8.1.LRP.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_0 import LRP0\n",
    "from nn_interpretability.interpretation.lrp.lrp_eps import LRPEpsilon\n",
    "from nn_interpretability.interpretation.lrp.lrp_gamma import LRPGamma\n",
    "from nn_interpretability.interpretation.lrp.lrp_ab import LRPAlphaBeta\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.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 = 'model_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": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "MnistVisualizer.show_dataset_examples(mnist_data_loader.trainloader)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = ModelRepository.get_general_mnist_cnn(model_name)\n",
    "\n",
    "if train:\n",
    "    criterion = nn.CrossEntropyLoss()\n",
    "    optimizer = optim.Adam(model.parameters(), lr=0.0005)\n",
    "\n",
    "    model.train()\n",
    "    ModelTrainer.train(model, criterion, optimizer, mnist_data_loader.trainloader)\n",
    "    \n",
    "    ModelRepository.save(model, model_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# I. LRP-0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = []\n",
    "\n",
    "for i in range(10):\n",
    "    \n",
    "    img = mnist_data_loader.get_image_for_class(i)\n",
    "    \n",
    "    # LRP0(model, target_class, transforms, visualize_layer)    \n",
    "    interpretor = LRP0(model, i, None, 0)\n",
    "    endpoint = interpretor.interpret(img)\n",
    "\n",
    "    images.append(endpoint[0].detach().cpu().numpy().sum(axis=0))\n",
    "    \n",
    "MnistVisualizer.display_heatmap_for_each_class(images)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison between LRP gradient and LRP  convolution transpose implementation \n",
    "For **convolution layers** there is no difference, we will obtain the same numerical results with either approach. However, for **pooling layers** the result from convolution transpose approach is **4^(n)** as large as for those from gradient approach, where n is the number of pooling layers. The reason is because in every average unpooling operation, s will be unpooled directly without multiplying any scaling factor. For gradient approach, every input activation influence the output equally therefore the gradient for every activation entrices is 0.25. The operation is an analog of first unpooling and then multiplying a scale of 0.25 to s. \n",
    "\n",
    "The gradient approach will be more reasonable to the equation described in Montavon's paper. As we treat pooling layers like convolutional layers, the scaling factor 0.25 from pooling should be considered in the steps that we multiply weights in convolutional layers (step1 and step3)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# II. LRP-ε"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iIl+/bBgouR9Pv3cWWwu7mAEAAEkEcQAAqkUQBwCgUuvOKKz39/kludqiL7+X5M29XLZNvnjnMTnxYeeyazg3AJTaujUdN222YvPkNa5xNHsBAACSCOIAAFSLIA4AQKUI4gAAVKrvu5j1SskOO3Gik89p2g2gB3pVdNF0d6Emu6rVWCgCYDCK1gdnzc3W6oZrGnK8iQMAUCmCOAAAlSKIAwBQqb4njPvZOGWQm5AMM1/T9NpNGyoAGH1NamY8TdaQfq5pwzSM++NNHACAShHEAQCoFEEcAIBKEcQBAKhUiLE8ER9COCvpRP9uBy20N8a4a9g3AWAF6/BYes91eF1BHAAAtAe/TgcAoFIEcQAAKkUQBwCgUgRxAAAqRRAHAKBSBHEAACpFEAcAoFIEcQAAKkUQBwCgUv8H32Im1+Pc1sIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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La+YXkmaYt3pN6TAML5hYLaSrOsc4ataboUYDoGwcMaQVi5n+Pr1zDZtKSdkBS9FjuY/dDtwo2ai5Ul3ijhoAgIqRqAEAqBiJGgCAig1co65i/Z7VE7L6woDrnYc1iTXQANBkfcxrE1MmUscuzQVqGkdDTXoS9eU2n7Wpz2G+43HijhoAgIqRqAEAqBiJGgCAik3lEdvTXOdtqn20qY3UvuYPwCZQOMug6fmm2D2OmvU41JZjuKMGAKBiJGoAACpGogYAoGIkagAAKjaVk8mm2aCTKYa9BsDsGjQGNF0/jgmqocVBR+OIXYOOdaPi5STfhztqAAAqRqIGAKBiJGoAACoWYmz/u3oI4VVJRyY3HHRkb4xxV9eDANCMODzTirF4oEQNAAA2Fj99AwBQMRI1AAAVI1EDAFAxEjUAABUjUQMAUDESNQAAFSNRAwBQMRI1AAAVI1EDAFCx/wHCvkUV8is/9wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = []\n",
    "\n",
    "for i in range(10):\n",
    "    img = mnist_data_loader.get_image_for_class(i)\n",
    "    \n",
    "    # LRPEpsilon(model, target_class, transforms, visualize_layer)    \n",
    "    interpretor = LRPEpsilon(model, i, None, 0)\n",
    "    endpoint = interpretor.interpret(img)\n",
    "\n",
    "    images.append(endpoint[0].detach().cpu().numpy().sum(axis=0))\n",
    "    \n",
    "MnistVisualizer.display_heatmap_for_each_class(images)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# III. LRP- γ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Fb8LheKIGAKBiBGoAACpGoAYAoGJTJTv7WM87yTnmkj9YGbReKt6brxHM5ahb12n+J2j9PjK5JdZRA+jVkSPNcS6/XOoB0cUc1kDXll/uA0/UAABUjEANAEDFCNQAAFSMBbljKOWPu+SXS+cc9+cADraZ1Kzk5i76NywMT9QAAFSMQA0AQMUI1AAAVIxADQBAxaaqDuijaGGScyyqwYcXbUxSCOb3TrMSAOManje6zEt9zDN9FLYu033ME0/UAABUjEANAEDFCNQAAFQsUur+XX1EnJd0ena3gwU5kVJaX/RNAChjHl5q2bl4rEANAADmi6++AQCoGIEaAICKEagBAKgYgRoAgIoRqAEAqBiBGgCAihGoAQCoGIEaAICKEagBAKjY/wCoYWXmEyQ3lgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = []\n",
    "\n",
    "for i in range(10):\n",
    "    img = mnist_data_loader.get_image_for_class(i)\n",
    "\n",
    "    # LRPGamma(model, target_class, transforms, visualize_layer)    \n",
    "    interpretor = LRPGamma(model, i, None, 0)\n",
    "    endpoint = interpretor.interpret(img)\n",
    "\n",
    "    images.append(endpoint[0].detach().cpu().numpy().sum(axis=0))\n",
    "    \n",
    "MnistVisualizer.display_heatmap_for_each_class(images)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IV. LRP-αβ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. LPP-α1β0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAACYCAYAAAAr8KpEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAMpElEQVR4nO3dT4heVxnH8d9jSgKNmTKaISFTOzrU0oHUBIriJtCFCwWLBIt/QJBCRdy4EFSwKF0IWheCuhFB/IOglopoF126UMQWuig1raQaGuqkEyd0NHEiCZkeFzOBuc89854z75+5z3vn+4Eszvve99x7QzhP7n2ec46llAQAAGJ6W9cXAAAAdkagBgAgMAI1AACBEagBAAiMQA0AQGAEagAAAtt3gdrMfmhmXx/3sQCAeozF9axP86jN7DVJxyTdkrQh6WVJP5f0o5TSWyP2/ZCkX6SU7q449qCkFyUdqTkeAPqk67HYzJ6Q9LikG9s+fl9K6cIo5+5KH5+oH04pHZG0IOnbkr4q6cd7fA1flrS6x+cEgEi6Hot/nVJ6+7Y/UxmkpX4GaklSSuk/KaXfS/qkpM+a2UlJMrOfmtk3bx9nZl8xszfM7JKZPWZmyczu3X6smR2W9KykE2b2360/J3LnNbP3SPqMpG9N+h4BILquxuI+6W2gvi2l9Lykf0o6478zsw9L+pKkD0m6V9JDO/SxLukjki5t+9/ZpR1O+QNJX5P0v9GvHgD6oYOx+GEze9PMzpnZF8ZxD13pfaDecknSOzKff0LST1JK51JK1yU9McpJzOyspAMppd+O0g8A9NSejMWSnpK0JGlO0uckfcPMPj1in53ZL4F6XtKbmc9PSHp9W/v1zDFVtl7JfEfSF4ftAwB6buJjsSSllF5OKV1KKW2klP4s6XuSHhmlzy7d0fUFTJqZvV+b/zj+lPn6DUnbKwffNaCrUnn8eyW9W9IfzUySDkq6y8xWJH0wpfRa5SUDQO/s4Vi8029siN+F0NsnajObMbOPSvqVNkv5X8oc9pSkR81syczulDRont5lSe80s7t2+P6v2vzHdXrrz2NbvzmtEf93CADTqoOxWGb2MTObtU0f0Oabzt+NcBud6mOgfsbMrmkzOD4u6buSHs0dmFJ6VtL3Jf1B0t8l/WXrqxuZY/8m6ZeSLpjZv32lYUrpVkpp5fYfbb7eeWurvTGmewOAadHJWLzlU1v9XNPm/O0nU0o/G+12utOrBU9GZWZL2nwyPpRSutX19QDAfsRY3NTHJ+pdMbOzZnbIzGYlPSnpGf5hAMDeYize2b4P1JI+L+lfkv6hzaXupnq+HQBMKcbiHfDqGwCAwHiiBgAgMAI1AACB7WrBk9nZ2TQ/Pz+pa0FHlpeXtba2NrWLAQD7CeNwf507d+5KSmnOf76rQD0/P6/fPP30+K4KIXz8kaldWQ/YdxiH++v+paWLuc959Q0AQGAEagAAAiNQAwAQGIEaAIDACNQAAATW+/2oAQBT6lZmqe877hh8zIbbrPDAgXYf/hjfhz9Hro/SdY0RT9QAAARGoAYAIDACNQAAgRGoAQAIjGIyAMDoSkVdUrso68aN3Z/n+vXB3+fO6x08OPg3N28223fe2e6jpsBsTHiiBgAgMAI1AACBEagBAAiMHHU0pYn3ADBpuYVGSouE+O9rcsWlHHXuOg4dGtxH6fsaPv+cu47SMWMcu3miBgAgMAI1AACBEagBAAis+wRo7t2/Ny152pp78Xwex+dTcvP3puXvA8B0qBm7/DF+rrEfu2ry3KUNNNbW2n3MzDTbKyvN9uxsuY/FxcF9+HuZm2v3cexYs+1z42PEEzUAAIERqAEACIxADQBAYHuf7Bxmk+9pnVtcM49wHHMRp+XvA8B0yI07pXoavwb3+nq7D58v9mPXhQuDzyG1c8HnzzfbS0uDj8+5enXwb4bJtzOPGgCA/YFADQBAYARqAAACI1ADABDYaNnumknypYXcazboLumqmKpUCFbz91NaNMBvcF6D4jIAu1FT1OvHpldeGdyH/z7H9+n78AuRSO0FTXwR2/Jys33mTLuP48eb7XvuabZ9MVmuIG2YWDUknqgBAAiMQA0AQGAEagAAAhtvMrNmcY5r1wZ/n8vJRsm5DrPphlfKwfj8S8115PJJAFDLjyE1Y7n/jc8N5zbD8Mf4PK/PFZ861e7Db6jh+/TxIrehhh9nazZD6hBP1AAABEagBgAgMAI1AACBTT75W8rr1uQGfL7Ez2nbqxx2aRF6fx25e79ypdn2eZwjR5rtmlwRAIxTru7Fj7sLC822z/v6XLIkPffc4PP6Pv1859x5csdsl7uX3caUmjqgCcYhnqgBAAiMQA0AQGAEagAAApt8ctfnAlZXm+2ZmYlfQhWff87lJHxO2rdrNhv39+/7OHx48HXlzgMA45TLt/oxsTR25/p48MFm+/LlZtvnqGv48dDXOeWuw6/X0VXdUyWeqAEACIxADQBAYARqAAACI1ADABDYeDPmueKpUgGWlyuU8v2WNvXOFWB5vuDAbxaSW3jFX3vpPLnFSvwCJzdvNtv+XlnwBMCk1RRPlQquagpy/fjmF4BaX2+2cxtq+LG5FA96gCdqAAACI1ADABAYgRoAgMB2l6NOafAmG7l8qs9b+LbPJ+Q2G/dKee7c9z5fUspr5O7TH+PP4+///Pl2H/7+fA6mJifdwxwMgClXM4b6BZ2OHm22l5cHH5/jY4o/b25hlmALmpTwRA0AQGAEagAAAiNQAwAQ2Hhf1Ndsru3VzIH2eVu/oHoN30epnePzy77t52LX5Kj9IvWlOeNS++95yvItAKaQH2dK405unPbrRvix7MKFZvull9p93H13sz0722z7eda5mLLbWNXxGMsTNQAAgRGoAQAIjEANAEBgk3/x7vMDPkfr8ws1ffj8wsrK4OOldv7YH7O42Gy/+mq7j2PHmm2/6bm/l9w6tX5On28H38AcAKrUjF0+n/zAA822z1lL7fHeH3PqVLN9/Pjur2OYeqsJ4okaAIDACNQAAARGoAYAIDACNQAAge2uUsmsWSDgF+fIFQ/44ii/sMjzzzfbuU05/G/8eV98sdleXW334Qu7fLHAyZPN9unT7T78AvILC4P7fOGFdh+lhVX8977IQaLADEA8NQVYpQWdfMFurtjYLyTlN/LwhcC5MdcXDw+zANYejsM8UQMAEBiBGgCAwAjUAAAENtpLdv+OPvde3+d1/SYUfvL6lSvtPq5fb7Z9Dvrs2Z2v8TafT/aT4P0CKEeOtPvwC8p7wyzmAgD7RSlm1MSU++5rtn2+2S+AklsAy4/VuVqgQHiiBgAgMAI1AACBEagBAAhsvBPBcvPo/Ly50qYUPt+Qk8s5bFczB85fq2/n+vD3UrquXE77/vubbT+PsNQGgAj8eFgz7pbG0NL3OaW1Oq5ebf/Gxx1/jK8v6niTDp6oAQAIjEANAEBgBGoAAAIbb456mLVPfR53mD5Kc/FyfF6jJjfi59r5+d3ewYPtzw4fHvybYBuWA0AVX6OTqyXyY3WpNig3Hvp+/ZxoP7bn+vDrZJTG5Y73V+CJGgCAwAjUAAAERqAGACAwAjUAAIFNPkPuk/C+XUriS+VCL9/nMJPmfYFCzeR9L7eRh+cL0moKHwBgkmoWLykdU1qISmoX4JYKdHMFu6Xz+CLe+fn2Mf68ftytKTbewwIznqgBAAiMQA0AQGAEagAAAut2FnfOMPnlYX7j+XxDbkONEp9PyV2X/8znRoJvYA6gB4bJN5dyw378q9lQ6OLFZtuPw7lz+n5L+ea5uXYfucWoBl1Hx3iiBgAgMAI1AACBEagBAAgs1ot4qbvcgM/RlHIYOT53krsX/1lpvl5NngcA9lopr72y0v6N/8yPh0ePNtu5mh1/jF+Lw+eoc2tTTNm4yhM1AACBEagBAAiMQA0AQGDxctRdqVljuzRf2+dTata+9ecNNn8PQA+Uxq6atSiuXWu219eb7bW1ch8LC822HyP9utwzM+U+98EYyhM1AACBEagBAAiMQA0AQGAEagAAAutf1n1YNQUIpaKFYYrJAKBrfhMiXygmSaurzbYf30oLj0jt4rDZ2Wa7ZlOiUuEvxWQAAGAvEagBAAiMQA0AQGD9e5k/Lrk8h18UwOdKfL4lt/B7aeOOKVssHsAU8OOMH8tqNiFaXBz8vR+7ahaR8tdV85tSHz3EEzUAAIERqAEACIxADQBAYP1/uT9Ou82F1OSb90F+BUAwftzxbT8nWmrntTc2mu1h8sul64IknqgBAAiNQA0AQGAEagAAAiMhME7kVwD0VSmvjYnhiRoAgMAI1AAABEagBgAgMAI1AACBEagBAAiMQA0AQGAEagAAAiNQAwAQmKWU6g82W5V0cXKXg44spJTmur4IAGWMw72WHYt3FagBAMDe4tU3AACBEagBAAiMQA0AQGAEagAAAiNQAwAQGIEaAIDACNQAAARGoAYAIDACNQAAgf0f6qSw3mfzwXAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = []\n",
    "\n",
    "for i in range(10):\n",
    "    img = mnist_data_loader.get_image_for_class(i)\n",
    "    \n",
    "    # LRPAlphaBeta(model, target_class, transforms, alpha, beta, visualize_layer)        \n",
    "    interpretor = LRPAlphaBeta(model, i, None, 1, 0, 0)\n",
    "    endpoint = interpretor.interpret(img)\n",
    "\n",
    "    images.append(endpoint[0].detach().cpu().numpy().sum(axis=0))\n",
    "    \n",
    "MnistVisualizer.display_heatmap_for_each_class(images)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. LPP-α2β1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = []\n",
    "img_shape = (28, 28)\n",
    "\n",
    "for i in range(10):\n",
    "    img = mnist_data_loader.get_image_for_class(i)\n",
    "    \n",
    "    # LRPAlphaBeta(model, target_class, transforms, alpha, beta, visualize_layer)    \n",
    "    interpretor = LRPAlphaBeta(model, i, None, 2, 1, 0)\n",
    "    endpoint = interpretor.interpret(img)\n",
    "\n",
    "    images.append(endpoint[0].detach().cpu().numpy().sum(axis=0))\n",
    "    \n",
    "MnistVisualizer.display_heatmap_for_each_class(images)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IV. Composite LRP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AAIGRqAEACIxEDQBAYP8H+enz45plAE4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAACYCAYAAAAr8KpEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAOb0lEQVR4nO3dX4icVxnH8d9js7shMRO2Jnbp1kRDG1wINlAs3ggt9ELBIsWiFQQpVMQbLwQVLEovBK0XgnojgvgHQW1TREspvfKiIuJVS5tWWg3d1qSpCY3ttrVJsz1e7Ab2PO/ZOe/MvLPz7Oz3A7k4M+973nem6XnyznPOcyylJAAAENN7Jn0DAABgcwRqAAACI1ADABAYgRoAgMAI1AAABEagBgAgsB0XqM3sp2b27a6PBQC0x1jcnk3TOmoze0HSNZIuS1qV9IykX0v6WUrp3RH7vkXSb1JK17U4dlbSk5L2tTkeAKbJpMdiM7tP0r2SLm54+SMppVOjXHtSpvGJ+vaU0j5JhyV9X9I3Jf18i+/h65LObfE1ASCSSY/Fv08pvXfDn20ZpKXpDNSSpJTSaymlP0n6nKQvmtkxSTKzX5rZd68cZ2bfMLOXzeyMmd1jZsnMrt94rJntlfSopGvN7I31P9eWrmtmH5L0BUnfG/dnBIDoJjUWT5OpDdRXpJT+Lunfkj7u3zOzT0j6mqTbJF0v6ZZN+nhT0iclndnwr7Mzm1zyJ5K+Jel/o989AEyHCYzFt5vZq2Z20sy+0sVnmJSpD9Trzki6uvD6ZyX9IqV0MqX0lqT7RrmImd0h6aqU0h9G6QcAptSWjMWSHpC0JOmgpC9J+o6ZfX7EPidmpwTqRUmvFl6/VtJLG9ovFY5pZf0nmR9I+uqwfQDAlBv7WCxJKaVnUkpnUkqrKaW/SvqRpDtH6XOSdk36BsbNzD6qtb8cfym8/bKkjTMHP9Cnq9r0+BskfVDS42YmSbOS9pvZWUkfSym90PKWAWDqbOFYvNk5NsR5IUztE7WZ9czsU5J+p7Wp/E8VDntA0t1mtmRmeyT1W6f3iqT3mdn+Td5/Wmt/uY6v/7ln/ZzjGvFfhwCwXU1gLJaZfdrM5m3NzVr7pfOPI3yMiZrGQP2wma1oLTjeK+mHku4uHZhSelTSjyX9WdI/Jf1t/a2LhWP/Iem3kk6Z2X/9TMOU0uWU0tkrf7T288676+3Vjj4bAGwXExmL19213s+K1tZv359S+tVoH2dypqrgyajMbElrT8ZzKaXLk74fANiJGItz0/hEPRAzu8PM5sxsXtL9kh7mLwYAbC3G4s3t+EAt6cuS/iPpX1ordbet19sBwDbFWLwJfvoGACAwnqgBAAiMQA0AQGADFTyZn59Pi4uL47oXTMjp06d14cKFbVsMANhJGIen18mTJ8+nlA761wcK1IuLizpx4qHu7kqSDVVkBl36zJ3btrIesOMsLi7qoRMnJn0bUy21KGI2jtj14aWl5dLr/PQNAEBgndb6Lv0Lw//LhCdoAMCWudxiKfauPBTa5Xf6vj+M0lN623jIEzUAAIERqAEACIxADQBAYJ3mqEf5Db5fH1vB3+e4PkvtOm2uQd4fwBVTPR60yS9fdBtsXbqUt2dnm+f4Y3wfe/bk7auuavZRy1vPzWXNUf678EQNAEBgBGoAAAIjUAMAEBiBGgCAwAaeTDbuiQptiqaM6zqTuEb1mMJkCutg8T0AjFVpIpgfu/wkLq/2viStrubt11/v/77UnCzmr+P7mJ9v9tHr1e+tIzxRAwAQGIEaAIDACNQAAAS2Y5OdXeS9x1JooM0CfwA72iQKQ/lr+qHKp59Lc2maY2aFzxWXLuSP8e+fPdvsY2Ehb9c+TClXXhurXcGTUfBEDQBAYARqAAACI1ADABDYaDnqITbkrvZROL7NhhlboXbdNjnr6jFvvZW3h8lztFhnPanvEMB4dbGh0DCaQ3mL+/C5X7/m+fz55oX8Gugnn8zbfs3zU081+7jttrz9+ON5+8KFvH3sWLOPm27qf90Wsa0tnqgBAAiMQA0AQGAEagAAAut2HXWb3+B30jrhYq3bmbztczS+XdqwvPQaAGyiNjdmYvsp+LHs+efz9nPPNc/x+eNHHsnbS0t5u7QG+rHH8vbyct7eu7d5To3Pr3e4JwNP1AAABEagBgAgMAI1AACBEagBAAhstGy3T577Yh1Sc7JAbZPvgwerlzXfp0vaj6uYR2NyRG1Be2HD8sad+e/MT3woFTzxx/jrdjiJAcD0GWaM9MNOab+MjUoFT3xNELt0qX+nfnKZ1JxM5ouiPP103r7rrmYfR4/m7Vtvzdv79uXtXq/Zhz9mjHiiBgAgMAI1AACBEagBAAhstGRmaSG55/O0pU28a336nHSUgh/D5IL993HuXN4u5UI8n9chJw1gi/mhemUlb5dSuH7o3u87OXAgb/uNL0r8OZ7PR0vSkSN5288V8sn0NsY4DvNEDQBAYARqAAACI1ADABBYt+uo2+SsfS7Ar5sr5Wj9WuIh1g13UoTer5uurWcubcrh1wD6tv+sbfLxUXL2AKaWH2Z8yQuf1i3ta2Gvv5a/4MdIf5LPJZdu5NChvO1jTJtaFHv25O3Z2eY5XqnfMeGJGgCAwAjUAAAERqAGACCwwXLUKZXzrv34fMETT+Ttw4fzdqn/LcjB+pRF6Tbm5may9q69M82DNrDLbzRffPHF/hfyuZIS1k0DmDA/LO+eS+UDN/LxwNeE8Lnh0rwnPzfK54p9sryUS/avDTM3yGMdNQAAOxOBGgCAwAjUAAAERqAGACCwwbPfPpG/kZ8oIDU3nXjllbztF7gvLDT78El6l+h/53JevMTXEJGk1dX8GD93wNddKc0/8B/P39bV824yRZtJDLWiKaXJFB0stPcFYACgnzb1nDJtNljyA6+fCFbacKM2maxNsRLfh7+vYBN2eaIGACAwAjUAAIERqAEACGy0gidtFoX7hLFPbPi2z1lIzRyE63PGvd/r7W904bt988287T9KKb1SW0fvc+Uzp083O2mTDN+oVABlC4vBA4DUnNeya5fb2KhN1SjPj2V+zFxcbJ5TG6x9n1MwhvJEDQBAYARqAAACI1ADABDY4DnqfuuoSzlrnwvw5/d6eXtlpdmHP6ey6ffuueZ67t1uPd7bq/mGGr7L0pJwf4y/LZ8KmSl9V/778Jue+7xOaU1g8DV/ALa3NnUWGse0mbPkxz+/TtrX3Vhebvbha2+U1lpv1C9mbcaPwxMeY3miBgAgMAI1AACBEagBAAhssB/ezfI8hN/0u5SjOH8+b/t1cjffXO+j5uzZvH34cPMYn3Sey9da++XNpSXQvtv3997O2mlud35AaTG2T2TXNjAvIScNYIySrPFaJ/sD1Ma3667L26WNG3wRDD94+/0iSmuxvVr98AnjiRoAgMAI1AAABEagBgAgMAI1AACBDT6ZbNCJTH4nC7+Q/MEH83Zp8oCfxeUnZPkJaEePNvs4dixr7l5aytoLC7tdu9nFzGo+eczfq/kJa6dONTvxn6+2WL9UUB4AOtRmolhpglnWh48NpVhR20Djmmvydml89DN9/WQyPw77ycZSc4JZB5PH/Pfjv9NRJujxRA0AQGAEagAAAiNQAwAQ2OCVM/oVJCkVP7/xxrztc64+j+uLskvNwio+53DDDXm7tGG5z1u4PMeM/1ylnEWpgMlG/t5LO3vUNikZpoA8AAxgmOIlnRQ88eNsbbwrxZsjR/qf43PWJW3y6RW1nH3t/UHwRA0AQGAEagAAAiNQAwAQWLfrqNvkdf36Nd/uIkdbylH7+66tTy714fnP5tulXMnx43nb52Da5MoBYF0nueMu+DFzXPNt/Bjpx3Zfu6Mg7ZrJ2mG+w03wRA0AQGAEagAAAiNQAwAQ2OCLx/oprXmr5YJra5M363cjv866lEev5YL9fZTyK7X7WFnp36ckzc72v46/99J9DLHmD8DOVatDPZTaHJ02Y3utrsS+fY1TfH7Zp8YvXszf9+FBag7lvV53a57HgSdqAAACI1ADABAYgRoAgMAI1AAABDbarKQ2k5r8MXv35u02hUW2gp/4UNpQo1bI3U98WFho9uE/f62gSW0CG4AdZ9DJYI3ja8VJ2ozLfpZWm4InvgjUwYP9r1GakOYmk/nL+CHWt0vd1r7PLjfYGAZP1AAABEagBgAgMAI1AACBUTljM6XciE+G+GPOn8/bpU05/Dk+B+3z3BQ8ATCqWs7Zv1+qEuLHLn+On9fT6zX78HNyzp7N24UCJ57tett1ubt6Tu02vEnnpD2eqAEACIxADQBAYARqAAACm3yyc5h8q8+N+D5K+ZjadXz+pZTE8K/56/j3Swv4/DF+0xKfk64lUwCga6X6DbU8tx9Dn322eYyfx3PgwGD3JTXvbYgcdSebkmwhnqgBAAiMQA0AQGAEagAAApt8jnoYtXzzMHnvWh1vqZk/rtX6Lqnl16ntDWCrleo1eCsredvXifBrokvzaw4d6n9dP4bOzzf7cP0Ok2/266Sj56x5ogYAIDACNQAAgRGoAQAIjEANAEBg23My2TgMU1jET/zyBU785IsSP7lsdnbw+wCAQfhJXH5iWGlTjuXl/n34iV+lMdUfs7CQt30BqJIONiXyk8eibcLh8UQNAEBgBGoAAAIjUAMAEBg56s2UCo/4nIw/xi/mLy3W9zkY3/Z5nQ7yMQB2uNo40uvlbb/BhiQdP96/Dz92tZlvM6HxLXpO2uOJGgCAwAjUAAAERqAGACAwEqCbKeVOahto+BxNKUc9zHWdWn6lzRrB6EXoAWxu4//TQ/2/7McZn6Mu8TUfanN2hrmPFrZbfrkLPFEDABAYgRoAgMAI1AAABEaOehRB1zjvxBwOgDHz490Yxj/GrjKeqAEACIxADQBAYARqAAACI1ADABBYzNlQQQ1aaGRcKFYC7GwRxoBhJn5FuG8pzn20xRM1AACBEagBAAiMQA0AQGCWUvvf6s3snKTl8d0OJuRwSungpG8CQB3j8FQrjsUDBWoAALC1+OkbAIDACNQAAARGoAYAIDACNQAAgRGoAQAIjEANAEBgBGoAAAIjUAMAEBiBGgCAwP4Pk9QRULB1vPEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "images = []\n",
    "img_shape = (28, 28)\n",
    "\n",
    "for i in range(10):\n",
    "    img = mnist_data_loader.get_image_for_class(i)\n",
    "    \n",
    "    # LRPMix(model, target_class, transforms, alpha, beta, visualize_layer)\n",
    "    interpretor = LRPMix(model, i, None, 1, 0, 0)\n",
    "    endpoint = interpretor.interpret(img)\n",
    "\n",
    "    images.append(endpoint[0].detach().cpu().numpy().sum(axis=0))\n",
    "\n",
    "MnistVisualizer.display_heatmap_for_each_class(images)"
   ]
  },
  {
   "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
}