12.Evidential_Interpretability.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "import torchvision\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "\n",
    "from nn_interpretability.interpretation.lrp.lrp_composite import LRPMix\n",
    "from nn_interpretability.model.model_trainer import ModelTrainer\n",
    "from nn_interpretability.model.model_repository import ModelRepository\n",
    "from nn_interpretability.uncertainty.evidential_dl import Evidential_DL\n",
    "from nn_interpretability.visualization.mnist_visualizer import MnistVisualizer\n",
    "from nn_interpretability.dataset.mnist_data_loader import MnistDataLoader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_name = 'evidential_cnn.pt'\n",
    "\n",
    "train = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mnist_data_loader = MnistDataLoader()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = ModelRepository.get_general_mnist_cnn(model_name)\n",
    "\n",
    "if train:\n",
    "    criterion = Evidential_DL.edl_mse_loss\n",
    "    optimizer = optim.Adam(model.parameters(), lr=0.001, weight_decay=0.005)\n",
    "\n",
    "    model.train()\n",
    "    ModelTrainer.train_evidence(model, criterion, optimizer, mnist_data_loader.trainloader, epochs=25)\n",
    "    \n",
    "    ModelRepository.save(model, model_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# I. Evidential Deep Learning\n",
    "## 1. Test Evidential Deep Learning\n",
    "Test the model trained on evidential deep learning and check its average evidence and uncertainty on the MNIST test dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Evidential Deep Learning Test loss: 0.175 | Accuracy: 97.37% | Evidence: 22.872 | Uncertainty: 0.359\n"
     ]
    }
   ],
   "source": [
    "Evidential_DL.edl_validate(model, Evidential_DL.edl_mse_loss, mnist_data_loader.testloader)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# II. Uncertainty Example - Rotated Images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/media/storage/dl_env/bdluam-p4-interpretability-of-nn/implementation/nn_interpretability/visualization/mnist_visualizer.py:83: FutureWarning: arrays to stack must be passed as a \"sequence\" type such as list or tuple. Support for non-sequence iterables such as generators is deprecated as of NumPy 1.16 and will raise an error in the future.\n",
      "  imgs_stack = np.hstack(image.squeeze(0).cpu().numpy().reshape(28, 28) for image in images)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = mnist_data_loader.get_image_for_class(1).cpu()\n",
    "rotate_imgs = []\n",
    "for i in range(0,-60,-6):\n",
    "    rotate_img = mnist_data_loader.rotate_image(1,i)\n",
    "    rotate_imgs.append(rotate_img)\n",
    "    \n",
    "MnistVisualizer.cat_images(rotate_imgs, 10, 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Prediction of  the evidential deep learning model\n",
    "If the predicted probability is **10%** it means any class is equally likely and the model answers **I don't know**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x1440 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cat_size = torch.Tensor(10,1,28,28)\n",
    "score, cls = Evidential_DL.predict_class(model, torch.cat(rotate_imgs, out=cat_size), top_k=2)\n",
    "MnistVisualizer.result_for_each_rotation(rotate_imgs, cls, score, 2, 10, 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Prediction of the evidential deep learning model with uncertainty\n",
    "After rotating the image to some extend, the model will classify it as another class or the model itself doesn't know which class it belongs. In these cases the uncertainty will remain high."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/media/storage/dl_env/bdluam-p4-interpretability-of-nn/implementation/nn_interpretability/visualization/mnist_visualizer.py:83: FutureWarning: arrays to stack must be passed as a \"sequence\" type such as list or tuple. Support for non-sequence iterables such as generators is deprecated as of NumPy 1.16 and will raise an error in the future.\n",
      "  imgs_stack = np.hstack(image.squeeze(0).cpu().numpy().reshape(28, 28) for image in images)\n"
     ]
    },
    {
     "data": {
      "image/png": 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vUqVKFSZMmMDQoUNtlLjwy7EPjlJqIdAWeAQ4B7wLuANorT9VllsLzgK6AInA4Kz632QWHByso6NzXEyIQsdsNuf5j0tqaipnzpzJtoA5ffo0GX9WPTw8CAgIuKvlJeOjbNmycpdV4dQ6dOhAbGwsx44dM6RlKi99cAB2nt6JXyk/fEr6cC7hHCf/OklwpXu6jYgc2LQPjtb6vl29rVdPvZTXkEI4I7PZfFcz+vHjxwkPD0drTZcuXbLtB3P8+HFu376dvh6lFFWqVCEwMJAOHTrcU8BUqlQJFxe5T6cousaNG0f79u2ZN28eL774otFxctS4cuP05z4lffAp6WNgmqIhV1dRFQRpwRHOKCAggKyuDlRKkfln7ZFHHrmncLlzKsnPzw8PDw97xRai0NFa06JFC06fPs3hw4fv6TdW0PLagiNsw2GvohLC2WV1lQdYfhnPmDHjrn4w3t7edk4nhPNQSjFu3DieeuopTCYTgwcPNjqScDDSgiOEDWXXguPv709cXJz9AwnhxLTlrvgkJCTw+++/4+rqardtSwuOMfLSgiMn8YWwocjIyHtOLXl5eRWKS1mFKGyUUkRERHDo0CGWLl1qdBzhYKTAEcKGQkNDadCgQXoHYH9/f2bPnl1oLmUVorDp2bMnNWvWJDIy0pA7GgvHJQWOEDZ07do19u7dy0svvYTWmri4OCluhChALi4uvPXWW+zfv5/Vq1cbHccQqampNGzYkG7duhkdxaFIgSOEDS1fvpzk5GTCwsKMjiJEkdG/f3+qVq3K5MmT77lasSj4+OOPqVmzptExHI4UOELYkMlkonr16jRu3DjnhYUQNuHm5sabb75JdHQ033//vdFxsnftGtSubflqI6dOnWLNmjUMGzbMZut0FlLgCGEjp06dYvPmzYSFhcldhIWws4EDB1KlShXH7tC/Zg3ExsLatTZb5ciRI3n//fflxp9ZkCMihI0sXLgQrbX0uRHCAJ6enrzxxhts3bqVqKgoo+PcLSQESpaE556zvB440PI6JCRfq/32228pX748QUFBNgjpfKTAEcJGzGYzTZs2lXtjCGGQYcOGUb58eSZPnmx0lLtNnAh+fnDnbsvu7uDvD5Mm5Wu1P/30E6tWrSIgIID+/fuzadMm6f+XgRQ4QtjA/v372bt3r7TeCGGg4sWLM2rUKDZs2MCOHTuMjvP/qle3FDm3b0OJEpavEyZAtWr5Wu17773HqVOniIuLY9GiRbRv3x6TyWSj0IWfFDhC2IDZbMbV1ZV+/foZHUWIIu2FF16gTJkyjtcXZ8kSS3EzYYLlq9yYsMBJgSNEPqWlpWE2m/nb3/5G+fLljY4jRJHm7e3NP/7xD1atWsW+ffuMjvP/Ro+Ggwdh1CjL19Gjbbr6tm3b8u2339p0nYWdFDhC5NO2bds4efKknPsWwkG88soreHt7M2XKFKOj/L/GjcHHx/LcxweC7xk6SdiYFDhC5JPJZKJEiRL06NHD6ChCCKBs2bK8+OKLLFmyhIMHDxodRxhEChwh8iE5OZmlS5fSs2dPSpQoYXQcIYTVa6+9RrFixZg6darRUYRBpMARIh/Wrl3L1atX5fSUEA6mfPnyhIeH89VXXxEXF2d0HGEAKXCEyAez2Uz58uXp0KGD0VGEEJm8/vrruLi48P777xsdRRhAChwhHtDVq1dZvXo1AwYMwM3Nzeg4QohMqlSpwuDBg5k7dy5nzpwxOo6wMylwhHhAy5Yt49atW3JzPyEc2JgxY0hNTWX69OlGRyn0VqxYQWxsbI7Lffrpp8yfP/++y8TExLDWhmNyZUUKHCEekNlspkaNGgTL5Z5COKyqVasSEhLCZ599xoULF4yOU2ilpKTkusAZMWIEAwcOvO8yUuAI4aBOnjzJ5s2bCQ0NlZHDhXBwY8eO5ebNm8yYMcOwDGazmYCAAFxcXAgICMBsNud7nXFxcdSpUyf99fTp0xk/fjxt27ZlzJgxNGnShBo1arB161YAUlNTef3116lTpw716tVj5syZAOzatYs2bdoQFBRE586diY+PByw3Dxw5ciTBwcFMmzaNVatWMXr0aBo0aMCRI0eYM2cOjRs3pn79+vTq1YvExEQAxo8fn95illWWW7du8c4777B48WIaNGjA4sWLefTRR9ML0LS0NKpXr57vglQKHCEewMKFCwHk9JQQhUDNmjXp1asXs2bN4urVq3bfvtlsJjw8nOPHj6O15vjx44SHh9ukyMlOSkoKO3bsYMaMGUyYMAGA2bNnExcXR0xMDPv27SM0NJTbt2/zyiuvsGzZMnbt2sWQIUOIiIhIX8+tW7eIjo4mIiKC7t2788EHHxATE0O1atV45pln2LlzJ3v37qVmzZrMnTs3V1k8PDyYOHEi/fr1IyYmhn79+hEWFpZ+PDZu3Ej9+vUpV65cvo6BFDhCPACTycQTTzxBtXwOlieEsI+IiAj++usvZs2aZci277Ru3JGYmHhXIWFrzzzzDABBQUHpl8lv3LiR559/Pv2iiLJly3Lw4EH2799Pp06daNCgAZMnT+bUqVPp67nf+Hr79++nVatW1K1bF7PZzIEDB3KdJbMhQ4ak99uZN28egwcPztP+ZkUu/RAij/bt28dvv/1myC9KIcSDadCgAU899RQfffQRI0eOpGTJknbb9okTJ/I0Pbfc3NxIS0tLf52UlJT+3NPTEwBXV1dSUlKyXYfWmtq1a/PLL79kOf9+NzAdNGgQK1asoH79+nz55Zds3rw5y+Vyk8XX1xcfHx82bdrEjh07bNK6JS04QuTRnZHD+/bta3QUIUQeREREcPnyZT777DO7btfPzy9P03PLx8eH8+fPc+nSJZKTk3McbLNTp0589tln6UXG5cuXeeyxx7hw4UJ6gXP79u1sW2K8vb25fv16+uvr169TsWJFbt++neeCJPO6AIYNG0ZYWBh9+vTB1dU1T+vLihQ4QuRBWloaCxYsoEuXLvk+PyyEsK9mzZrRoUMHpk+ffldrR0GLjIzEy8vrrmleXl5ERkbma73u7u688847NGnShE6dOvH444/fd/lhw4bh5+dHvXr1qF+/PgsWLMDDw4Nly5YxZswY6tevT4MGDfj555+zfH///v354IMPaNiwIUeOHGHSpEk0bdqUFi1a5LjtzNq1a0dsbGx6J2OA7t27k5CQYJPTU4ClecqIR1BQkBaisPnxxx81oBcsWGB0FCHEA9i0aZMG9CeffJKv9Rw6dChPy5tMJu3v76+VUtrf31+bTKZ8bd8Z7dy5U7ds2fK+y2R13IFonUWdIS04QuSB2WymZMmSMnK4EIVU27Ztad68OdOmTePWrVt2225oaChxcXGkpaURFxcnV2BmMnXqVHr16sV7771ns3VKgSNELiUlJbF06VKeeeaZe5qbhRCFg1KKiIgITpw4gclkMjqOsHrzzTc5fvw4LVu2tNk6pcARIpfWrl3LtWvX5D8vIQq5J598koYNG/Lee++Rmpr6wOuxnB0R9pLX4y0FjhC5ZDKZqFChAu3btzc6ihAiH5RSjBs3jsOHD7NkyZIHWoenpydXrlyRIsdOtNZcuXIl/ZLz3FBGfXOCg4N1dHS0IdsWIq+uXLlChQoVePHFF/noo4+MjiOEyKe0tDTq1q2Li4sLe/fuxcUlb//vp6SkEB8fT3JycgElFJl5enpSsWLF9BsV3qGU2qW1vmdQQLnRnxC5cGfk8LCwMKOjCCFswMXFhbfeeouwsDBWrVrF3//+9zy9383NDV9f3wJKJ2xBWnCEyIU2bdpw7tw5fv/9dxlcUwgnkZKSwmOPPUaZMmXYuXOn/GwXUtm14EgfHCFycOLECaKioggLC5NfgEI4ETc3N8aOHcuuXbv4/vvvjY4jbEwKHCFysGDBAgBCQkIMTiKEsLWBAwdSpUoVJk+ebHQUYWNS4AhxH1prTCYTzZs3p2rVqkbHEULYmIeHB2+88Qbbtm0jKirK6DjChqTAEeI+9u3bx4EDB+TeN0I4sWHDhlG+fHlpxXEyUuAIcR9msxk3NzcZOVwIJ1a8eHFGjRrFhg0b2LFjh9FxhI1IgSNENlJTU9NHDn/kkUeMjiOEKEAvvPACZcqUyfcI38JxSIEjRDaioqI4ffq03PtGiCLA29ubkSNHsmrVKvbu3Wt0HGEDUuAIkQ2TyUTJkiV5+umnjY4ihLCDV155BW9vb6ZMmWJ0FGEDUuAIkYWkpCSWLVtGr169ZORwIYqIMmXK8NJLL7F06VIOHjxodByRT1LgCJGFb7/9lr/++ktOTwlRxPzzn/+kWLFivPfee0ZHEfkkBY4QWTCbzVSsWJF27doZHUUIYUfly5cnPDwck8lEXFyc0XFEPkiBI0Qmly9fZs2aNQwYMABXV1ej4wgh7Oz111/H1dWVadOmGR1F5EOuChylVBel1EGl1GGl1JtZzPdTSv2olNqjlNqnlOpq+6hC2MeyZcu4ffu23NxPiCKqSpUqDBo0iHnz5nH69Gmj44gHlGOBo5RyBT4BngRqAQOUUrUyLTYOWKK1bgj0B/5j66BC2IvJZKJmzZo0bNjQ6ChCCIOMGTOG1NRUPvzwQ6OjiAeUmxacJsBhrfVRrfUtYBHQI9MyGnjI+rwUcMZ2EYWwn+PHj7N161ZCQ0Nl5HAhirCqVasSEhLCp59+yoULF4yOIx5AbgqcysDJDK9PWadlNB4IU0qdAtYCr2S1IqVUuFIqWikVLR8Y4Yhk5HAhxB1jx44lKSmJGTNmGB1FPABbdTIeAHypta4CdAW+Ukrds26t9WytdbDWOrhcuXI22rQQtnFn5PAWLVoQGBhodBwhhMFq1qxJ7969mTlzJleuXDE6jsij3BQ4pwHfDK+rWKdlNBRYAqC1/gUoBhg2eM+1pGvU/qQ215KuGRVBFEJ79+4lNjZW7n0jhEj31ltvcf36dWbNmmV0FJFHuSlwdgKPKqUClVIeWDoRr8q0zAmgA4BSqiaWAsewc1BrDq0h9mIsaw+tNSqCKIRMJhNubm706dPH6ChCCAfRoEEDunXrxowZM0hISDA6jsiDHAscrXUK8DKwHvgdy9VSB5RSE5VS3a2LjQKGK6X2AguBQVprXVChsxOyPISSU0ry7DfPAhD2TRjFI4vTf1l/e0cRhUxqaioLFy6ka9euPPzww0bHEUI4kIiICC5fvsynn35qdBSRB8qAOgSA4OBgHR0dbdN1Hr58mO4Lu3P48mFup91On17CvQQt/FrQ0rclLf1a0qRyE0p4lLDptkXh9sMPP9CxY0cWL15M3759jY4jhHAwHTt25MCBAxw9epTixYsbHUdkoJTapbUOzjzdqe5kXL1sdSa2m4hGU8K9BK7KlVebvsrA+gOJvx7Pu5vfpf389pSeVpqmnzdl1PpRfPP7N5y/cd7o6MJgZrMZb29vGTlcCJGlcePGcfbsWebNm2d0FJFLTtWCA9B3aV++P/I9b7d+m0lRk+hcrTOL+ywG4MrNK/xy6he2ndjGTyd/Yvup7SSnJgPwaNlHaenXMv3xaNlH5T4oRcTNmzfx8fGhV69efPHFF0bHEUI4IK01LVu25OTJkxw+fBgPDw+jIwmr7FpwnK7A2Xl6J36l/PAp6cO5hHOc/OskwZXu2W8AklOS2R2/m20ntrHt5DZ+OvETl25eAqCcV7n0YqeFbwsaVmyIh6t8oJ3R0qVL6du3Lxs3bqRDhw5GxxFCOKh169bRtWtX5s6dy5AhQ4yOI6yKTIGTH1prDl46aCl4rI8jV44AUNytOE2rNE3vx9PMtxkPeT6UwxpFYdCjRw+io6M5ceKEDK4phMiW1prg4GD++usvfv/9d9zc3IyOJJAC54HFX4/np5M/pRc8MWdjSNWpuCgX6vnUo4Vvi/SWnioPVTE6rsijS5cuUbFiRV599VWmT59udBwhhIP7+uuv6dWrFwsWLGDAgAFGxxFIgWMzCbcS2H5qe/pprV9O/sKN2zcA8C/lf1c/nlrlauFy7w2dhQP59NNPeeGFF9izZw8NGjQwOo4QwsGlpaVRt25dlFLs27cPFxf5HW80KXAKSEpaCnvP7k0veLad2MbZhLMAlC5Wmha+LdJbeRpXbkwxt2IGJxYZtWzZkitXrrB//37pVC6EyBWz2UMBdd0AACAASURBVExYWBhff/01PXv2NDpOkScFjp1orTl29dhd/Xh+v/g7AB6uHgRXCk7vx9PctzkPe8lN5Yxy7NgxqlatypQpUxg7dqzRcYQQhURKSgqPP/44pUuXZufOnfLPkcGkwDHQxcSL/Hzy5/SCJ/pMdPqNCGs+UvOu01qBpQPlh8VOIiMjGTduHHFxcfj7+xsdRwhRiHz++ecMHz6cdevW0aVLF6PjFGlS4DiQm7dvEn0m+q7L068lWwYGrViy4l0FTz2feri5WHrqX0u6RvO5zfl56M+UKlbKyF0o9LTW1KpVi3LlyhEVFWV0HCFEIXPr1i2qVauGv78/W7dulX9MDZRdgSPXuBmguHtxWvm3opV/KwDSdBoHzh+4q+BZGrsUgJIeJXmiyhO09G1Jcmpy+iCiA+pK7/382LNnD3/88QcjR440OooQohDy8PBgzJgxvPLKK0RFRdGmTRujI4lMpAXHQZ28djL98nTzb2auJl1Nn+eqXCnmVozuj3VnQa8FBqYsvEaNGsXMmTM5e/YsZcuWNTqOEKIQunnzJoGBgdStW5cNGzYYHafIKhJjUTkT31K+9K/Tn1ldZ7Fz+E5qlK2Bh4vlTsqpOpWHPB9iYtuJBqcsnDKOHC7FjRDiQRUvXpxRo0axceNGtm/fbnQckYkUOIVA9bLViewQSRppeLl5oVDEJ8Qzfst4Em4lGB2v0Pnxxx+Jj48nLCzM6ChCiEJuxIgRlC1blsjISKOjiEykwCkklhxYQgn3EkxsNxFvD2/qlKvDwv0LCZ4dzL5z+4yOV6iYTCYeeughunXrZnQUIUQh5+3tzT/+8Q9Wr17N3r17jY4jMpA+OIVEVoOIJtxKYMDyAVxNusrMJ2cytOFQ6cmfg8TERCpUqECfPn2YO3eu0XGEEE7gypUr+Pv78+STT7J48WKj4xQ50genkGtcuTE+JX0A8CnpQ3ClYNoGtCXm+Rha+rVk+OrhDFwxUE5Z5WD16tVcv36d0NBQo6MIIZxEmTJleOmll1i6dCl//PGH0XGElRQ4hZxPSR++C/2OiW0nsuC3BTSe05j95/cbHcthmc1mKleuLJd0CiFs6p///CfFihVj6tSpRkcRVlLgOAFXF1febvM2G5/dyNWkqzSZ04R5e+Zh1OlHR3Xx4kXWrVtHSEgIrq6uRscRQjiR8uXL8/zzz2MymTh27JjRcQRS4DiVdoHtiHk+hua+zRm6aijPrXhOTlllsHTpUlJSUuT0lBCiQLz++uu4uroybdo0o6MIpMBxOj4lfVgftp4JbSdg2meSU1YZmEwm6tSpQ7169YyOIoRwQpUrV2bw4MF88cUXnD592ug4RZ4UOE7I1cWVd9q8w8aBG7ly8wpN5jThiz1fGB3LUEePHuXnn38mNDRUrjQTQhSYMWPGkJqayvTp042OUuRJgePE2ge2J2ZEDM18mzFk1RAGrRjEjVs3jI5liAULLENahISEGJxECOHMAgMDCQ0N5bPPPuPChQtGxynSpMBxchVKVuD7sO8Z32Y88/fOp/Gcxhw4f8DoWHaltcZkMtG6dWv8/PyMjiOEcHJjx44lKSmJjz76yOgoRZoUOEWAq4sr77Z9lw3PbuDyzcs0ntOYL2O+NDqW3ezevZuDBw/K0AxCCLt4/PHH6d27N7NmzeLKlStGxymypMApQjpU7UDMiBieqPIEg1cOLjKnrEwmEx4eHvTu3dvoKEKIIiIiIoLr168za9Yso6MUWVLgFDEVSlZgw7MbeKf1O8zfO58mnzch9kKs0bEKTEpKCosWLeKpp56iTJkyRscRQhQR9evXp1u3bsyYMYOEBLldhxGkwCmCXF1cmdBuAt8/+z0XEy/SeE5j5u+db3SsArFp0ybOnj0r974RQthdREQEly9f5tNPPzU6SpEkBU4R1rFqR2Kej6FJ5SY8t+I5hqwcQuLtRKNj2ZTZbKZUqVI89dRTRkcRQhQxTzzxBB07dmT69OncvHnT6DhFjhQ4RVxF74psfHYjb7d+my9jvqTJHOc5ZZWYmMjXX39N7969KVasmNFxhBBFUEREBOfOnWPu3LlGRylypMARuLq4MrHdRNaHref8jfM0ntOYr/Z+ZXSsfFu1ahUJCQly9ZQQwjBt2rShRYsWvP/++9y6dcvoOEWKFDgiXadqnYgZEUPjSo0ZuGIgQ1cOLdSnrEwmE1WqVKF169ZGRxFCFFFKKSIiIjh58iRffVX4/3EsTKTAEXep5F2JjQM3Mq7VOL6I+YKmnzflj4t/GB0rzy5cuMD69esJCQnBxUU+5kII43Tp0oVGjRoxdepUUlJSjI5TZMhvfnEPNxc3JrWfxHdh33E24SzBs4Mx7TMZHStPlixZQkpKipyeEkIYTinFuHHjOHz4MEuWLDE6TpGhtNaGbDg4OFhHR0cbsm2Re6f/Ok3I1yFEHY9iaMOh/PvJf+Pl7mV0rBw1b96chIQE9u3bZ3QUIYQgLS2NevXqobXmt99+k5ZlG1JK7dJaB2eeLkdY3Fflhyrzw8AfiGgVwdw9cwvFKasjR47wyy+/SOuNEMJhuLi48NZbbxEbG8vKlSuNjlMkSIEjcuTm4sbk9pP5LvT/T1mZ95mNjpUts9mMUooBAwYYHUUIIdL17duXatWqMXnyZIw6e1KUSIEjcq1z9c7EPB9Do4qNCPsmjPDV4dy87Vg3r9JaYzabadOmDb6+vkbHEUKIdG5ubowdO5bdu3ezfv16o+M4PSlwRJ5Ufqgym57bxNiWY5mzew5NP2/KwYsHjY6VLjo6mj///FOGZhBCOKRnn30WX19fJk2aJK04BUwKHJFnbi5uTOkwhXWh6zhz/QxBs4NY8NsCo2MBltNTMnK4EMJReXh48MYbb/Dzzz+zZcsWo+M4NSlwxAPrUr0LMSNiaFixIaFfhxp+yiolJYWFCxfSrVs3SpcubVgOIYS4n6FDh+Lj40NkZKTRUZyaFDgiX6o8VIUfn/uRN1u8yZzdc3hi7hP8eelPQ7L88MMPnD9/Xq6eEkI4tOLFizNq1Cg2btzI9u3bjY7jtKTAEfnm5uLGex3fY03IGk7/dZqg2UEs/G2h3XOYTCZKly5N165d7b5tIYTIixEjRlC2bFlpxSlAUuAIm+n6aFf2PL+Hej71CPk6hBHfjrDbKasbN27wzTff0KdPHzw9Pe2yTSGEeFDe3t6MHDmS1atXExMTY3QcpyQFjrAp31K+bH5uM2NajOGzXZ/RbG4zu5yyWrlyJTdu3JCrp4QQhcbLL7+Mt7c3U6ZMMTpKwbh2DWrXtnw1gBQ4wubcXd2Z2nEqa0LWcPKvkwTNDmLx/sUFuk2z2Yyvry+tWrUq0O0IIYStlClThpdffplly5ZRuXJlXFxcCAgIwGx23Bup5smaNRAbC2vXGrJ5KXBEgen6aFdino+hbvm69F/enxe+fYGklCSbb+f8+fOsX7+e0NBQGd9FCFGo+Pr6orXmzJkzaK05fvw44eHhhbvICQmBkiVh4EDL62eftbwOCbFrDPlrIAqUbylftgzawujmo/l016c0m9uMQ5cO2XQbS5YsITU1VU5PCSEKnWnTpt0zLTExkYiICAPS2MjEiVC2LKSmWl67uYG/P0yaZNcYuSpwlFJdlFIHlVKHlVJvZrNMX6VUrFLqgFLKMe76JhyCu6s773d6n9UDVnPi2gmbn7IymUzUr1+fOnXq2GydQghhDydOnMjT9EJhwwY4dcryvHhxS6EzYQJUq2bXGDkWOEopV+AT4EmgFjBAKVUr0zKPAmOBFlrr2sDIAsgqCrluNbqx5/k91Clfh/7L+/PimhdJSkniWtI1an9Sm2tJee+IdujQIbZv3y6tN0KIQsnPzy9P0x1aaiqMGgUvvggVKsBDD1labUqUgKVL7R4nNy04TYDDWuujWutbwCKgR6ZlhgOfaK2vAGitz9s2pnAWfqX82DJoC683e53/Rv+X5nObM3fPXGIvxrL2UN47oi1YsEBGDhdCFFqRkZF4eXndNU0pxWuvvWZQogeUmAh9+sC//gWvvAJffw1//mkpeA4ehNGj7R5J5TTYl1KqN9BFaz3M+vpZoKnW+uUMy6wA/gRaAK7AeK31d1msKxwIB/Dz8ws6fvy4rfZDFEJtvmhD1Imo9NduLm54unrS/bHuLOiV81lOrTU1atTA19eXTZs2FWRUIYQoMGazmYiICE6cOEH58uW5du0aFSpU4IcffqBq1apGx8vZ2bPQvTtER8OMGfDqq3bdvFJql9Y6OPN0W3UydgMeBdoCA4A5Sql7BgPSWs/WWgdrrYPLlStno02Lwmpuj7lUL1M9/bW7izv+pf2Z1C53HdF27tzJ4cOHZWgGIUShFhoaSlxcHGlpaZw9e5aoqCiuXbtG69at+eOPP4yOd38HDkDTppavK1bYvbi5n9wUOKcB3wyvq1inZXQKWKW1vq21PoalNedR20QUzqp62eq81/E9FAqAW6m3mNB2AtXK5q4jmslkwtPTk169ehVkTCGEsKvGjRuzefNmbt++TevWrdm3b5/RkbK2cSM0bw63bkFUlKUVx4HkpsDZCTyqlApUSnkA/YFVmZZZgaX1BqXUI0AN4KgNcwonteTAEkq4lwAsLThLD+SuI9rt27dZtGgRTz/9NKVKlSrIiEIIYXf16tUjKioKDw8P2rZty44dO4yOdLe5c+HJJy2Xf2/fDkFBRie6R44FjtY6BXgZWA/8DizRWh9QSk1USt0p19YDl5RSscCPwGit9aWCCi2cx+jmozn86mGaVm6KX2k/Xm/+eq7et3HjRi5cuCBXTwkhnNZjjz3G1q1bKV26NB07dmTr1q1GR4K0NBg7FoYNgw4dYNs2cNArvnLVB0drvVZrXUNrXU1rHWmd9o7WepX1udZav6a1rqW1rqu1XlSQoYXzaFy5MT4lfRjeaDh/XvqTW6m3cvU+s9lMmTJlePLJJws4oRBCGCcwMJCoqCgqVapE586d2bBhg3Fhbt6EAQNg6lR4/nlYvdpyKbiDkjsZC4fQr04/vD28mb17do7LJiQkyMjhQogio0qVKmzZsoVHH32Ubt26sWpV5l4idnDhgqXFZskS+OAD+O9/wd3d/jnyQAoc4RBKepQktG4oSw4s4crNK/ddduXKlSQmJsrVU0KIIsPHx4cff/yR+vXr06tXLxYvLtgBjO9y8CA88QTs2QPLlsHrr4NS9tv+A5ICRziM8KBwklKSMP92/0HmTCYTfn5+tGjRwk7JhBDCeGXLlmXjxo00a9aMkJAQvvjii4Lf6JYt0KwZJCTA5s1QiK5alQJHOIyGFRsSVDGI2btmk90NKM+dO8eGDRtk5HAhRJH00EMPsW7dOjp06MCQIUP45JNPCm5jX30FnTpZhl349VfL/W4KEfkLIRxKeFA4v53/je2nt2c5f/HixaSmpsrpKSFEkVWiRAlWrVpF9+7defnll3n//fdtuwGtYfx4GDgQWrWCn3+GwEDbbsMOpMARDmVAnQGUcC/BnF1zspxvNptp0KABtWrVynK+EEIUBcWKFWPZsmX069ePMWPG8O6772bb8p0nycmWwmbCBBg8GNatg9L3DExQKEiBIxyKt6c3A+oMYNGBRfeMLv7nn3+yY8cOab0RQgjA3d0ds9nM4MGDmThxIqNHj85fkXP5Mvztb2AyQWSk5WZ+Hh62C2xnUuAIhxMeFE7i7UQW/Hb3gJtmsxmlFP379zcomRBCOBZXV1c+//xzXnrpJT788ENefPFF0tLS8r6iw4ctnYm3b4eFC+GttwrFlVL342Z0ACEyC64UTIMKDZi9ezYjgkeglEJrjdlspn379lSuXNnoiEII4TBcXFyYOXMmJUqU4P333ycxMZG5c+fi5pbLP/E//QQ9elie//ADOMkVqtKCIxyOUorhjYYTczaGXfG7ANi+fTtHjhyRoRmEECILSimmTp3KxIkTmT9/PiEhIdy6lYs7wy9aZLmBX9myliulnKS4ASlwhIMKrRtKcbfizN5lubOx2WymWLFiPPPMMwYnE0IIx6SU4u233+bDDz9k6dKlPPPMMyQlJWW9sNYwZYpl6IUmTeCXX6B6dfsGLmBS4AiHVKpYKfrX6c+C3xZwOeGyjBwuhBC59Nprr/Hf//6XNWvW0K1bN27cuHH3ArduwdChEBEBoaGwYQM8/LAxYQuQFDjCYYUHhXPj9g3Gzx3PxYsX5eopIYTIpREjRvC///2PH3/8kc6dO3PtmvWq1KtX4ckn4Ysv4N13LTfzc9Ix/ZRNrpt/AMHBwTo6OtqQbYvCQWtNvU/rcebLM3AY4uPj8SjElywKIYS9LVu2jAEDBlC/fn3Wz57Nw2FhliumPv/ccr8bJ6CU2qW1Ds48XVpwhMNSSjHwsYFc3n2Z9t3aS3EjhBB51Lt3b1asWMH+336jbZMmnD19Gr7/3mmKm/uRAkc4NO9j3pACKbVTjI4ihBCF0lNJSazRmqNpabQuU4aT1aoZHckupMARDm3F0hWUKF+Cjbc3cuPWjZzfIIQQwkJrmD4d+vShQ3Aw369axbkrV2jVqhVHjhwxOl2BkwJHOKyzZ8+yYcMGnunzDAkpCSw+sNjoSEIIUTikpMALL8Do0dC7N/zwAy26dWPTpk1cv36d1q1b8/vvvxudskBJgSMc1uLFi0lLS2PMC2Oo+UhN5uzOegBOIYQQGfz1F3TrBp99BmPHWm7mV7w4AEFBQWzZsoXU1FTatGlDTEyMwWELjhQ4wmGZTCYaNWpE7dq1CQ8K59dTv7Lv3D6jYwkhhOM6eRJatoSNG2HOHMvN/Fzu/lNfp04doqKi8PT0pF27dmzfvt2gsAVLChzhkA4ePEh0dHT60AzP1nsWD1cP5uySVhwhhMjSrl3QtCkcPw7r1sGwYdkuWqNGDbZu3UrZsmXp2LEjUVFRdgxqH1LgCIdkNptxcXFJHzn8Ya+H6V2rN1/t+4rE24kGpxNCCAezejW0bg3u7vDzz9CpU45vCQgIYOvWrfj6+tKlSxfWr19vh6D2IwWOcDgZRw6vVKlS+vTwRuFcS77GsthlBqYTQggH8+9/W0YDr1ULtm+H2rVz/dZKlSqxZcsWatSoQffu3Vm5cmUBBrUvKXCEw/n11185evToPUMztPZvTY2Ha6QPwCmEEEVaaiq8+ir84x+WAmfLFqhQIc+rKVeuHD/++CMNGzakV69eLFy4sADC2p8UOMLhmEwmihUrRs+ePe+arpRieKPh/HTyJw6cP2BQOiGEcAAJCfD3v8PMmTBqFCxbBl5eD7y6MmXKsGHDBlq0aEFoaCjz5s2zYVhjSIEjHMrt27dZvHgxPXr04KGHHrpn/nP1n8PdxZ3Pd39uQDohhHAAZ85Y+tusXQv/+Y/lZn6urvlerbe3N+vWreNvf/sbQ4cOZebMmTYIaxwpcIRDWb9+PZcuXUq/eiqzciXK0bNmT/63938kpSTZOZ0QQhhs717LlVKHDlk6Fr/wgk1X7+XlxcqVK/n73//Oq6++ytSpU226fnuSAkc4FLPZzMMPP0znzp2zXSa8UThXkq6wPHa5HZMJIYTBvvvOco8brWHbNujatUA24+npyZIlSxgwYABjx47l7bffRmtdINsqSFLgCIdx/fp1Vq5cSd++fe87cni7wHZUK1ON2buls7EQooj49FPL3YmrV7dcKVW/foFuzt3dna+++oqhQ4cyefJkRo0aVeiKHClwhMP45ptvuHnz5j1XT2XmolwY3mg4UcejOHjxoJ3SCSGEAdLS4PXXLaeiunSBrVuhcmW7bNrV1ZXZs2fz6quv8tFHHzFixAjS0tLssm1bkAJHOAyTyURgYCDNmjXLcdlBDQbh5uIm41MJIZxXYqJloMwPP4SXX4YVK6BkSbtGcHFxYcaMGYwdO5bZs2fz3HPPkZKSYtcMD0oKHOEQ4uPj+eGHHwgNDUUplePyPiV96PFYD76M+ZLklGQ7JBRCCDs6exbatrUUNTNmWC4Hd3MzJIpSiilTpjB58mRMJhP9+/fn1q1bhmTJCylwhENYtGgRaWlp2V49lZXwoHAu3bzEij9WFGAyIYSwswMH4IknLF+/+cZyIz8HEBERwUcffcTy5cvp2bMnN2/eNDrSfUmBIxyC2WwmKCiIxx9/PNfv6Vi1IwGlA6SzsRCi8Lt2zTLEwqpV0KIFJCdDVJTlDsUOZOTIkXz22WesW7eOp556ioSEBKMjZUsKHGEos9lM5cqV2bVrF0ePHsVsNuf6vS7KhWENh7Hp2CYOXz5cgCmFEKKArVkDsbHwzDPg62u5UiooyOhUWQoPD2f+/PlERUXRuXNnrl69anSkLEmBIwxjNpsJDw/nzJkzAFy5coXw8PA8FTmDGw7GVbnKnY2FEIVTSIil4/Cdq0fT0uDoUXjzTWNz5SAsLIzFixezc+dOOnTowMWLF42OdA8pcIRhIiIiSExMvGtaYmIiERERuV5HJe9KdKvRjS9ivuBWquN3ehNCiLtMnAiPPGK5eR+ApycEBMCkSYbGyo1evXqxYsUKYmNjadu2LfHx8UZHuosUOMIwx48fz3L6iRMn8rSe8KBwzt84z6qDq2wRSwgh7KdaNShWzPLcywtSUmDCBMv0QqBr166sXbuWuLg4Wrduneff3wVJChxhiNOnT2d7t2I/P788ratztc74PuTL7F3S2VgIUcisWgUHD0Lx4pbWnBIlYOlSo1PlSbt27diwYQMXLlygVatWHD7sGH0ipcARdrdz504aN26Mi4sLnp6ed83z8vIiMjIyT+tzdXFlWKNhbDi6gWNXjtkyqhBCFJzUVHjrLfD3twyeOWqUpdgZPdroZHnWrFkzNm3axI0bN2jdujWxsbFGR5ICR9jX4sWLad26NZ6enuzcuZO5c+fi7++PUgp/f39mz56dp3vh3DGk4RBclIt0NhZCFB7z51uunPrww/8ffsHHB4KDjc31gBo1asSWLVvQWvPEE09QqVIlXFxcCAgIyNPFI7aijBo8Kzg4WEdHRxuybWF/WmsmTJjAhAkTaNmyJV9//TXlypWz6TaeXvg00WeiOTHyBO6u7jZdtxBC2NTNm1CjBlSqBL/+Crm4g3th8eGHHzJ69Oi7Buf08vJ64H9gc6KU2qW1vqcqlBYcUeASExPp378/EyZMYNCgQWzcuNHmxQ1AeKNwziacZc2hNTZftxBC2NQnn8CpUzBtmlMVNwAzZ868Z+TxvF4hawtS4IgCdfr0adq0acPSpUt5//33mTdv3j39bmzlyUefpJJ3JelsLIRwbFevwpQpltHB27Y1Oo3NZXcllb2vsJICRxSYXbt20aRJE/744w9WrlzJ6NGjczWQ5oNyc3FjaMOhfHf4O45fzfoSdCGEMNy0aZYiZ+pUo5MUiOyuhM3rFbL5JQWOKBBLly6lVatWuLu78/PPP/P000/bZbtDGw4FYO6euXbZnhBC5MmZM/Dxx5Y7GNevb3SaAhEZGYmXl9dd0x7kCtn8kgJH2JTWmokTJ9K3b18aNmzIjh07qFu3rt2271/an87VOzNvzzxS0lLstl0hhMiVCRMsN/MrBHcqflChoaHMnj3bJlfI5ocUOMJmbt68SUhICO+++y4DBw5k06ZNlC9f3u45whuFc/r6adYdWmf3bQshRLYOHoS5c+GFFyAw0Og0BSo0NJS4uDjS0tKIi4uze3EDuSxwlFJdlFIHlVKHlVLZjgCmlOqllNJKqcJ5Eb94YPHx8bRp04bFixczbdo0vvzyywLrTJyTbjW6UaFkBWbvls7GQggHEhFhuWOxna8mKqpyLHCUUq7AJ8CTQC1ggFKqVhbLeQP/ALbbOqRwbLt376Zx48bExsbyzTff8MYbbxRoZ+KcuLu6M6TBENYeWsupv04ZlkMIIdJt3w7Ll8Prr4MBLdtFUW5acJoAh7XWR7XWt4BFQI8slpsETAOSbJhPOLjly5fTsmVLXF1d+emnn+jRI6uPhv0NbTSUNJ3GvD3zjI4ihCjqtIY337QUNq+9ZnSaIiM3BU5l4GSG16es09IppRoBvlrr+95hTSkVrpSKVkpFX7hwIc9hhePQWhMZGUnv3r1p0KABO3bsoL4DXRFQtUxVOlXtxOe7Pyc1LdXoOEKIomz9eti8Gd5+G7y9jU5TZOS7k7FSygX4FzAqp2W11rO11sFa6+CCuJOtsI+bN28SFhbGuHHjCAsLY9OmTfj4+Bgd6x7hQeGc/Osk3x/53ugoQoiiKi3N0npTtSqEhxudpkjJTYFzGvDN8LqKddod3kAdYLNSKg54AlglHY2d09mzZ2nXrh0LFixgypQpzJ8/n2LFihkdK0vdH+tOOa9y0tlYCGGchQth716YPBk8PIxOU6TkpsDZCTyqlApUSnkA/YFVd2Zqra9prR/RWgdorQOAX4HuWmsZSdPJxMTE0KRJE3777Te+/vprxo4da2hn4px4uHowuMFgVh9czZnrZ4yOI4Qoam7dspyWatgQ+vUzOk2Rk2OBo7VOAV4G1gO/A0u01geUUhOVUt0LOqBwDN988w0tWrRAa822bdvo2bOn0ZFyZVijYaTqVL7Y84XRUYQQRc1nn8GxY/Dee+Ait52zN5V5xE97CQ4O1tHR0sjj6LTWTJ06lbfeeoumTZuyYsUKKlSoYHSsPGn/v/Ycu3qMI68ewUXJLxkhhB1cvw7VqkHdurBxo9ONGO5IlFK7tNb3dIuR3/YiW0lJSQwcOJC33nqLkJAQNm/eXOiKG7B0No67GsfGoxuNjiKEKCo+/BAuXLAMqCnFjSGkwBFZOnfuHO3atcNkMjF58mRMJpPDdibOSc/He/Jw8YeZvUs6Gwsh7ODcOUuB07s3NG5sdJoiSwoccY+9e/fSuHFj9u3bx7Jly4iIiHDozsQ58XTzZFCDQaw8uJJzCeeMjiOEcHaTJ8PNm2Dn0bPF3aTAEXdZuXIlLVq0IC0tja1bt9KrVy+jI9nEsEbDSElL4cuYLxcbPAAAHuhJREFUL42OIoRwZkePWjoXDxsGNWoYnaZIkwJHAJbOxNOmTaNnz57UqlWLnTt30qhRI6Nj2czjjzxOa//WzNk9hzSdZnQcIYSzevttcHODd94xOkmRJwWOIDk5mUGDBvHmm2/Sr18/tmzZQsWKFY2OZXPhjcI5cuUIPx770egoQghntGcPLFgA//wnVKpkdJoiTwqcIu78+fN06NCB+fPnM3HiRBYsWEDx4sWNjlUgetXqRZliZZize47RUYQQzmjsWChbFt54w+gkAnAzOoAwzr59++jevTvnz59nyZIl9OnTx+hIBaqYWzEG1h/If3b+hws3LlCuhIyHJoSwkU2bLINqTp8OpUoZnUYgLThF1urVq2nRogW3b99m69atTl/c3DG80XBup93mf3v/Z3QUIYSz0NoyoKavL7z0ktFphJUUOEWM1poPPviAHj168Pjjj7Nz506CgoKMjmU3tcvXprlvc+bsnoNRd/EWQjiZ5cth506YOBEK6f3CnJEUOEVIcnIyQ4YM4Y033qBPnz5s2bKFSkWwI1x4o3D+vPQnUcejjI4ihCjsbt+GiAioXRuefdboNCIDKXCKiAsXLtCxY0e+/PJLxo8fz6JFi/Dy8jI6liH61O5DKc9SzN4tdzYWQuTTvHnw55+WATVdXY1OIzKQAqcI2L9/P02aNCE6OppFixbx7rvvFuo7E+eXl7sXz9Z7luWxy7mUeMnoOEKIwioxESZMgBYtoFs3o9OITKTAcXJr1qyhWbNmJCcnExUVRb9+/YyO5BCGBw0nOTWZr/Z9ZXQUIURh9fHHEB8P06bJgJoOSAocJ6W15l//+hdPP/00NWrUYOfOnTSWQd/S1fOpR9PKTZm9a7Z0NhZC5N2lS5aRwrt3t7TgCIcjBY4TunXrFsOGDWPUqFH06tWLrVu3UrlyZaNjOZzwoHB+v/g7P538yegoQojC5r33ICEBpkwxOonIhhQ4TubixYt06tSJefPm8fbbb7N48eIi25k4J/1q98Pbw1vubCyEyJsTJ2DWLBg40HL1lHBIUuA4kQMHDtCkSRO2b9/OggULmDhxIi4u8i3OTgmPEoTWDWXJgSX/1969R1dVHfoe/87sPCAPnqaBBMIjgAqIJASsoFWCCm05YFuPFen1heScM67Wth7aqlWrQKu1p7Z1tFoQFSv4QDyjqAi1QJHHVRIwKkGRRyGBBBIhhEdeJJn3j5WEJCQkwCYze+f3GWOPvbL2TvJb7jHij7nmWpOi0iLXcUQkUDz6qPf82GNuc8gZ6f9+QeK9997jyiuvpLS0lLVr1zJt2jTXkQJC+qh0yirLeOXTV1xHEZFAsHUrvPwy3HMPJCa6TiNnoIIT4Ky1PP3000yePJmkpCQ2bdrEFVdc4TpWwEjuncyo3qN0Z2MRaZ0HH4ToaG9hTWnXVHACWEVFBenp6fzkJz/hxhtvZP369fTt29d1rICTPiqdzwo+46P9H7mOIiLt2fr18Pbb3rpTPXu6TiMtUMEJUIcOHeKGG27g+eef56GHHmLJkiVERUW5jhWQpg2fRlRYFPM2687GItKM2gU1e/eG++5znUZaQQUnQCxatIj+/fsTEhJCQkICQ4cO5cMPP+SVV15hzpw5mkx8HmIiYrj1slt5betrFJcVu44jIu3R22/Dhg3eBGNdmRoQ9H/FALBo0SLS09PZu3cv1lry8vIoKCjggQceYPr06a7jBYWZKTMprSxl8WeLXUcRkfamqsqbezNkCNx1l+s00koqOAHgwQcfpKSk5LT9L774ooM0wSk1PpWRvUbyl81/0WRjEWnor3+F7GyYOxfCwlynkVZSwWmHrLVs3bqVP/zhD0ydOpWcnJwm39fcfjl7xhjSU9L55OAnZOZluo4jIu1FWRk88giMHg3f+57rNHIWQl0HEK/Q/Otf/2LVqlWsXr2a1atXU1BQAEBSUhLR0dEcP378tO9L1D0Y/OrWy27lv9//b+Zvmc/oBK3bJSLAn/4EubmwcKEW1AwwGsFxJD8/n0WLFjFjxgwGDBhAUlIS6enprF27tm6phT179rBz506ee+6505ZbiIyMZO7cuY7SB6eunbry/WHfZ/FnizlWfsx1HBFx7cgRb62piRNh/HjXaeQsaQSnjRQVFfHPf/6T1atXs2rVKj7//HMAunXrxvjx45k1axZpaWlccsklmEb/SqidSPzQQw+Rk5NDYmIic+fO1QTjCyB9VDovZr3Iq1tfJX1Uuus4IuLSb34Dhw97C2tKwDGuJlSmpqbazMzgnetw4sQJ1q9fX1dotmzZgrWWyMhIrr76aiZMmEBaWhojR47E5/O5jis1rLWMeG4EnUI7kTEzw3UcEXElLw8GDYLvfAcWLXKdRs7AGLPZWpvaeL9GcPykoqKCjz76qK7QfPjhh5w8eZKwsDC+/vWv8+ijj5KWlsYVV1xBeHi467jSjNrJxj9c8UO25G8hpXeK60gi4sLjj0NlJcye7TqJnCON4JyjqqoqPvnkk7qJwevWrePEiRMYY0hJSSEtLY0JEyZw1VVX6Q7DAaaotIj438Vzx+V38OzkZ13HEZG2tn07DBsG//Vf8MwzrtNICzSCc56stWzfvr2u0KxZs4aioiIALr30Uu644w4mTJjANddcQ48ePRynlfPRvXN3bh52M4s+W8RTNzxFdHi060gi0pZ+8Qvo3Bkefth1EjkPKjhnkJOT0+DS7by8PMC7PPvGG29kwoQJjB8/nvj4eMdJxd9mpszk5U9e5o3sN7grWXcuFekwNm2CN9/0lmT42tdcp5HzoFNU9RQUFLBmzZq6eTS7du0CIDY2tu6UU1paGgMHDjztSicJLtZahv15GF0iuvDh3R+6jiMibcFamDABtm6FXbsgJsZ1ImkFnaJqwtGjR1m7dm1dofnss88A6NKlC9dccw333nsvaWlpDB8+XIWmgzHGkD4qnR+v/DGfHvyUEXEjXEcSkQvt73+HNWvgj39UuQkCQTeCs2jRombvF1NaWsrGjRvrCk1mZiZVVVV06tSJcePG1Y3QjBo1itDQDt39BDhUcoj438WTnpLOM9/SREORoFZdDaNGQXExfPEF6GrXgNHcCE5QFZzaVbfrL0wZERHBlClTOHToEBs2bKC8vByfz8eYMWPqTjtdeeWVdOrUya9ZJDhMf2s67375Lnn35xEZFtnyN4hIYFq8GKZPh1de8Z4lYHSIgtO/f3/27t3b5GuXX355XaG5+uqr6dKli19/twSntXvWcu3Ca3lp6kvcPvJ213FE5EKoqIBLL/VOS23ZAiFaxSiQdIg5OGdaXTsrK6sNk0iw+Ea/bzCk5xDmb5mvgiMSrObNg9274b33VG6CSFB9ks2trt2vX782TiLBwhjDzJSZbMjdQHZBtus4IuJvx455dy2+9lpvUU0JGkFVcObOnatVt8Xvbr/8dsJCwpi/Zb7rKCLib7/7HRQWwpNPgq6WDSpBVXCmT5/OvHnz6NevH8YY+vXrx7x587TqtpyX2KhYvnvpd3n5k5cpqyxzHUdE/KWgAH77W/je92DMGNdpxM+CquCAV3L27NlDdXU1e/bsUbkRv5iZMpOisiKWblvqOoqI+MucOVBaChrlD0pBV3BELoTxA8aT1D2JeVvmuY4iIv6wezc89xzMmAEXX+w6jVwAKjgirRBiQpiZMpMP9n7AF1994TqOiJyvRx6B0FBvzSkJSio4Iq10x8g7CA0J5fktz7uOIiLnIysLFi2C++4DLZYctFRwRFopLjqOqRdP5aWslyivLHcdR0TO1QMPQPfu8LOfuU4iF1CrCo4xZpIxZrsxZqcx5udNvP4TY8w2Y8ynxphVxhjdeEaCUvqodA6VHuJ/v/hf11FE5FysWQMrVsCDD0K3bq7TyAXUYsExxviAPwHfBIYC04wxQxu97WMg1Vo7AngT+I2/g4q0B9cNvI7+3fozb7MmG4sEHGvh5z+HPn3gnntcp5ELrDUjOGOAndba3dbaCuA1YGr9N1hr11hra1e4/BDo49+YIu1DiAnh7uS7WbNnDTsO7XAdR0TOxltvwaZN3p2LtcBy0GtNwUkAcut9va9mX3NmAO819YIxJt0Yk2mMySwsLGx9SpF25M7kO/EZnyYbiwSSykrvtNTQoXDbba7TSBvw6yRjY8wPgFTgqaZet9bOs9amWmtTY2Nj/fmrRdpMfEw8/3bxv/Fi1otUVFW4jiMirfHCC/Dll/CrX4HP5zqNtIHWFJz9QN96X/ep2deAMeY64CFgirVWl5hIUJuZMpPCkkKWbV/mOoqItKSkBH75Sxg7FqZMcZ1G2khrCk4GMNgYM8AYEw7cAjT4q26MSQb+glduCvwfU6R9mZg0kb5d+mqysUgg+OMfIT9fC2p2MC0WHGttJXAPsBL4HHjDWpttjHncGFNbhZ8CooElxpgsY4z+WStBzRfi4+6Uu3l/9/vsLtrtOo6INOfwYXjiCZg8Ga66ynUaaUOtmoNjrV1urR1irU2y1s6t2feItXZZzfZ11to4a+3ImofGACXo3ZV8FyEmhAVbFriOIiLN+fWv4ehR71k6FN3JWOQc9enSh28N/hYvZL3AyaqTruOISGO5ufDMM95VU8OHu04jbUwFR+Q8pKekc+D4Ad758h3XUUSksUcf9W7u99hjrpOIAyo4Iufhm4O/SXxMPPO2aLKxSLuybRssXOjdsbifVg/qiFRwRM5DaEgoM5JnsHLnSvYe2es6jojUevBBiI72nqVDUsEROU8zkmcAsOBjTTYWaRc2bIC//Q1++lPo2dN1GnFEBUfkPPXr1o9Jgyax4OMFVFZXuo4j0rHVLqjZqxf86Eeu04hDKjgifjAzZSZ5x/J4b0eTy7CJSFt5911Yv96bYBwV5TqNOKSCI+IHk4dMpld0L002FnGpqsobvRk8GGbMcJ1GHFPBEfGDMF8Yd428i+U7lpNbnOs6jkjH9MorkJ0Nc+dCWJjrNOKYCo6In8xImUG1reaFj19wHUWk4ykrg0cegdRUuOkm12mkHVDBEfGTgd0Hcv3A61nw8QKqqqtcxxHpWP78Z8jJ8dad0oKaggqOiF+lj0on92guK3etdB1FpOMoLvZOS91wA0yY4DqNtBMqOCJ+NOXiKcRGxjJvsyYbi7SZ3/zm1KrhIjVUcET8KNwXzp0j7+SdL99hyB+HUFxW7DqSSHDLz4enn4ZbboHkZNdppB1RwRHxs7tT7qbKVrGjaAfLdyx3HUckuD3+OJw8CXPmuE4i7YwKjogf3br0VpL/kozBm+Q4/a3pRMyO4JoXr+GTA59wuPQw1lrHKUWCxJdfwvz58B//AUlJrtNIO2Nc/bFNTU21mZmZTn63yIWy8/BOprw6hV1Fu6ioqmjyPVFhUSR2Tax79O3St8HXfbr0ISI0oo2TiwSgm2+G5cth1y6Ii3OdRhwxxmy21qY23h/qIoxIsBrUYxCPj3+caUunERUWRVllGc9OfpbL4y4ntziXnOIc73HUe846kMXBEwdP+zlxUXENSk/jIhQbFUuI0QCsdGAZGbBkiXfvG5UbaYIKjoifvZH9BlFhUTz8jYeZ/cFs/rHrH8xMmcmYhDFNvr+ssox9R/fVlZ+6InQ0h+zCbN7b+R4lJ0safE+EL4K+XfueNvpT+3Xfrn2JDo9ui8MVaXu1C2pedBHcf7/rNNJO6RSViJ9l7M8gsWsicdFxHDx+kNyjuaTGnzZ62mrWWorKik6N/tQWoaOnRoTyjuVRbasbfF+Pzj2aPAVWu693TG9CQ87u3zjFB3MoHDmY2KwddI1LPOdjam+C8biC8ZjAO67jlyaRUFQJv/893Hef60jimE5RibSR0QmjvRuPDRtG3MaNxJ1HuQEwxtCjcw96dO7ByF4jm3zPyaqT5B3La1B6ah97i/eyLmcdR8qONPgen/GR0CWh2blAiV0T6RrRFVPvrrBbX3yScQcq2PjSU4z92TPndVztSTAeVzAeE8DWBU8wrqiSsu4xdPrP/3QdR9oxjeCIXAiLF8P06d7ztGn++7nWQnU1VFZ6KydXVbV6+3hpMQeL8ygozqPg2AEKj+ZTeOwAh44e5NCxAopOfAWVVfgs+KohtBqifBF8LaInUfsLSDhUyUUlEH0SLFBl4EjPSC4a/23/HV8b+2rNu3Q7VILPgrFgTeAfVzAeE5w6rh6lkHwQ9kdD13L45Ip+jFu3x3U8cai5ERwVHBF/+v73YdkyKC/3yogx3qNHD+8y1rMsJadtV1e3nEEkyK1LhGvugC4VMKLPKK6+ZCKjE0YzOn40CV0SXMeTNqZTVCIXyu7dsHIlrFgBq1Z5qxrXMgY6dYIhQyAmBnw+7xEaemq78det2XbwvswFc7j4V/M43BkiqmDrrNsZefvP3P1395OshU8y/KmFlPuC57iC8Zjg1HH5quDP78J7372MnNAqntzwJFXWW+C2d3TvurIzOn40oxNG06NzD8fJxQUVHJGzdeIE/POfXqFZuRJ27PD2DxgAt93mFZn/+R+v2JSXw8KFcNNNTiP7w8mVy6kOgX/dNpnk+e8QuXIVFz36kutY5y1qxSo6V8IXdwbPcQXjMcGp46r4zmSmzX+HEeFFjN2YS8nJErIOZJGxP4PM/Ewy9mewbPuyuu8b2H1gg8KT0jtFVxl2ACo4Ii2xFrZuPTVKs24dVFRAZCSMHw/33guTJsGgQd6Izc03Q3Q0PPwwzJ7t3asjCApO11/MoeLSUVw7cDiFP95Kt+1bXEfyi2A8rmA8Jmj+uCLDIhnbdyxj+46te29xWTGb8zeTsT+DTXmb2Ji7kdezXwcgxIRw6UWXNhjpGRE3QjfYDDKagyPSlMOH4R//OFVq8vK8/cOHe2Vm0iS46iqIaOIPYkYGJCZ6Nx87eBBycyH1/K6kEpHzd/D4QTLyMsjYn+E952XwVclXgLdQ7oi4EYyJH1NXfC656BJ8IT7HqaUlmmQsciZVVV4xqS00mzZ5E3q7dYPrr/cKzQ03QJ8+rpOKiJ9Ya9lbvLdB4dmct5ljFccAb1mVUfGjGpzeGtBtQINbJ4h7KjgijeXleYVm5Up4/31v1MYYGDPGKzQTJ8Lo0d4kWxHpEKptNdu/2t5gpCfrQBblVeUA9Ozck9T41LrCMzp+NL1jejtO3bGp4IiUl8OGDacmB3/6qbe/d2+vzEyaBNddBz17us0pIu1KRVUFWwu2NhjpyS7IrrtyKyEmocF8ntT4VLp37u44dcehgiMd086dpwrN6tVQUgJhYXD11adGaS67zBu5ERFppZKTJXyc/3Fd4cnYn8GOwzvqXh/UY1CDU1vJvZKJCo9q9ucVlxUzdsFYNs7YSNdOXdviEIKG7oMjHcPx47BmzalSs2uXt3/QILjzTq/UXHutd5WTiMg5igyLZFziOMYljqvbd6TsCJl5mXUjPety1vHq1lcB78qtYbHDGpzauizuMsJ94QC8u+Ndtn21jeU7ljPtMj/e/bwD0wiOBDZrvVNNtZOD16+HkychKgrS0rwRmokTvYIjItLGDhw/0ODUVsb+DA6VHgIgwhdBdHg0xeXFVNtqqm01PuMjwhfB1Eumsvh7ix2nDww6RSXB49Ahb1LwihXw979Dfr63//LLT82lGTu26Uu4RUQcstay58ieurLzQc4HZOZlUm0bLsMSFRZFfEw8vaJ70TumN72iap6je9E7unfd/osiLyLEhDg6mvZBBUcCV2Wldwn3ihXeIyPDG7np0cO7dHviRO85Pt51UhGRs/Z69utMXzqd0JBQTlaf5JbhtxAbGUv+8XwOHD9A/jHvufby9fp8xkdcdFzD4lOvANX/unNYZwdHd+FpDo60X8XF3ojLxo3QtWZy3b59DS/hPnIEQkLgiivgl7/0Sk1qqrdWkohIAFu6bSnR4dE8/I2Hmf3BbCqrKvn9pN+f9r4TFSe8wtOo+NTuyzuWx+b8zRScKDhtRAiga0TXJotP40LUs3PPoLjXj0ZwxL3Fi2H6dHjgAW8JhBUrIDvbey0hoeEl3N116aWIBJeM/Rkkdk0kLjqOg8cPkns0l9T4c7/7eVV1FYUlhQ1KUF0pqleO8o/nU3Ky5LTvDwsJa9WoUFx0HJ1COzWbo62uDNMpKnGnpAQKC089Cgq85wULvMu4q6q8U0614uJg1iyv2Awbpku4RUQukOMVx08vQcfyOXCiYTkqPFGI5fS+0L1T92ZHhbILs/n1+l+zcOpCbht52wU7BhUc8Z/S0oZFpf52U/tOnGj654SHe8sh1Bac8HAYOBDeeQeSktr2mEREpFmV1ZUUnChoclSocTkqrSxt8L0+46NTaCemXDzlglwZpjk40rzawtLa0nKmwvK1r0FsrPcYMuTUdu3++q/HxMDSpTBtmnfFU3m5t/q2yo2ISLsSGhJKfEw88THxcIaVKay1ZB3M4qbXb2LfsX1UVFUQFhJGv279mD1+dtsFRgUnsDQ1Gbcp9QtLa0rL8eNN/5zw8IalZPDghgWl8XZMzNmfTnrjDe+eNQ8/7JWbJUvgppvO7meIiEi7YIwhuVcyT17/JNOWTiMqLIryqnIeu/Yxknq07T9eg7PgtLYItDdVVd4oRkWF99x4++23Yds2bzJuUlLzpaW5whIW1rCUDB7cdFGp3e7S5cLPf5k1C555xpt384MfQG7uhf19IiJywb2R/QZRYVF1V4YtyV7CTUPb9h+vwTkHp/aqnMWLvdMf9Vnr3em2qQLR1HZLr5/PduN9VVVnd5whIdCr15lHVeo/t0VhERGRDs/fV4adSceYZHzrrbBsmXeKprrmHgDGeCMXtXM8Kir8+zt9Pu9UTkSE92hqu6XXW9ouKoKnnvJGaCoqvP39+3uTcbUEgYiIdGAdY5Lx449DVpZ36XF1tVc+YmLg29/2RjDOpWS09Hpb3WguPt4bjYqK8oranDkqNyIiIs0IroIzaJBXcuoXgfnzg2PSqibjioiItFrwrdBVWwQee8x7XrLEdSL/mDULtm+H++/3nmfNcp1IRESk3QquOTjgLcSYmOhdlXPwoHdVTuqFmdgkIiIibjU3B6dVIzjGmEnGmO3GmJ3GmJ838XqEMeb1mtc/Msb0P//I52j0aK/cgPesciMiItLhtFhwjDE+4E/AN4GhwDRjzNBGb5sBFFlrBwFPA0/6O6iIiIhIa7VmBGcMsNNau9taWwG8Bkxt9J6pwMKa7TeBCSYY1loXERGRgNSagpMA1L+97L6afU2+x1pbCRQDPRv/IGNMujEm0xiTWVhYeG6JRURERFrQpldRWWvnWWtTrbWpsbGxbfmrRUREpANpTcHZD/St93Wfmn1NvscYEwp0BQ75I6CIiIjI2WpNwckABhtjBhhjwoFbgGWN3rMMuL1m+yZgtXV1/bmIiIh0eC3eydhaW2mMuQdYCfiAF6y12caYx4FMa+0yYAHwV2PMTuAwXgkSERERcaJVSzVYa5cDyxvte6Tedhnw7/6NJiIiInJugm+pBhEREenwnC3VYIwpBPY6+eWB7SLgK9chpFX0WQUWfV6BQ59V4GiLz6qftfa0S7OdFRw5N8aYzKbW3JD2R59VYNHnFTj0WQUOl5+VTlGJiIhI0FHBERERkaCjghN45rkOIK2mzyqw6PMKHPqsAoezz0pzcERERCToaARHREREgo4KjoiIiAQdFZwAYIzpa4xZY4zZZozJNsbc5zqTtMwY4zPGfGyMecd1FmmeMaabMeZNY8wXxpjPjTFXus4kzTPG/Ljm7+BWY8yrxphOrjOJxxjzgjGmwBiztd6+HsaY940xO2qeu7dVHhWcwFAJ3G+tHQp8Hfi/xpihjjNJy+4DPncdQlr0B2CFtfYS4HL0mbVbxpgE4IdAqrV2ON76iFr7sP14CZjUaN/PgVXW2sHAqpqv24QKTgCw1uZba7fUbB/D+wOc4DaVnIkxpg/wbeB511mkecaYrsA38BYMxlpbYa094jaVtCAU6GyMCQUigTzHeaSGtfYDvAW365sKLKzZXgjc2FZ5VHACjDGmP5AMfOQ2ibTg98BPgWrXQeSMBgCFwIs1pxOfN8ZEuQ4lTbPW7gd+C+QA+UCxtfbvblNJC+Kstfk12weAuLb6xSo4AcQYEw0sBX5krT3qOo80zRgzGSiw1m52nUVaFAqkAM9aa5OBE7ThELqcnZr5G1Pximk8EGWM+YHbVNJa1rsvTZvdm0YFJ0AYY8Lwys0ia+1brvPIGY0Dphhj9gCvAWnGmFfcRpJm7AP2WWtrR0TfxCs80j5dB/zLWltorT0JvAWMdZxJzuygMaY3QM1zQVv9YhWcAGCMMXhzBD631v7OdR45M2vtA9baPtba/ngTIFdba/WvzHbIWnsAyDXGXFyzawKwzWEkObMc4OvGmMiav4sT0KTw9m4ZcHvN9u3A39rqF6vgBIZxwP/BGwnIqnl8y3UokSBxL7DIGPMpMBL4leM80oyakbY3gS3AZ3j/D9OyDe2EMeZV4P8BFxtj9hljZgBPANcbY3bgjcA90WZ5tFSDiIiIBBuN4IiIiEjQUcERERGRoKOCIyIiIkFHBUdERESCjgqOiIiIBB0VHBEREQk6KjgiIiISdP4/a1dz7U0fySYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x72 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.offsetbox import (TextArea, DrawingArea, OffsetImage, AnnotationBbox)\n",
    "\n",
    "cls_logits, cls_prob, cls_u = Evidential_DL.edl_predict(model, torch.cat(rotate_imgs, out=cat_size))\n",
    "\n",
    "plt.figure(figsize=(8, 5))\n",
    "\n",
    "\n",
    "plt.scatter(np.tile(np.arange(1, 11), cls_prob.shape[0]), cls_prob[:, :, 1].flatten(), \\\n",
    "            c='g', marker='*', linewidth=None, alpha=1, label='1');\n",
    "plt.plot(np.tile(np.arange(1, 11), cls_prob.shape[0]), cls_prob[:, :, 1].flatten(), c='g')\n",
    "\n",
    "plt.scatter(np.tile(np.arange(1, 11), cls_prob.shape[0]), cls_prob[:, :, 4].flatten(), \\\n",
    "            c='r', marker='*', linewidth=None, alpha=1, label='4');\n",
    "plt.plot(np.tile(np.arange(1, 11), cls_prob.shape[0]), cls_prob[:, :, 4].flatten(), c='r')\n",
    "\n",
    "\n",
    "plt.scatter(np.tile(np.arange(1, 11), cls_logits.shape[0]), cls_u[:, :, :].flatten(), \\\n",
    "            c='k', marker='o', linewidth=None, alpha=1, label='uncertainty');\n",
    "plt.plot(np.tile(np.arange(1, 11), cls_prob.shape[0]), cls_u[:, :, :].flatten(), c='k')\n",
    "\n",
    "plt.title('Probability of Rotated \"1\" and Uncertainty');\n",
    "plt.legend(framealpha=0.7);\n",
    "plt.tight_layout();\n",
    "\n",
    "MnistVisualizer.cat_images(rotate_imgs, 8, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Use LRP to interpret uncertainty\n",
    "Here we want to explore how assigning evidence and uncertainty to our nerual network during training will affect the intepretation of our model. We first interpret predictions from base CNN model with `composite LRP`. Then compare interpretated results with the same attributtion method but from the model trained under `evidential deep learning` approach. \n",
    "\n",
    "Check out how we use our **nn_interpretability** API by just calling `LRPMix()` and `interpretor.interpret()` two lines!\n",
    "### 3.1.1 Interpret base model with composite LRP\n",
    "Here **NO UNCERTAINTY** is introduced"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_name_no_uncertain = 'model_cnn.pt'\n",
    "model_no_uncertain = ModelRepository.get_general_mnist_cnn(model_name_no_uncertain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.nn.functional as F\n",
    "from nn_interpretability.interpretation.lrp.lrp_composite import LRPMix\n",
    "\n",
    "def prediction_lrp_mix(model, image):\n",
    "    model.eval()\n",
    "    image = image.to(Evidential_DL.device)\n",
    "    # Consturct LRPMix\n",
    "    interpretor = LRPMix(model, 'predicted', None, 1, 0, 0)\n",
    "    heatmap = interpretor.interpret(image)\n",
    "    predicted = interpretor.get_class()\n",
    "    logits = model(image)\n",
    "    evd = F.relu(logits)\n",
    "    alpha = evd + 1\n",
    "    return heatmap.detach().cpu().numpy(), predicted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = []\n",
    "predicted = []\n",
    "for i in range(len(rotate_imgs)):\n",
    "    out, pred = prediction_lrp_mix(model_no_uncertain, rotate_imgs[i])\n",
    "    images.append(out[0].sum(axis=0))\n",
    "    predicted.append(pred)\n",
    "\n",
    "MnistVisualizer.edl_heatmap_for_each_rotation(images, predicted, None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1.2 Interpret evidential deep learning model with composite LRP\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def uncertain_prediction_lrp_mix(model, image):\n",
    "    model.eval()\n",
    "    image = image.to(Evidential_DL.device)\n",
    "    # Consturct LRPMix\n",
    "    interpretor = LRPMix(model, 'predicted', None, 1, 0, 0)\n",
    "    heatmap = interpretor.interpret(image)\n",
    "    predicted = interpretor.get_class()\n",
    "    logits = model(image)\n",
    "    evd = F.relu(logits)\n",
    "    alpha = evd + 1\n",
    "    uncertainty = logits.size(1) / torch.sum(alpha, dim=1, keepdim=True)\n",
    "    return heatmap.detach().cpu().numpy(), predicted, uncertainty.cpu().item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = []\n",
    "predicted = []\n",
    "uncertainty = []\n",
    "for i in range(len(rotate_imgs)):\n",
    "    out, pred, uncer = uncertain_prediction_lrp_mix(model, rotate_imgs[i])\n",
    "    images.append(out[0].sum(axis=0))\n",
    "    predicted.append(pred)\n",
    "    uncertainty.append(uncer)\n",
    "\n",
    "MnistVisualizer.edl_heatmap_for_each_rotation(images, predicted, uncertainty)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2.1 Interpret base model with  LRP-α1β0 (Deep Taylor Decomposition)\n",
    "Here **NO UNCERTAINTY** is introduced"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from nn_interpretability.interpretation.lrp.lrp_ab import LRPAlphaBeta\n",
    "\n",
    "def prediction_lrp_mix(model, image):\n",
    "    model.eval()\n",
    "    image = image.to(Evidential_DL.device)\n",
    "    # Consturct LRPMix\n",
    "    interpretor = LRPAlphaBeta(model, 'predicted', None, 1, 0, 0)\n",
    "    heatmap = interpretor.interpret(image)\n",
    "    predicted = interpretor.get_class()\n",
    "    logits = model(image)\n",
    "    evd = F.relu(logits)\n",
    "    alpha = evd + 1\n",
    "    return heatmap.detach().cpu().numpy(), predicted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = []\n",
    "predicted = []\n",
    "for i in range(len(rotate_imgs)):\n",
    "    out, pred = prediction_lrp_mix(model_no_uncertain, rotate_imgs[i])\n",
    "    images.append(out[0].sum(axis=0))\n",
    "    predicted.append(pred)\n",
    "\n",
    "MnistVisualizer.edl_heatmap_for_each_rotation(images, predicted, None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2.2 Interpret evidential deep learning mode with  LRP-α1β0 (Deep Taylor Decomposition)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def uncertain_all_lrp_ab(model, image, T=1000):\n",
    "    model.eval()\n",
    "    image = image.to(Evidential_DL.device)\n",
    "    # Consturct LRPMix\n",
    "    interpretor = LRPAlphaBeta(model, 'predicted', None, 1, 0, 0)\n",
    "    heatmap = interpretor.interpret(image)\n",
    "    predicted = interpretor.get_class()\n",
    "    logits = model(image)\n",
    "    evd = F.relu(logits)\n",
    "    alpha = evd + 1\n",
    "    uncertainty = logits.size(1) / torch.sum(alpha, dim=1, keepdim=True)\n",
    "    return heatmap.detach().cpu().numpy(), predicted, uncertainty.cpu().item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = []\n",
    "predicted = []\n",
    "uncertainty = []\n",
    "for i in range(len(rotate_imgs)):\n",
    "    out, pred, uncer = uncertain_all_lrp_ab(model, rotate_imgs[i])\n",
    "    images.append(out[0].sum(axis=0))\n",
    "    predicted.append(pred)\n",
    "    uncertainty.append(uncer)\n",
    "\n",
    "MnistVisualizer.edl_heatmap_for_each_rotation(images, predicted, uncertainty)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}