PJdbOjeJcDxHZjMWHropLV5A9+OTgeWz7vhQSCfD6nLHw++UULBGRLVh86KraB5yPl9Wh1WwROQ25otOVDUj5sG2u57Gbb8RNIwaInIiIHBWLD11VsLc73JUyGFstOFXZIHYccjHGVjOWbC9EvbEV44d448lpI8SOREQOjMWHrkoqlfBGhiSal/55DIfPGdDfXYG188ZCLuM/W0TUffwXhK5JuL8GAIsP9a3PDumx9T8/AwDS7x8Lf61a5ERE5OhYfOiaRPhrAfDKLuo7pVWN+OMHPwAAHr1pKKaGDRQ5ERE5AxYfuia8sov6UkurBY9vL0RdcyuiB/fDU9NDxY5ERE6CxYeuSaifBlIJUFnfgoq6ZrHjkJN75fPjOHi2Flq1AuvmR0PBuR4i6iH814SuiVopQ4ivBwCe7qLelXu0HG99cwoA8Np9Y3BDP871EFHP6Vbx2bBhA0JCQqBSqRATE4N9+/Zdcf/MzEyEh4dDrVYjNDQUb7/9doevb9myBRKJpNOjufnXIwtZWVkYPXo0vLy84OXlhYkTJ+Kzzz7r8Drl5eVYtGgRAgIC4O7ujttvvx0lJSXd+YjUhYiAX+Z8eLqLesnZ6kY89f5BAMBDk0NwW4SfyImIyNnYXHx27NiBpKQkPPfccygqKsKUKVMwY8YMlJaWdrl/VlYWUlJSsGLFChw5cgSpqalITEzEJ5980mE/Ly8v6PX6Dg+V6tc7swYGBuLll1/GgQMHcODAAdxyyy24++67ceTIEQCAIAiYPXs2Tp48iY8//hhFRUUIDg7GtGnT0NDAe8/0hPalK47p60ROQs7IZLbg8e1FqG0yYUygFs/cHiZ2JCJyRoKNxo8fLyxevLjDtrCwMGHZsmVd7j9x4kThqaee6rBt6dKlQnx8vPXPf/3rXwWtVmtrFKF///7Cpk2bBEEQhBMnTggAhMOHD1u/3traKnh7ewtvvvnmNb1ebW2tAECora21OYsr+Op4uRD8zKfCLa99JXYUckIv/fOoEPzMp0Lk858LpVUNYschIgdiy+9vuS0lqaWlBQUFBVi2bFmH7QkJCcjLy+vyOUajscORGwBQq9XIz8+HyWSCQqEAANTX1yM4OBhmsxljx47FqlWrEBUV1eVrms1mvP/++2hoaMDEiROt7wOgw3vJZDIolUp88803ePjhh7vM1v48ADAYeArnStqv7DpZ2YAGYys83Gz660O9YG/xBbz1zSmYHHwpEYsg4LuTFwEAr947GkHe7iInIiJnZdNvrsrKSpjNZvj5dTzv7ufnh7Kysi6fM336dGzatAmzZ89GdHQ0CgoKsHnzZphMJlRWVsLf3x9hYWHYsmULRo0aBYPBgLVr1yI+Ph4HDx7E8OHDra916NAhTJw4Ec3NzfD09MRHH32EiIgIAEBYWBiCg4ORkpKCjRs3wsPDA+np6SgrK4Ner+8yW1paGlJTU235Fri0gRoVbuinxrmaJry2+wSev3Ok2JFc2omyOjzyzgE0mxy79FzqwYnBuD3SX+wYROTEuvW/7BKJpMOfBUHotK3d8uXLUVZWhri4OAiCAD8/PyxatAirV6+GTCYDAMTFxSEuLs76nPj4eERHR2PdunXIyMiwbg8NDYVOp0NNTQ0++OADPPjgg9izZw8iIiKgUCjwwQcf4KGHHoK3tzdkMhmmTZuGGTNmXPZzpKSkIDk52fpng8GAoKCg7nxLXMaq2SPxv1sO4K/fnkbcUB9MHzlI7EguqbGlFYnbCtFssmDSjT6YO36w2JGum4+HEpNu9BE7BhE5OZuKj6+vL2QyWaejOxUVFZ2OArVTq9XYvHkzNm7ciPLycvj7+yM7OxsajQa+vr5dPkcqlWLcuHGdrshSKpUYNmwYACA2Nhb79+/H2rVrsXHjRgBATEwMdDodamtr0dLSggEDBmDChAmIjY3t8n3c3Nzg5uZmy7fA5d0S5odHbhqK7L0n8fT7BxHh78XTEiL488dH8GNFPQZq3JAxLwq+nvx7TER0LWy6qkupVCImJga5ubkdtufm5mLSpElXfK5CoUBgYCBkMhlycnIwa9YsSKVdv70gCNDpdPD3v/Ihb0EQOszotNNqtRgwYABKSkpw4MAB3H333Vf5ZGSLp6eHImpwPxiaW/H49iK0tDrPqRZH8EHBWfy94CykErD0EBHZyOZTXcnJyVi4cCFiY2MxceJEZGdno7S0FIsXLwbQdvro3Llz1nv1FBcXIz8/HxMmTEB1dTXS09Nx+PBhbN261fqaqampiIuLw/Dhw2EwGJCRkQGdTofMzEzrPs8++yxmzJiBoKAg1NXVIScnB19//TU+//xz6z7vv/8+BgwYgMGDB+PQoUNYunQpZs+ejYSEhG5/g6gzhUyKjLlRmJmxD7ozNXj1i+N4bmaE2LFcwo8VdfjTPw4DAJKmjUDcUJ4aIiKyhc3FZ86cOaiqqsLKlSuh1+sRGRmJXbt2ITg4GACg1+s73NPHbDZjzZo1OHHiBBQKBaZOnYq8vDwMGTLEuk9NTQ0eeeQRlJWVQavVIioqCnv37sX48eOt+5SXl2PhwoXQ6/XQarUYPXo0Pv/8c9x2223WffR6PZKTk62n1B544AEsX768O98Xuoogb3e8et8YPPpOAd7cdwpxQ31wazhvNtebmlrMSPxbEZpMZsQP80Hi1GFiRyIicjgSQRAEsUPYC4PBAK1Wi9raWnh5eYkdxyGkfnIEf/32NPq5K7DriSkI4PICvWbZBz8gZ/8Z+Hq6YdfSyRioUV39SURELsCW399cq4uuS8qMcIwO1KKm0YTHtxc5/P1k7NXHunPI2X8GEgmwdu5Ylh4iom5i8aHropRLsX5eNDRuchT8XI01u4vFjuR0Tl6ox7MfHgIAPD51GOKHdX01JBERXR2LD123wT7uWH3vaADAX/b8hK9OVIicyHk0m8xI3FaEhhYzJoR4Y+m0EWJHIiJyaCw+1CNmjPLHAxPbBtz/8N5BlNU2i5zIOaz69CiO6Q3w8VAiY14UZNKubxRKRETXhsWHesyzd4RjZIAXLja04IntRWjlvM91+fSH8/jb921XSKbPGQs/L871EBFdLxYf6jEqhQyZ86Ph6SZH/umLeOPLkqs/ibp0urIByz5om+t57OYb8ZsRA0RORETkHFh8qEcN8fVA2u9GAQAyv/4R+0ouiJzI8RhbzViyvRD1xlaMG9IfybdxroeIqKew+FCPu3NMAOZPGAxBAJ7coUOFgfM+tnjpn8dw+JwB/d0VyJgXBbmM/5kSEfUU/otKveLPsyIQNkiDyvoWLM3RwWzhfTKvxWeH9Nj6n58BAOn3j4W/ljeEJCLqSSw+1CtUChkyF0TDXSnDf05WYd2/Oe9zNaVVjfjjBz8AAB69aSimhg0UORERkfNh8aFec+MAT7z420gAwNp/lSDvp0qRE9mvllYLHt9eiLrmVkQP7oenpoeKHYmIyCmx+FCv+m1UIO6PDYQgAEtzdLhQZxQ7kl165fPjOHi2Flq1AuvmR0PBuR4iol7Bf12p16XeFYkRfp64UGdE8ns6WDjv00Hu0XK89c0pAMBr943BDVzolYio17D4UK9TK9vu76NWyLCvpBIbvv5R7Eh242x1I556/yAA4KHJIbgtwk/kREREzo3Fh/rEcD8NVt49EgCQnluM709WiZxIfCazBY9vL0JtkwljArV45vYwsSMRETk9Fh/qM/fFBuF30TfAIgBP5BShqt61531e++IEikproFHJsX5+NJRy/udIRNTb+C8t9alVd0fixgEeKDcYkfzeQZed9/n38XJs3HsSAPDqvaMR5O0uciIiItfA4kN9ysNNjswF0XCTS7Gn+IL1l78r0dc24Q/vtc31PDgxGLdH+ouciIjIdbD4UJ8LG+SF1Lva5n1e230CB05fFDlR32k1W/DE9iJUN5oQeYMXnp0ZLnYkIiKXwuJDopgzLgh3jw2A2SLg8e1FqG5oETtSn0jPLcb+09XwdJNj/bxouMllYkciInIpLD4kColEghd/Owohvh7Q1zbjqfcPQhCce95nT/EFbPj6JwDAy/eMwhBfD5ETERG5HhYfEo2nmxzr50dBKZfiX8crsGnfKbEj9ZpyQzOSd+gAAAsmDMas0QHiBiIiclEsPiSqkQFaLJ8VAaBt2Yai0mqRE/W89rmeqoYWhPt7WT8vERH1PRYfEt3vJwzGzFH+aLUIWLKtCLWNJrEj9aiMf5Xg+1MX4aGUIXN+FFQKzvUQEYmFxYdEJ5FIkHbPKAz2dse5miY8/Xfnmff5pqQS675qW6Ljpd+NwtABniInIiJybSw+ZBe8VApkzo+GUibF7qPl2JJ3WuxI162irhlJO3QQBGDuuCDcPfYGsSMREbk8Fh+yG6MCtXj2jrb1ql7adQw/nK0RN9B1MFsEPLlDh8p6I0L9NHj+zpFiRyIiIrD4kJ15cNIQ3D5yEEzmtnkfQ7NjzvtkfvUjvv2xCmqFDJkLoqBWcq6HiMgesPiQXZFIJHjl3tEI7K9G6cVGLPvgB4eb9/nuZBXe+LIYALBqdiSGDdSInIiIiNqx+JDd0aoVWD8/GgqZBLsOleHd734WO9I1q6w34ontRbAIwD3Rgbg3JlDsSEREdAkWH7JLY4P64Znb2+Z9Vn16DIfP1Yqc6Oosv8z1VNQZMWygJ1bN5lwPEZG9YfEhu/XQ5BBMC/dDi9mCJdsKUWfn8z5Ze37CvpJKqBRSZM6PhrtSLnYkIiL6Lyw+ZLckEgleu280ArQqnK5qxLMfHbbbeZ/9py8iPbdtrif1rpEIHcS5HiIie8TiQ3atn7sS6+ZHQSaV4JOD57E9/4zYkTq52NCCx7cVwWwRMHtsAO6PDRI7EhERXQaLD9m9mGBvPD09FACQ+skRHNMbRE70K4tFwB/e06HM0Iyhvh544bejIJFIxI5FRESXweJDDuGRKUNxc+gAGFstSNxWiAZjq9iRAABv7juJr05cgFIuxfr50fB041wPEZE9Y/EhhyCVSpB+/1gM8lLh5IUG/Okf4s/7FPxcjdVfnAAAPH9nBCICvETNQ0REV8fiQw7D20OJjHlt8z4fFZ3D+wfOipalprEFT2xvm+uZNdof88cPFi0LERFdOxYfcijjQ7yRfNsIAMCfdx5GcXldn2cQBAFPvf8DztU0YYiPO9J+x7keIiJHweJDDuf//eZGTBnui2aTBYl/K0RjS9/O+2z+9jS+PFYOpaxtrkejUvTp+xMRUfex+JDDkUoleH3OWAzUuKGkoh7Pf3ykz9774JkavPzZMQDAn2aFI/IGbZ+9NxERXT8WH3JIvp5uWDs3ClIJ8H7BWXxY2PvzPrVNJiRuK4TJLGBG5CAsjAvu9fckIqKexeJDDmvijT5YemvbvM+f/nEYP1bU99p7CYKAZ/7+A85WNyHIW42X7xnNuR4iIgfE4kMObcktwzDpRh80tpixZFshmk3mXnmft//zMz4/UgaFTIL186KhVXOuh4jIEbH4kEOTSSV4Y+5Y+HoqcbysDqmf9Py8z+FztXjxn21zPctmhGNMUL8efw8iIuobLD7k8AZqVHhjThQkEmB7/hl8rDvXY69d19w219NituC2CD/8b/yQHnttIiLqeyw+5BQmD/fFkqnDAADPfngIJy9c/7yPIAhY9uEh/FzViBv6qfHqvZzrISJydCw+5DSW3joc40O80dBiRuK2ouue9/nb96X45w96yKUSrJsfhX7uyh5KSkREYmHxIachl0mRMTcK3h5KHNMb8MI/j3b7tY6cr8XKT9ue/8fbQxE9uH9PxSQiIhGx+JBTGaRVIf3+MQCAd78rxac/nLf5NeqNrViyrQgtrRbcEjYQD08e2tMxiYhIJCw+5HRuDh2I/3fzjQCAZR8cws9VDdf8XEEQ8NxHh3CqsgH+WhXW3DcGUinneoiInAWLDzmlP9w2ArHB/VFvbEXitkIYW69t3mfH/jP4WHceMqkE6+ZFob8H53qIiJwJiw85JblMiox5UejnrsDhcwak7Tp+1eccLzPg+Z1t9wH6Q8IIxA7x7u2YRETUx1h8yGkF9FNb53225J3G54f1l923wdiKxL8VwthqwW9GDMDim27sq5hERNSHWHzIqd0S5odHbmobTn767z/gzMXGLvf788dH8NOFBvh5uSH9fs71EBE5KxYfcnpPTw9F1OB+qGtuxZLtbVdrXervBWfxQeFZSCXA2rlR8PF0EykpERH1tm4Vnw0bNiAkJAQqlQoxMTHYt2/fFffPzMxEeHg41Go1QkND8fbbb3f4+pYtWyCRSDo9mpubrftkZWVh9OjR8PLygpeXFyZOnIjPPvusw+vU19djyZIlCAwMhFqtRnh4OLKysrrzEcmJKGRSrJsXBS+VHAfP1GD157/O+5SU12H5Pw4DAJKmjUDcUB+xYhIRUR+wufjs2LEDSUlJeO6551BUVIQpU6ZgxowZKC0t7XL/rKwspKSkYMWKFThy5AhSU1ORmJiITz75pMN+Xl5e0Ov1HR4qlcr69cDAQLz88ss4cOAADhw4gFtuuQV33303jhz5dVHKJ598Ep9//jneffddHDt2DE8++SQef/xxfPzxx7Z+THIygf3d8ep9bfM+m745hS+PlqOpxYzEbYVoMpkRP8wHib8seUFERM5LIgiCYMsTJkyYgOjo6A5HUsLDwzF79mykpaV12n/SpEmIj4/Hq6++at2WlJSEAwcO4JtvvgHQdsQnKSkJNTU1NoX39vbGq6++ioceeggAEBkZiTlz5mD58uXWfWJiYnDHHXdg1apVV309g8EArVaL2tpaeHl52ZSFHEPqJ0fw129PQ6tWYNKNPvjscBl8Pd3w2dIpGKDhKS4iIkdky+9vm474tLS0oKCgAAkJCR22JyQkIC8vr8vnGI3GDkduAECtViM/Px8mk8m6rb6+HsHBwQgMDMSsWbNQVFR02Rxmsxk5OTloaGjAxIkTrdsnT56MnTt34ty5cxAEAV999RWKi4sxffr0y2YzGAwdHuTcUmaEY3SgFrVNJnx2uAwSCbB27liWHiIiF2FT8amsrITZbIafn1+H7X5+figrK+vyOdOnT8emTZtQUFAAQRBw4MABbN68GSaTCZWVlQCAsLAwbNmyBTt37sT27duhUqkQHx+PkpKSDq916NAheHp6ws3NDYsXL8ZHH32EiIgI69czMjIQERGBwMBAKJVK3H777diwYQMmT57cZba0tDRotVrrIygoyJZvBzkgpVyK9fOioXGTAwAev2U44of5ipyKiIj6irw7T5JIOl7qKwhCp23tli9fjrKyMsTFxUEQBPj5+WHRokVYvXo1ZDIZACAuLg5xcXHW58THxyM6Ohrr1q1DRkaGdXtoaCh0Oh1qamrwwQcf4MEHH8SePXus5ScjIwPfffcddu7cieDgYOzduxePPfYY/P39MW3atE7ZUlJSkJycbP2zwWBg+XEBg33c8eFjk3DkvAF3jgkQOw4REfUhm4qPr68vZDJZp6M7FRUVnY4CtVOr1di8eTM2btyI8vJy+Pv7Izs7GxqNBr6+Xf+ftlQqxbhx4zod8VEqlRg2rG0ANTY2Fvv378fatWuxceNGNDU14dlnn8VHH32EmTNnAgBGjx4NnU6H1157rcvi4+bmBjc3nuJwRcP9NBjupxE7BhER9TGbTnUplUrExMQgNze3w/bc3FxMmjTpis9VKBQIDAyETCZDTk4OZs2aBam067cXBAE6nQ7+/v5XfE1BEGA0GgEAJpMJJpOp02vKZDJYLJaunk5EREQuxuZTXcnJyVi4cCFiY2MxceJEZGdno7S0FIsXLwbQdvro3Llz1nv1FBcXIz8/HxMmTEB1dTXS09Nx+PBhbN261fqaqampiIuLw/Dhw2EwGJCRkQGdTofMzEzrPs8++yxmzJiBoKAg1NXVIScnB19//TU+//xzAG2Xw//mN7/B008/DbVajeDgYOzZswdvv/020tPTr+ubRERERM7B5uIzZ84cVFVVYeXKldDr9YiMjMSuXbsQHBwMANDr9R3u6WM2m7FmzRqcOHECCoUCU6dORV5eHoYMGWLdp6amBo888gjKysqg1WoRFRWFvXv3Yvz48dZ9ysvLsXDhQuj1emi1WowePRqff/45brvtNus+OTk5SElJwYIFC3Dx4kUEBwfjxRdftJYyIiIicm0238fHmfE+PkRERI6n1+7jQ0REROTIWHyIiIjIZbD4EBERkctg8SEiIiKXweJDRERELoPFh4iIiFwGiw8RERG5DBYfIiIichksPkREROQybF6ywpm138TaYDCInISIiIiuVfvv7WtZjILF5xJ1dXUAgKCgIJGTEBERka3q6uqg1WqvuA/X6rqExWLB+fPnodFoIJFIevS1DQYDgoKCcObMGa4DZgf487Av/HnYH/5M7At/HlcmCALq6uoQEBAAqfTKUzw84nMJqVSKwMDAXn0PLy8v/qW1I/x52Bf+POwPfyb2hT+Py7vakZ52HG4mIiIil8HiQ0RERC6DxaePuLm54fnnn4ebm5vYUQj8edgb/jzsD38m9oU/j57D4WYiIiJyGTziQ0RERC6DxYeIiIhcBosPERERuQwWHyIiInIZLD59YMOGDQgJCYFKpUJMTAz27dsndiSXlZaWhnHjxkGj0WDgwIGYPXs2Tpw4IXYs+kVaWhokEgmSkpLEjuKyzp07h9///vfw8fGBu7s7xo4di4KCArFjuaTW1lb86U9/QkhICNRqNYYOHYqVK1fCYrGIHc2hsfj0sh07diApKQnPPfccioqKMGXKFMyYMQOlpaViR3NJe/bsQWJiIr777jvk5uaitbUVCQkJaGhoEDuay9u/fz+ys7MxevRosaO4rOrqasTHx0OhUOCzzz7D0aNHsWbNGvTr10/saC7plVdewV/+8hesX78ex44dw+rVq/Hqq69i3bp1YkdzaLycvZdNmDAB0dHRyMrKsm4LDw/H7NmzkZaWJmIyAoALFy5g4MCB2LNnD2666Sax47is+vp6REdHY8OGDXjhhRcwduxYvPHGG2LHcjnLli3Dt99+y6PSdmLWrFnw8/PDW2+9Zd12zz33wN3dHe+8846IyRwbj/j0opaWFhQUFCAhIaHD9oSEBOTl5YmUii5VW1sLAPD29hY5iWtLTEzEzJkzMW3aNLGjuLSdO3ciNjYW9913HwYOHIioqCi8+eabYsdyWZMnT8a//vUvFBcXAwAOHjyIb775BnfccYfIyRwbFyntRZWVlTCbzfDz8+uw3c/PD2VlZSKlonaCICA5ORmTJ09GZGSk2HFcVk5ODgoLC7F//36xo7i8kydPIisrC8nJyXj22WeRn5+PJ554Am5ubnjggQfEjudynnnmGdTW1iIsLAwymQxmsxkvvvgi5s2bJ3Y0h8bi0wckEkmHPwuC0Gkb9b0lS5bghx9+wDfffCN2FJd15swZLF26FLt374ZKpRI7jsuzWCyIjY3FSy+9BACIiorCkSNHkJWVxeIjgh07duDdd9/Ftm3bMHLkSOh0OiQlJSEgIAAPPvig2PEcFotPL/L19YVMJut0dKeioqLTUSDqW48//jh27tyJvXv3IjAwUOw4LqugoAAVFRWIiYmxbjObzdi7dy/Wr18Po9EImUwmYkLX4u/vj4iIiA7bwsPD8cEHH4iUyLU9/fTTWLZsGebOnQsAGDVqFH7++WekpaWx+FwHzvj0IqVSiZiYGOTm5nbYnpubi0mTJomUyrUJgoAlS5bgww8/xL///W+EhISIHcml3XrrrTh06BB0Op31ERsbiwULFkCn07H09LH4+PhOt3coLi5GcHCwSIlcW2NjI6TSjr+mZTIZL2e/Tjzi08uSk5OxcOFCxMbGYuLEicjOzkZpaSkWL14sdjSXlJiYiG3btuHjjz+GRqOxHo3TarVQq9Uip3M9Go2m03yVh4cHfHx8OHclgieffBKTJk3CSy+9hPvvvx/5+fnIzs5Gdna22NFc0p133okXX3wRgwcPxsiRI1FUVIT09HT87//+r9jRHBovZ+8DGzZswOrVq6HX6xEZGYnXX3+dl06L5HKzVX/961+xaNGivg1DXbr55pt5ObuIPv30U6SkpKCkpAQhISFITk7G//3f/4kdyyXV1dVh+fLl+Oijj1BRUYGAgADMmzcPf/7zn6FUKsWO57BYfIiIiMhlcMaHiIiIXAaLDxEREbkMFh8iIiJyGSw+RERE5DJYfIiIiMhlsPgQERGRy2DxISIiIpfB4kNEREQug8WHiIiIXAaLDxEREbkMFh8iIiJyGSw+RERE5DL+P8vEAs1+Ls5fAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn.fit(10, lr=0.000005)\n",
    "plt.plot(L(learn.recorder.values).itemgot(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "c4088a77-202f-413e-9ccb-e85160568cf6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 2.3794, -4.4954, -0.9659, -1.0014, -1.7335,  6.4931, -2.8767, -0.2632,\n",
      "          4.2000,  7.2766]])\n",
      "The model predicts the digit is: 9\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from PIL import Image\n",
    "import torchvision.transforms as transforms\n",
    "\n",
    "img = Image.open((path/\"testing/5/\").ls().sorted()[1])\n",
    "img_tensor = tensor(img).float()\n",
    "show_image(img_tensor)\n",
    "img_tensor = img_tensor.view(-1, 28*28)  # Flatten\n",
    "\n",
    "with torch.no_grad():  # No need to calculate gradients\n",
    "    learn.model.eval()\n",
    "    output = learn.model(img_tensor)\n",
    "    print(output)\n",
    "    predicted_class = torch.argmax(output, dim=1)\n",
    "\n",
    "print(f\"The model predicts the digit is: {predicted_class.item()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "22dbc555-d1e9-4b87-9a0a-5c610a0db3ad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(9)\n"
     ]
    }
   ],
   "source": [
    "print(train_ys[55000])"
   ]
  },
  {
   "attachments": {
    "cc681ad0-dbcf-47aa-8e69-14cf72876289.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "73f03ced-72d2-4a92-ad8a-a29bb93903ab",
   "metadata": {},
   "source": [
    "# Summary\n",
    "\n",
    "Eventually, I was able to get pretty good results at classifying all the digits.\n",
    "\n",
    "After setting up the model, I spent a good amoung of time trying to find a good learning rate for my (arbitrarily chosen) set of model parameters.\n",
    "\n",
    "![image.png](attachment:cc681ad0-dbcf-47aa-8e69-14cf72876289.png)\n",
    "\n",
    "This was an iterative process where I:\n",
    "- Got the model working at all (fixed bugs in my code)\n",
    "- Did some epochs of training\n",
    "- Adjusted parameters (like learning rate) until 5-10 epochs of training led to _any_ improvement\n",
    "- Set up a \"manual\" test process where I could check what my model's predicted weights were across all classes\n",
    "- Save a snapshot of the model with `learn.save`\n",
    "- Adjust the learning rate and train more\n",
    "- If the accuracy got worse, reload from the snapshot with `learn.load`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "24c51706-aa82-4cdd-b281-373ab1a93c67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "preds, targs = learn.get_preds()\n",
    "\n",
    "# Calculate individual losses\n",
    "loss_func = learn.loss_func\n",
    "losses = loss_func(preds, targs, reduction='none')\n",
    "\n",
    "# Sort by loss\n",
    "sorted_indices = torch.argsort(losses, descending=True)\n",
    "\n",
    "# Get the worst examples\n",
    "worst_n = 20  # Number of worst examples you want to see\n",
    "worst_indices = sorted_indices[:worst_n]\n",
    "\n",
    "# Access the worst-performing examples from the DataLoader\n",
    "val_dl = learn.dls.valid\n",
    "worst_examples = [val_dl.dataset[i] for i in worst_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d24d6356-a540-4d61-88f8-51d9436f3923",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >,\n",
       " <Axes: >]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGEAAABhCAYAAADGBs+jAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAAANhklEQVR4nO2cy48kR16Av4jIyMzKenR39bvbPZ7xeMZjI8u7gFlZ2jWLWP4AkOCEOIDEgeseOcKd/wBuSAghJJAQEquV9rDWmpWMsfH6NU/PeKbfXdX1ylfEj0P1vGz3eGz1I3u2Pqml7lZWVkZ8Ge/4hRIRYcKpok/7ASZMJFSCiYQKMJFQASYSKsBEQgWYSKgAEwkVYCKhAgRPe+Ef6D8+zud4Jvkv/89Pdd2kJFSAiYQKMJFQASYSKsBEQgWYSKgAEwkVYCKhAkwkVICnHjFXFRUEqCAAa1FJDRWGSGSReoyEAS4OKBrjZIadnGB3gMoL/PYuvtc75acfc7YlKIVuNlFTTaQWMTo3RTobkLUU/fNQNjzhwpDfWbtGpB0/+dUVmu8vEHWE+bdj+ODj004BcJYlKAVKo6IQSWJ8PSKdDRguaLIZ4Hyf5ek+31+8zo/nfk6kNH+R13h350VcpHHN6LRT8IBqS9AG055G1WpIHOJm6vgowNUMRcPgA8WorchmFC6GbKHETKXUk4xXF+6xWuvw3eQWFoWv8M6eSkvQoUWW5skW62TTAd0XDEVTyGc84eKQWlTw8twGb0xfJ9EZa3aHWTPAKk9TlVgFsVI0dEzXp6ednEM5XQlKoYwBpUHf/12B1iilUEmNfKZGNhOQTmuyWaFoOexMxgvzO7SjIW9MX+OHySckytE2hkSFgAHsl77OizrxJD4NpyNBG5QeN6pybglXD8mnQ4bzAT6EvKUoGuAioZgtsa2UuJbzyswuM9GQhajHxXiTlh5x3m4zpR2hGmdwIQ6jFPoM9b5PXsL9t18r1FST/RdbpG3NYFmRvZhSq2e8NL/JG+3rTJkRF8MNlkyfWDmaWmFRaKUwPJrRIQAFjgKHF4VVnBkRxypB2RAV2nGmhxYVRRAYpF7DR5bRbEx/xZBPQbbgmJnp005GXGxscynaoKlHrAX7tDUYNFZpNJqhFGx7IRdNTyw9H1NIwMBHpGKZN/t8J+owo+PjTN6RcfQSHqnnzeI8xdocrhYwWLYMFzVlAqPzOdPzfZJojyvNDlN2xHzY53J8j7rOWQo6rJghVkFdaSIVkEnJlispULw1usB/bL/KXpZwa2uGcruGyhXhvsaMYHCh5G9/71/4k8bmkSfvODiekmAMyhhkqsFwNSZvaLoXobwwYqo15MeXfsaftm4DT6oyao/9VeDoSUDPh7w7OMc7t87hepb6zYD5655g6Knd62F2emz/YJX3vrf26ytB12ropQV8EtO7NMXuS4ayKZQrGecW9lhIeizZzhPra4+nEEchni0v9LzldjnPT7svs5k1+d+7q5ibMVFfkdwT4p0CnTl0WsITxgOps5hMYTJQpacqI4ejlzA/y84bS4wWNPsvlfzR67/gUm2D+aDHfLBPrArOBzlweH099AUd79n1IT/p/wbv91b51fYi6X/PkmwIczue+o19dJqjhikyHI8BVGghMF95Tw90s5hwTxHtCXpU4I468d+SI5cgUUg6qxkuCvNre/z57M+5bMNHrtA8KsDjH/u8E2EgnqEYOr7G1eEC17qz7G20WP7U07wxwOz28bc+xxX5I7c9GF0HyVc+lxMhLQKCFIJMoKyKgmNqmF0IPhJCM07o/Yx2IvSl4K10kU+zRfaKOlcH8+znMYU3DAuLiCIrArIioMgD/HpMtKeZ3oXGnSFmtw+9Acjj8nQc4deWSJcSBquKOTueIe36lC2nuF3OsLvdZO1OSbRXoPrDI0/6t+XoJQQGF4Gveep2/KY6kXEfXjy3S8vf3/0+H3y2jHRCWp8aoo4QjDxxz6NKT8MJqhSU8wQ726jBCCkKpD/A5wWIR8rysa9VtZju5SadS5rR+Zw1uwvAllO8nZ7narpI9FlE8907SK+P6w+OPOnflqOXIILyoJxiUISsuwaJ6pKKpsBws5jjTncKtiOiPU39niPeKQmGBWZ3gCodeA/OQ1niu/u44VO8tdpQJIqiJdh6QaIzADIx7JYNdos6JmUssj9AivJrbnhyHL2EnQ6Lv2ySXbN0PlviL7f+jKhWUBYGV2r8wNL6KGD5tiMYFtTu9lGDFJUVyGiEiICX8dvuPJLnX/+dgIpCRguK4EKPC3M7LJhxdbTuWryzf46b+23CHpAXYwFfqM5OkyOX4Da3CH/WITKaqYvP07k5QxnHBKkQZB4z8iSf3sXfXR9nsnj8QaY/xjederYB6bznd9ducDHZom1SIGazbHK1M8f2XpN2T8bVmK9OowzHVB1JkSMFBP0hUaeJDTUm85jMoUclMhji0yOaWj6YDJTQ4iNhLurTDvrYg1FAKiGj3OIyg3YyruoqxrHOHfndDslHgDHgHJQOKUuku39k32EadVSzQT7fIJhLebP5EbN6wLQeDwb3yjq9bg2zF2CHQhXDto9XQq93vIvpSkEtRlp1ipZlqtnlFbtNXSsiNV5PGPoQGQYEA4XJqlUN3edszPUehtKoWkw5k5C3DPUwJ1ZgUZiD9YW9IiHoGsKuwoz8uNGvGJVe3vw6lFa4+Sm6FxOGy4rXGh2aOsAqg0bj8Xw2aNO6AY27JdF6D+eqVxrOtASUxsUBeVNR1KFl0wfV0H0GZUi4L0S743mmKnK2q6NnhImECjCRUAEmEirAREIFmEioABMJFWAioQI88xKM8nircJFBDtkEcNo88xKSICdvKvLpAImrE5PwKM+8hNA4fAguVIgdrz1UjWdagkbzYn2L3ouOvSuadCUZx7epaok42xN4T8EbjU+5+p15bu3P0N1aJIkjVFkizn3zJdRj4syXBOUFXQq6BCfqS5vJpvWQF5Jt1podyhrjgJSKcaZLgjiHvbtHW0G/H/NJd4HdpYxYaRJt0WjWgiFvNj9mOezyXuvyeIt+ECBeQKqxtlC91+Kb4B3u9ucE73zC1Ic97u216HhNTzzuoKpZNjXejHv8qP4hRUtQ1o53jVeogT7bEhiXBslzdFZQZAF3XZMtF5LJw81dVhli5aloyNrZl4AI4hwqzdH3Yv5h4wf82/532argWvJhnOk24QEikBeEHcX7m8sM25ZOK/z6z1WEZ0MCgIx7SKPUMigiCjHwhTAQsR5pJuiyxIt8aVPxafHsSHCOoA/9TsxmrcHAR8DDhX2jQNVL0tUWYRKinYen2Wh8ApxNCYeMeHUpqEyPYxt4fLJOA8Z6ykaIKUJMFD5+n1McuJ24BGVDzOoSfqqOWIOrW7x5iv6BYty70QoXafKGRgyUscJF4+DzwZWMtZVdLk1tsWq6PJq8WClef/4Wv/j9y5hBTG3zeaLOOUwmxHsOk371HlXlhaCboYcZKs3wG1tHt4/2gBOXoOs1hlcW2X8+oKwp0jnBPc3kphbEgGhBzeSsLnRohBkvt9Z5tX6HRGcsBV2mdUpdlSyax5PW1CF/89y/c3Npip6v8X+j57idznCzN8sn15Yx3a9uyHUB9c9j4l1PvFtSG6ZwZiUcHI2DDclbhrStKBMhn3Oo+ClGrlrQgUcDC+19Xp+7xawd8NvJdV6Pug8CzY0yjEPPHy9dGs25oMZzQcrQ91gyXT6PZ3gvWuNer0k/PCTWLdPkfYvJFUFqUMewJnFiEnSjga4nuNU5tn5Tsfpbn1O3OYtxj3qQff3nlWCVQyth0e7zUnyXuspZCXpEyj7YewpPPk5BMw5OXwlGNHVOU4+wLzg28+ZXXr+etvhlcAEXj6vNVu3oTwk4GQlKoesJfm6G0Uqd2dc2+acr/zhuLA/OqvgmPHquhVHhNz7DwirDsqmxaDwXggHfi//n0GuvFoa/zv+Qj1lGFyESH/344+SqoyBAIoMLFY0wf+K5E56Hcz/3/y7E0xNPcfBvx+HiLDI+jORgxtSL4BDuOsN62cSjsarEIFhVMq0dVj1smJ0ohhIwkJDr+QIbvSaqH2BGHEvo7QmVBI0kMflsjWxKMxc8OQ6t53O6XnAoCtE4FLfLNj/tvsK9dIpSNLk7/NHn4z4/nP6I1WDv4B4B+z7m7679iO33FlAefCj4UJC6Y2Vll/naw2jO3Btu7rQZbSWYoaZ5XbOy7oh3U9jtHFWuPOBEJCitkNhSNAxlooiD4onXD0XY8RFeNKlYHIqP0xXe2rzATreOdwZf3u+zfpn61Ih2OCCNLQ5N5i0bRYvND+e58J8ZqvAUTUuZaNK2Zf2VBe7NPHwmKRW1GyFLNzzBSKjf3sdsdSHLcb3+keYNnJAE8YIeZkR7Bc4q3v74Bf4qePPQ67tFzH4eI6IoReO8ZmeQMLjdJOhrjAdbqi/OSjxg1Aj51/Q1mo3LeK9xosjzgPodTdDJUM6hnIx7O96S3zEUnYf9ZOUgWZdxaG/q0L0UshwpinHY1xFzMtWRd8jdDcLOPlEc07zR5mr7lUMvV15QTh5kciDCUimYYR9VOPCgnjDCFWtwiUVs/eD7DwZdWxuwvjW+pzFgNJG1ND+og30kK0TGZ2aMUnAOGaUPg9jPrATAD4cP52rufM636WMIh778X0Id/DzKodl371s8zBFy9tcTngEmEirAREIFmEioABMJFWAioQJMJFSAiYQKMJFQAZRU8eyZXzMmJaECTCRUgImECjCRUAEmEirAREIFmEioABMJFWAioQL8P1/Fwlk7xHuHAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JHStqbQcZe/h1n/BuBZXsfyDjCOKyIAvBuKBDi3EsdrbPE0vrHAk6PFtc5YjqEgqNKwZmZ98mbOmMnlV8o/5Jvv/6Y3g7irmb2SCJ4BAYbh1zN6JwA/pxntdzVRrzDlVr9nw5C0rxV0tfp1H1SK0isi6JVbwRLfFK7QTddN/p7zsZxwvbzHtNCipiyd0hL2OKMqIsE1wseSkIhULioXYPYG2TcSGZYT0r860rj7H8TcjdaaE262Q/J6PvIBiuCGmG17FkbUG351PTIXXVJhBqUMwhFMuOy8quuxlSDDFT6hIA7fsyJgKZcjq4y4JTpyhSFhxBKDwG59H9++4VlLRNQmota9rjWjLDnbiCbnjkNvqo9Z1BgsEhpcEMN9ui2aJ8qUR+zWdThvxZ5UucKO3wmcmLvBReI5SKQDhI1AN+/1nV5/nwKpHdr/BxheaI7FGUBk8I3PuGdu/ZewUla1mOf9j6FK9tVmm2Q+RqDrctmL9mUOv1QfwgOry65qGKoJstxLlLuEoxa5/gdnGGH05NkzyteH5xFdC4UuHsnl7vfcxZleOI0sBgzdZ2kLIi8fdiA/eWNHnf0fdeQcn5eIlvn3+c8jmXmW1D+bUN7PoWpCnZIVhD72S4h7XdHFGyDKed4NcCsIpL2zN8u3KGSadD1akzqXoEQnNECnzhoITAYd+fI+/LXzVAZDOaRpPagVdUW4FBcClZ4Go8y5udedwdh6Bm8BsZNNoH5hp5GEYmniBvbTL/fYsOPZrXyvzt8ufJcpZ0PqFQ7rNUbvDH1Vd4yr9LUVgmlb+XRg8M0uhNQs/C22mFf28+zVq/RKRd2olPlDms35givOHgdqH6s4TcagMRxUMVAEZIBL2xCRubSKk4sjrP5GyZrOhRO+3Tn/N5ayHPG5OLVJ06qIiStXszAHaDMlbQMB5Xkjl+tLHCdr2IjhWirxCxYPqCYPq1OqIXw9YOutEc4oj3GRkR9tjN2pbtCEdbwi0XYSUidfnXyrO8MnmCvJMw5XcfECGzknoc0s9c1ttF2jdKuG2BmwhUDDKFcDtDdCNElGAOOGT5fhhBESym0UT0ekilKG0WKHkuNueTfSdE+zO0JDSVeDDYYi1CW4SFmcQw32kjUo2wFrJB5rZodTCtNkbrA48bvx9GTwTApsm+X+i+clbBw3fYcqje6P8Xj2ZkbcQYizACjEUYAcYijABjEUaAsQgjwFiEEWAswggwFmEEENYOsYp6DDCeCSPBWIQRYCzCCDAWYQQYizACjEUYAcYijABjEUaAsQgjwP8BQfAksD3/AnsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Iawtwr8BnnHFLKABjCQVgLKEAjCUUgLGEAjCWUADGEgrAWEIBGEsoAP8Ll+RIV2bzr1IAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "[show_image(ex[0].view(28,28)) for ex in worst_examples]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8c2ed6c4-5f6d-4f0e-8ddc-8ce4f5eb703f",
   "metadata": {},
   "outputs": [],
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