gradients_x_inputs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradients $\\times$ Input\n",
    "\n",
    "The gradients $\\times$ input attribution method produces an image-specific attribution map which corresponds to the gradient of the output with respect to the input times the input, hence the name \"gradients $\\times$ input\". This method is derived from the standard gradient method, shown in a seperate notebook. Its as simple as the gradient attribution method, but provides clearer results. It can be used with any classification model, since it only depends on the inputs gradients, not any gradients from the hidden layers and the input themselves.\n",
    "\n",
    "For more technical information on the gradients $\\times$ input attribution method see: [Learning Important Features Through Propagating Activation Differences](https://arxiv.org/abs/1704.02685)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import jax.numpy as jnp\n",
    "import flax.linen as nn\n",
    "import jax\n",
    "from jax import random\n",
    "from jax import grad\n",
    "import optax\n",
    "import urllib.request\n",
    "import zipfile"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load training data\n",
    "Check if the training data exists. If not, automatically download it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_dir = os.path.abspath(\"./digit-recognizer\")\n",
    "os.makedirs(data_dir, exist_ok=True)\n",
    "train_data_path = f\"{data_dir}/train.zip\"\n",
    "train_data_url = \"https://huggingface.co/datasets/ChristianOrr/mnist/resolve/main/train.zip\"\n",
    "\n",
    "if not os.path.exists(train_data_path):\n",
    "    print(\"Downloading training data...\")\n",
    "    urllib.request.urlretrieve(train_data_url, train_data_path)\n",
    "    with zipfile.ZipFile(train_data_path) as zip_file:\n",
    "        zip_file.extractall(data_dir)\n",
    "\n",
    "data_df = pd.read_csv('./digit-recognizer/train.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "val_size = 1000\n",
    "m, n = data_df.shape\n",
    "Y = jnp.array(data_df[\"label\"])\n",
    "data_df = data_df.drop(\"label\", axis=1)\n",
    "X = jnp.array(data_df)\n",
    "\n",
    "\n",
    "X_train = X[val_size:]\n",
    "X_train = X_train / 255.\n",
    "Y_train = Y[val_size:]\n",
    "\n",
    "X_val = X[:val_size]\n",
    "X_val = X_val / 255.\n",
    "Y_val = Y[:val_size]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the classification model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\u001b[3m                              _forward_fn Summary                               \u001b[0m\n",
      "┏━━━━━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━┓\n",
      "┃\u001b[1m \u001b[0m\u001b[1mpath        \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mmodule     \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1minputs        \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1moutputs      \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mparams        \u001b[0m\u001b[1m \u001b[0m┃\n",
      "┡━━━━━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━┩\n",
      "│              │ _forward_fn │ \u001b[2mfloat32\u001b[0m[5,784] │ \u001b[2mfloat32\u001b[0m[5,10] │                │\n",
      "├──────────────┼─────────────┼────────────────┼───────────────┼────────────────┤\n",
      "│ Sequential_0 │ Sequential  │ \u001b[2mfloat32\u001b[0m[5,28,… │ \u001b[2mfloat32\u001b[0m[5,24… │                │\n",
      "├──────────────┼─────────────┼────────────────┼───────────────┼────────────────┤\n",
      "│ Conv_0       │ Conv        │ \u001b[2mfloat32\u001b[0m[5,28,… │ \u001b[2mfloat32\u001b[0m[5,26… │ kernel:        │\n",
      "│              │             │                │               │ \u001b[2mfloat32\u001b[0m[3,3,1… │\n",
      "│              │             │                │               │                │\n",
      "│              │             │                │               │ \u001b[1m144 \u001b[0m\u001b[1;2m(576 B)\u001b[0m    │\n",
      "├──────────────┼─────────────┼────────────────┼───────────────┼────────────────┤\n",
      "│ Conv_1       │ Conv        │ \u001b[2mfloat32\u001b[0m[5,26,… │ \u001b[2mfloat32\u001b[0m[5,24… │ kernel:        │\n",
      "│              │             │                │               │ \u001b[2mfloat32\u001b[0m[3,3,1… │\n",
      "│              │             │                │               │                │\n",
      "│              │             │                │               │ \u001b[1m4,608 \u001b[0m\u001b[1;2m(18.4 \u001b[0m   │\n",
      "│              │             │                │               │ \u001b[1;2mKB)\u001b[0m            │\n",
      "├──────────────┼─────────────┼────────────────┼───────────────┼────────────────┤\n",
      "│ Dense_0      │ Dense       │ \u001b[2mfloat32\u001b[0m[5,184… │ \u001b[2mfloat32\u001b[0m[5,10] │ bias:          │\n",
      "│              │             │                │               │ \u001b[2mfloat32\u001b[0m[10]    │\n",
      "│              │             │                │               │ kernel:        │\n",
      "│              │             │                │               │ \u001b[2mfloat32\u001b[0m[18432… │\n",
      "│              │             │                │               │                │\n",
      "│              │             │                │               │ \u001b[1m184,330 \u001b[0m\u001b[1;2m(737.3\u001b[0m │\n",
      "│              │             │                │               │ \u001b[1;2mKB)\u001b[0m            │\n",
      "├──────────────┼─────────────┼────────────────┼───────────────┼────────────────┤\n",
      "│\u001b[1m \u001b[0m\u001b[1m            \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m           \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m              \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m        Total\u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m189,082 \u001b[0m\u001b[1;2m(756.3\u001b[0m\u001b[1m \u001b[0m│\n",
      "│\u001b[1m              \u001b[0m│\u001b[1m             \u001b[0m│\u001b[1m                \u001b[0m│\u001b[1m               \u001b[0m│\u001b[1m \u001b[0m\u001b[1;2mKB)\u001b[0m\u001b[1m           \u001b[0m\u001b[1m \u001b[0m│\n",
      "└──────────────┴─────────────┴────────────────┴───────────────┴────────────────┘\n",
      "\u001b[1m                                                                                \u001b[0m\n",
      "\u001b[1m                      Total Parameters: 189,082 \u001b[0m\u001b[1;2m(756.3 KB)\u001b[0m\u001b[1m                      \u001b[0m\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "class _forward_fn(nn.Module):\n",
    "\n",
    "    @nn.compact\n",
    "    def __call__(self, x):\n",
    "        batch_size = x.shape[0]\n",
    "        # Unflatten for the convolution layers\n",
    "        x = x.reshape(batch_size, 28, 28, 1)\n",
    "        mlp = nn.Sequential([\n",
    "            nn.Conv(features=16, kernel_size=(3, 3), padding=\"VALID\", use_bias=False), jax.nn.relu,\n",
    "            nn.Conv(features=32, kernel_size=(3, 3), padding=\"VALID\", use_bias=False), jax.nn.relu,       \n",
    "        ])\n",
    "        x = mlp(x)\n",
    "        x = x.reshape((batch_size, -1))\n",
    "        x = nn.Dense(10)(x)\n",
    "        return jax.nn.softmax(x)\n",
    "\n",
    "# Create the model object\n",
    "forward_fn = _forward_fn()\n",
    "# Display the model details\n",
    "dummy_x = X_train[:5]\n",
    "rng_key = random.PRNGKey(64)\n",
    "initial_params = forward_fn.init(rng_key, dummy_x)\n",
    "print(forward_fn.tabulate(rng_key, dummy_x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the loss function and update method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_fn(params, X, Y):\n",
    "    logits = forward_fn.apply(params, X)\n",
    "    loss = optax.softmax_cross_entropy_with_integer_labels(logits, Y)\n",
    "    loss = loss.mean()\n",
    "    return loss\n",
    "\n",
    "def update_params(params, opt_state, X, Y, optimizer):\n",
    "    grads = grad(loss_fn, argnums=0)(params, X, Y)\n",
    "    updates, opt_state = optimizer.update(grads, opt_state, params)\n",
    "    params = optax.apply_updates(params, updates)\n",
    "    return params, opt_state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_predictions(logits):\n",
    "    return jnp.argmax(logits, axis=1)\n",
    "\n",
    "def get_accuracy(predictions, Y):\n",
    "    return jnp.mean(predictions == Y)\n",
    "\n",
    "def gradient_descent(X, Y, batch_size, optimizer, epochs):\n",
    "    dataset_size = len(X)\n",
    "    steps_per_epoch = dataset_size // batch_size\n",
    "\n",
    "    rng = jax.random.PRNGKey(42)\n",
    "    params = forward_fn.init(rng, X[0: batch_size, :])\n",
    "    opt_state = optimizer.init(params)\n",
    "    for epoch in range(epochs):\n",
    "        dataset_step = epoch % steps_per_epoch\n",
    "        dataset_index = dataset_step * batch_size\n",
    "        input = X[dataset_index: dataset_index + batch_size, :]\n",
    "        label = Y[dataset_index: dataset_index + batch_size, ...]\n",
    "\n",
    "        params, opt_state = update_params(params, opt_state, input, label, optimizer)\n",
    "        if epoch % 10 == 0:\n",
    "            print(\"Epochs: \", epoch)\n",
    "            logits = forward_fn.apply(params, input)\n",
    "            predictions = get_predictions(logits)\n",
    "            print(get_accuracy(predictions, label))\n",
    "    return params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epochs:  0\n",
      "0.48200002\n",
      "Epochs:  10\n",
      "0.85700005\n",
      "Epochs:  20\n",
      "0.883\n",
      "Epochs:  30\n",
      "0.92800003\n",
      "Epochs:  40\n",
      "0.91800004\n",
      "Epochs:  50\n",
      "0.9250001\n",
      "Epochs:  60\n",
      "0.93900007\n",
      "Epochs:  70\n",
      "0.93500006\n",
      "Epochs:  80\n",
      "0.9480001\n",
      "Epochs:  90\n",
      "0.952\n",
      "Epochs:  100\n",
      "0.96800005\n",
      "Epochs:  110\n",
      "0.96000004\n",
      "Epochs:  120\n",
      "0.96900004\n",
      "Epochs:  130\n",
      "0.97300005\n",
      "Epochs:  140\n",
      "0.96800005\n",
      "Epochs:  150\n",
      "0.96800005\n",
      "Epochs:  160\n",
      "0.97200006\n",
      "Epochs:  170\n",
      "0.96700007\n",
      "Epochs:  180\n",
      "0.98300004\n",
      "Epochs:  190\n",
      "0.96900004\n"
     ]
    }
   ],
   "source": [
    "optimizer = optax.adam(learning_rate=0.001)\n",
    "\n",
    "params = gradient_descent(X_train, Y_train, 1000, optimizer, 200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display predictions and attribution maps\n",
    "\n",
    "The jax \"grad\" function is used to extract the gradients used for the attribution map. The only gradients needed are the input gradients, hence agrnums=1. This is different to how grad is used for training, shown above. When training only the gradients for the models parameters are needed. Its also possible to extract the input gradients while training, which could be useful for debugging. As you can see below the only difference in the code to the standard gradients method is that the gradients are multiplied by the inputs before displaying the attribution map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_predictions(X, params):\n",
    "    logits = forward_fn.apply(params, X)\n",
    "    predictions = get_predictions(logits)\n",
    "    return predictions\n",
    "\n",
    "def prep_image(image):\n",
    "    # Normalize the gradient values to be between 0-1\n",
    "    max_val= np.max(image)\n",
    "    min_val = np.min(image)\n",
    "    image = (image - min_val) / (max_val - min_val)\n",
    "    # Convert the grads to uint8 for displaying\n",
    "    image = np.uint8(image * 255)\n",
    "    return image  \n",
    "\n",
    "def display_prediction(index, params):\n",
    "    current_image = X_val[None, index]\n",
    "    prediction = make_predictions(X_val[None, index], params)\n",
    "    label = Y_val[index]\n",
    "    print(\"Prediction: \", prediction)\n",
    "    print(\"Label: \", label)\n",
    "\n",
    "    display_image = current_image.reshape((28, 28)) * 255\n",
    "    plt.gray()\n",
    "    plt.imshow(display_image, interpolation='nearest')\n",
    "    plt.axis('off')\n",
    "    plt.title(\"Input Image\")\n",
    "    plt.show()\n",
    "\n",
    "    # Calculate the derivative WRT the input image\n",
    "    grads = grad(loss_fn, argnums=1)(params, current_image, label[None, ...])[0]\n",
    "    # Multiply gradients by the input\n",
    "    attributions = grads * current_image\n",
    "\n",
    "    attributions = attributions.reshape((28, 28))\n",
    "    attributions = prep_image(attributions)\n",
    "    plt.gray()\n",
    "    plt.imshow(attributions, interpolation='nearest')\n",
    "    plt.axis('off')\n",
    "    plt.title(\"Attribution Map\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction:  [1]\n",
      "Label:  1\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction:  [4]\n",
      "Label:  4\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction:  [0]\n",
      "Label:  0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction:  [5]\n",
      "Label:  5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction:  [8]\n",
      "Label:  8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction:  [7]\n",
      "Label:  7\n"
     ]
    },
    {
     "data": {
      "image/png": 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AEAUAQhQACFEAIFpN0zTDWthqjfZeYEx1dna2PbNr1662Z3bu3Nn2TFXVlClTRjQHLxjOH/dOCgCEKAAQogBAiAIAIQoAhCgAEKIAQIgCACEKAIQoABCiAECIAgBx7FhvAI4UI3np46tf/eq2Z+6+++62Z+BwcVIAIEQBgBAFAEIUAAhRACBEAYAQBQBCFAAIUQAgRAGAEAUAQhQACFEAILwlFf7fwMBA2zOPPvpo2zP79+9vewYOFycFAEIUAAhRACBEAYAQBQBCFAAIUQAgRAGAEAUAQhQACFEAIEQBgGg1TdMMa2GrNdp7AWAUDeePeycFAEIUAAhRACBEAYAQBQBCFAAIUQAgRAGAEAUAQhQACFEAIEQBgDh2uAuH+d48AP6HOSkAEKIAQIgCACEKAIQoABCiAECIAgAhCgCEKAAQ/wfQg2qqFwQtcQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_prediction(0, params)\n",
    "display_prediction(3, params)\n",
    "display_prediction(5, params)\n",
    "display_prediction(8, params)\n",
    "display_prediction(10, params)\n",
    "display_prediction(50, params)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}