chapter02_mathematical-building-blocks.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%aimport tensor_toolbox\n",
    "%autoreload 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "# 2. The mathematical building blocks of neural networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "## 2.1 A first look at a neural network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "**Listing 2.1: Loading the MNIST dataset**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== train_images | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (60000, 28, 28) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================== train_labels | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (60000,) | nDims: 1 | dtype: uint8\n",
      "Content: [5 0 4 1 9 2 1 3 1 4 3 5 3 6 1 7 2 8 6 9]\n",
      "... (showing only the first 20 elements)\n",
      "\n",
      "==================== test_images | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (10000, 28, 28) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================== test_labels | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (10000,) | nDims: 1 | dtype: uint8\n",
      "Content: [7 2 1 0 4 1 4 9 5 9 0 6 9 0 1 5 9 7 3 4]\n",
      "... (showing only the first 20 elements)\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tensorflow.keras.datasets import mnist\n",
    "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
    "# In Keras over TensorFlow, MNIST data gets loaded as numpy arrays.\n",
    "tensor_toolbox.tensor_info(train_images, \"train_images\")\n",
    "tensor_toolbox.tensor_info(train_labels, \"train_labels\")\n",
    "tensor_toolbox.tensor_info(test_images, \"test_images\")\n",
    "tensor_toolbox.tensor_info(test_labels, \"test_labels\")\n",
    "\n",
    "# Draw first 9 images:\n",
    "tensor_toolbox.draw_grid(train_images[:10], train_labels[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== train_dataloader | tensor_info ====================\n",
      "Type: <class 'torch.utils.data.dataloader.DataLoader'>\n",
      "Batch size: 128\n",
      "-- First batch of features\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([128, 1, 28, 28]) | nDims: 4 | dtype: torch.float32\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "-- First batch of labels\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([128]) | nDims: 1 | dtype: torch.int64\n",
      "Content: tensor([5, 0, 4, 1, 9, 2, 1, 3, 1, 4, 3, 5, 3, 6, 1, 7, 2, 8, 6, 9])\n",
      "... (showing only the first 20 elements)\n",
      "\n",
      "\n",
      "==================== test_dataloader | tensor_info ====================\n",
      "Type: <class 'torch.utils.data.dataloader.DataLoader'>\n",
      "Batch size: 128\n",
      "-- First batch of features\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([128, 1, 28, 28]) | nDims: 4 | dtype: torch.float32\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "-- First batch of labels\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([128]) | nDims: 1 | dtype: torch.int64\n",
      "Content: tensor([7, 2, 1, 0, 4, 1, 4, 9, 5, 9, 0, 6, 9, 0, 1, 5, 9, 7, 3, 4])\n",
      "... (showing only the first 20 elements)\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from torchvision.datasets import MNIST\n",
    "from torchvision.transforms import ToTensor\n",
    "from torch.tensor_toolbox.data import DataLoader\n",
    "\n",
    "# PyTorch has objects Dataset to hold the samples and labels, and DataLoader to iterate easily.\n",
    "training_data = MNIST(\n",
    "    root='data',\n",
    "    train=True,\n",
    "    download=True,\n",
    "    transform=ToTensor()\n",
    ")\n",
    "# Dataloaders support automatic batching!\n",
    "batch_size = 128\n",
    "train_dataloader = DataLoader(training_data, batch_size=batch_size)\n",
    "test_data = MNIST(\n",
    "    root='data',\n",
    "    train=False,\n",
    "    download=True,\n",
    "    transform=ToTensor()\n",
    ")\n",
    "test_dataloader = DataLoader(test_data, batch_size=batch_size)\n",
    "\n",
    "tensor_toolbox.tensor_info(train_dataloader, \"train_dataloader\")\n",
    "tensor_toolbox.tensor_info(test_dataloader, \"test_dataloader\")\n",
    "# They are identical as both work in 128-sized batches.\n",
    "# Dimension corresponds to [Samples, Color, Height, Width]\n",
    "\n",
    "# Draw first nine images from first batch. I could iterate directly over the dataset, but didn't feel like it:\n",
    "X, y = next(iter(train_dataloader))\n",
    "tensor_toolbox.draw_grid(X[:10], [label.item() for label in y[:10]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "**Listing 2.2: The network architecture**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "from tensorflow import keras\n",
    "from tensorflow.keras import layers\n",
    "# Keras is very straightforward!\n",
    "model = keras.Sequential([\n",
    "    layers.Dense(512, activation=\"relu\"), # 512 units, ReLU activation\n",
    "    layers.Dense(10, activation=\"softmax\") # 10 units, softmax activation (one-hot encoded label)\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense (Dense)               (1, 512)                  401920    \n",
      "                                                                 \n",
      " dense_1 (Dense)             (1, 10)                   5130      \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 407050 (1.55 MB)\n",
      "Trainable params: 407050 (1.55 MB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Build the model and print the summary\n",
    "model.build(input_shape=(1,28*28))\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch import nn\n",
    "import torch.nn.functional as F\n",
    "# In PyTorch, models inherit from nn.Module. We define the layers in the constructor and the forward\n",
    "# prop in the function forward. More verbose but easier to customize.\n",
    "class TorchModel(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(TorchModel, self).__init__()\n",
    "        self.flatten = nn.Flatten() # Transforms the 28x28 image into a 1D tensor\n",
    "        self.stack = nn.Sequential(\n",
    "            nn.Linear(28*28, 512), # 512 units\n",
    "            nn.ReLU(), # ReLU activation\n",
    "            nn.Linear(512, 10) # 10 units\n",
    "        )\n",
    "    \n",
    "    def forward(self, x): # Forward prop\n",
    "        x = self.flatten(x)\n",
    "        output = self.stack(x)\n",
    "        return F.log_softmax(output, dim=1) # Log-softmax activation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----------------------------------------------------------------\n",
      "        Layer (type)               Output Shape         Param #\n",
      "================================================================\n",
      "           Flatten-1                  [-1, 784]               0\n",
      "            Linear-2                  [-1, 512]         401,920\n",
      "              ReLU-3                  [-1, 512]               0\n",
      "            Linear-4                   [-1, 10]           5,130\n",
      "================================================================\n",
      "Total params: 407,050\n",
      "Trainable params: 407,050\n",
      "Non-trainable params: 0\n",
      "----------------------------------------------------------------\n",
      "Input size (MB): 0.00\n",
      "Forward/backward pass size (MB): 0.01\n",
      "Params size (MB): 1.55\n",
      "Estimated Total Size (MB): 1.57\n",
      "----------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "# Torchsummary prints very similar information to Keras summary()\n",
    "torchmodel = TorchModel() # Instantiate the model\n",
    "\n",
    "from torchsummary import summary\n",
    "summary(torchmodel, input_size=(1, 28*28))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "**Listing 2.3: The compilation step**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Again, Keras is pretty straightforward here.\n",
    "model.compile( # Compile the model with the optimizer, loss function and metrics\n",
    "    optimizer='rmsprop',\n",
    "    loss='sparse_categorical_crossentropy',\n",
    "    metrics=['accuracy']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.optim as optim\n",
    "import torch.nn as nn\n",
    "\n",
    "import torch # Import PyTorch\n",
    "\n",
    "# Define RMSprop optimizer\n",
    "optimizer = optim.RMSprop(torchmodel.parameters())\n",
    "\n",
    "# Define loss function (CrossEntropyLoss for integer labels)\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "\n",
    "def train(train_dataloader, model, loss_fn, optimizer):\n",
    "    model.train()\n",
    "    total_loss = 0.0\n",
    "    total_correct = 0\n",
    "    total_samples = 0\n",
    "    \n",
    "    for X, y in train_dataloader: # Iterate over batches \n",
    "        # Compute prediction error\n",
    "        y_hat = model(X)\n",
    "        loss = loss_fn(y_hat, y)\n",
    "\n",
    "        # Backpropagation\n",
    "        optimizer.zero_grad() # Set gradients to zero\n",
    "        loss.backward() # Compute gradient\n",
    "        optimizer.step() # Update weights\n",
    "\n",
    "        # Accumulate loss and calculate accuracy\n",
    "        total_loss += loss.item()\n",
    "        total_correct += (torch.argmax(y_hat, dim=1) == y).sum().item()\n",
    "        total_samples += y.size(0)\n",
    "\n",
    "    # Calculate overall average loss and accuracy\n",
    "    avg_loss = total_loss / len(train_dataloader)\n",
    "    accuracy = total_correct / total_samples\n",
    "\n",
    "    return avg_loss, accuracy\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "**Listing 2.4: Preparing the image data**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== train_images | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (60000, 28, 28) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": 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mk4mioqIJ7QS9Wia9uOSeID8/nxtvvBGtVovX66Wrq4tkMinsnUQigcvloq+vb0gdOp1OHDN37lwWLFhAbm6uEFcgEMDpdBIIBAiFQvT19aHT6cSOX1OZSS+u3NxctFotxcXFLF68mJqaGrq7u2lqaiIej1NUVERRURF+v58333xzmLj0ej3FxcVYLBaWLFnC3XffjcFgEDZSOBwWfrLm5maOHj1KKpXC4XBMeFfC1TKpxQUIe0fuTQASiQR9fX0kk0nsdjt2u53c3FyMRiO5ubnCySr7owwGA3l5eeTn5+NwOIS45OFPpVIRiUQIhUIUFhYSj8cxGAxKz3WtG/BeodfrueGGG7Db7RQVFVFSUkI6ncZisWCxWBgYGKCjo4NUKkUwGMTlcgmxLFiwgIKCAsrLy4XtJvdKWq0Wq9UqbCuj0Ug6naa6uvqaJ5271kwZcRkMBsrLy8VktBwiI7sXBgYGaGtrIxaL4Xa7hfO1qKiI+fPnU1xcTEVFBTqdbsgTnTzhDFBQUEB1dTWgbMMHU0hcwJDeRp68HjwNM9jfpFKpkCRJTAVdzOkqD3+KoIYypcQlIzsuAeFfkt0WsqdcFszAwADHjx8X839z584V/imFizMlxTWSs1KlUgnRaTQa0csFAgHa2trw+XwiclTh8piS4hoJjUZDUVERFRUVSJJEQUEB4XAYrVZLOBwmJycHn8+H3+8nmUyKJ0aF0VHE9T/kbYgrKys5c+YMnZ2dwo/V1dWFRqOhubmZxsZGrFYrFRUVFBYWXutmX9co4vofarWagoICrFYrwWCQgoICbDYbsViMUCiESqUScfEqlUqEMyu21+go4vofss2lUqmw2WzU1tZis9k4deoUHo+HWCxGV1cX//73v7FYLHg8HoqLi4XzVavVikiIyTT5fDUod2EQGo0GSZIoLi7mtttuIxgMYjQaOX78OIlEgsbGRtxuN0ajkaqqKkpKSsjLy6OsrAyj0Uh1dbWIh1dQxDUMeT7SarWKKSOTySTi771eL9FoFLPZDIDZbEar1WIymcTUjzw1JD9xTtWhUxHXCMihx3q9nlmzZvHRj34Uj8dDS0sLra2tJJNJOjo6cLvd6HQ6Wlpa0Gq19Pb2Auc99Q6HA4fDIUJypuJQOfWu+DLQaDSYTCYkScLpdPKRj3wEr9fL3r17OXv2LLFYDJ/PJyJaZSes1+tFp9NRVFTEnDlzhkxwK+JSEIwUTeFwOCguLiYcDhMIBAiHw2KuUl7M0dfXhyRJ9PX14fV6RdyXVqsVUadTBUVcl8Bms1FTUyNsqRkzZuDz+Th69CgtLS1iyVokEsHlcnHgwAGMRiM9PT243W5sNhvz58+nsrISjUYj4uanAoq4LoHRaMRoNJLJZERkRX9/P+FwmEgkgs/nY2BgAACv14vX6xWee5VKJcJ77Ha7iGpVxKUwBPkpMi8vj1QqRUVFBdFoFK/XKxysfr+fgYEBsYy/p6eHRCJBa2ureAKVI2OnAoq4LhOVSoXJZEKv11NQUIDRaGTRokUMDAxw+vRpvF4vJ06cYP/+/QQCAVwuF16vF4PBQF9fHw0NDTidTmw226RZl3gpFHGNAdkwl6NRi4uLGRgYIJlM4vV6cbvdIlYsGAwSDAbFyupoNIperx/zkraJjCKuK2BwyI7JZKK8vBybzUZzc7NYACunA5Az6ahUKnp7e+nt7aWwsBCDwYDJZJrUT4+KuK4AObBQ7sXMZjOpVIrGxkZ0Ot0Qj3wymRRh03l5ebS2tmIwGLDb7SIwcbKiiGsMyKHRgEhnKTM4ovXCz8gBholEglQqJTLsTPYdoBVxXSaSJBGJRMQco9vtxu/3E4/H8fv9JBIJ3nnnHcLh8BDhyN5+o9GIw+GgrKyM8vJyTCbTpPfaT+6rG0cGe+BDoRCnTp0SyXPl187OTuG1l8nJycFsNmOz2YaIS84PMZlRxDUCg3OiJpNJke7S7XaLBHJutxuPx0MoFGJgYIBIJEIkEhkWYy9P+ciG/kgZbyYrirhGIJVKEQgESCQSdHV10dzcTCgUor29nfb2dqLRKD09PWI4jEaj4nVwojg5ANFgMGCxWMjLyxO22VRAEdcIyFkGo9EoLpeLY8eO4fP5aGxspLm5mXg8TigUIhKJjFrH4NRI8rTP4CRwU4Gpc6WjIOeFkLMQxuNxgsEgHR0dBINBWltbcblcBAIBfD6f2LxgpCVm8sJaOfmb3FtVV1dTWlpKVVUVBoPhGlzltWHKi0teTR2JRGhqahLRDEePHhX+qe7ubnFcLBYTCXsvxGg0YrfbMRqNzJs3j3nz5mEymZg9ezbTpk3DYDDgcDiuwVVeG6a0uAYv149Go/T399PV1YXL5eLMmTP09PQQiUTwer2XTLo7eGLbbDZTVlZGTU0NVquVG2+8kWnTpr1HV3X9MGXEJT/5ZTIZEokEsViMZDJJa2srHR0dhEIhzpw5Q3d3Nz6fj/7+fiKRCLFYbJizU61Wi3TeRqOR4uJi8Tp9+nTy8vJwOp1UVlaK3KdTkSkjrnQ6TTQaJZlMEggE6OvrIxKJcODAAQ4ePChCZOTwZTll+GAPu4xGoyE/P5/8/HxKSkpYvHgxxcXFlJeXM2vWLIxGozDi5amiqcikFpc87MkbPoVCISEun89HKBTC4/HQ09Mj/FWBQGBIHYPXMw5++rNYLNhsNgoLC3E4HJSWllJSUkJJSYmS+O1/TEpxyfN3kUiEU6dO0dXVJWyqWCxGIBDA4/EQj8c5e/YsbrebRCJBPB4fVpfRaMRms6HVaikvLxdrFKuqqnA4HFitVmbMmIHVasVisYhYeYVJLK5YLIbX6+XIkSO8++67hEIhuru7CYfDBINBvF6v2EXjYnsqynOCZrOZhQsXsnDhQiwWC06nk9LSUpHnfnDvpnCeCS0uediTdxmT7aRwOCx2znC73fT39xONRvH7/USjUeEgHekJUI7V0uv15OTkUFBQQGlpKWazGYfDQUFBASaTCZPJhMFgICcnR+mtRmFCiysejwvhyO6DcDhMf3+/eNprbGyku7tbeN3lp8WRnKByXq78/HxmzZpFfn4+TqeTuro6sbOYw+FAq9WKldYjhdkonGdCiyuVSuH3+wkGg7S0tHD48GGxr2FPT4/wtofD4UvWNdhgN5lMzJgxg5KSEmpra1m6dClWq1V44BUujwktLnnLOq/XS19fH/39/fh8PoLBoIhkkIe+wREJcmaawbkc1Go1hYWFmEwm7HY7TqdTpBGXbSrFnhobE1pckUiEs2fP4nK5OHXqFMePHycQCJBMJkkmk0N8VLJvSt60oLKyUoQkyyt7FixYwPTp04eEIRuNRiwWi5IH9QqY0OKSc8bLi1F9Pt8wPxX8f8y7vFmBzWajtLRUTCLLE81z5sxh9uzZaDQaDAbDlIm7yhYTWlx5eXnMnDmTwsJCiouLKSsrG3VHV3nnVp1OR0FBASUlJUMWU8iTznJUg9JLXT0qaQKvEpCndFKplHBFjHY5gw12tVo9zH0ge97lqRpFXFfPhBaXwvWN8vijkDUUcSlkDUVcCllDEZdC1lDEpZA1FHEpZA1FXApZQxGXQtZQxKWQNRRxKWQNRVwKWUMRl0LWUMSlkDUUcSlkDUVcCllDEZdC1vg/RapDe9qaqQIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================== train_images_reshaped | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (60000, 784) | nDims: 2 | dtype: float32\n",
      "train_images_reshaped[0]: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "... (showing only the first 20 elements)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# In tf, we used the numpy array operation reshape and divided by the scalar 255\n",
    "# so that all values go between 0 and 1.\n",
    "# The MNIST dataset loaded in PyTorch is already normalized, and it gets flattened\n",
    "# in the input of the neural network.\n",
    "tensor_toolbox.tensor_info(train_images, \"train_images\")\n",
    "train_images_reshaped = train_images.reshape((60000, 28 * 28)).astype(\"float32\") / 255\n",
    "test_images_reshaped = test_images.reshape((10000, 28 * 28)).astype(\"float32\") / 255\n",
    "tensor_toolbox.tensor_info(train_images_reshaped*255, \"train_images_reshaped\", image=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "**Listing 2.5: \"Fitting\" the model**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/5\n",
      "469/469 [==============================] - 1s 2ms/step - loss: 0.2522 - accuracy: 0.9276\n",
      "Epoch 2/5\n",
      "469/469 [==============================] - 1s 2ms/step - loss: 0.1013 - accuracy: 0.9699\n",
      "Epoch 3/5\n",
      "469/469 [==============================] - 1s 2ms/step - loss: 0.0668 - accuracy: 0.9802\n",
      "Epoch 4/5\n",
      "469/469 [==============================] - 1s 2ms/step - loss: 0.0489 - accuracy: 0.9849\n",
      "Epoch 5/5\n",
      "469/469 [==============================] - 1s 2ms/step - loss: 0.0370 - accuracy: 0.9888\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.src.callbacks.History at 0x31d031c50>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(train_images_reshaped, train_labels, epochs=5, batch_size=128)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/5\n",
      "Average Loss: 0.9796, Accuracy: 0.9185\n",
      "Epoch 2/5\n",
      "Average Loss: 0.1373, Accuracy: 0.9601\n",
      "Epoch 3/5\n",
      "Average Loss: 0.1014, Accuracy: 0.9706\n",
      "Epoch 4/5\n",
      "Average Loss: 0.0816, Accuracy: 0.9766\n",
      "Epoch 5/5\n",
      "Average Loss: 0.0733, Accuracy: 0.9792\n"
     ]
    }
   ],
   "source": [
    "# Manually write the loop in PyTorch!\n",
    "epochs = 5\n",
    "for epoch in range(1, epochs + 1):\n",
    "    print(f\"Epoch {epoch}/{epochs}\")\n",
    "    avg_loss, accuracy = train(train_dataloader, torchmodel, criterion, optimizer)\n",
    "    print(f\"Average Loss: {avg_loss:.4f}, Accuracy: {accuracy:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "**Listing 2.6: Using the model to make predictions**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Keras predictions | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (1, 10) | nDims: 2 | dtype: float32\n",
      "Content: [[3.1102139e-13 8.4679232e-07 1.0307289e-09 1.7857026e-08 9.9955875e-01\n",
      "  1.6810060e-09 6.1202233e-12 2.1882030e-05 5.6759120e-07 4.1789198e-04]]\n",
      "\n",
      "==================== PyTorch predictions | tensor_info ====================\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([1, 10]) | nDims: 2 | dtype: torch.float32\n",
      "Content: tensor([[2.5503e-18, 1.9363e-12, 1.1503e-15, 1.2043e-17, 9.9999e-01, 1.7735e-08,\n",
      "         4.3232e-15, 2.6740e-08, 2.1523e-12, 8.2600e-06]])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test_image = test_images_reshaped[42].reshape((1, 28 * 28))\n",
    "test_label = test_labels[42]\n",
    "\n",
    "# Keras: predict() method returns the probabilities of each class.\n",
    "keras_prediction = model.predict(test_image, verbose=0)\n",
    "tensor_toolbox.tensor_info(keras_prediction, \"Keras predictions\")\n",
    "\n",
    "#PyTorch: torch.softmax() returns the probabilities of each class.\n",
    "test_images_tensor = torch.tensor(test_image) # Convert numpy array to PyTorch tensor\n",
    "torchmodel.eval() # Set the model to evaluation mode\n",
    "with torch.no_grad(): \n",
    "    logits = torchmodel(test_images_tensor) # Compute the logits without gradient tracking\n",
    "\n",
    "torch_prediction = torch.softmax(logits, dim=1) \n",
    "tensor_toolbox.tensor_info(torch_prediction, \"PyTorch predictions\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Keras predicts: 4. PyTorch predicts: 4. The label is 4.\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(f\"Keras predicts: {keras_prediction.argmax()}. PyTorch predicts: {torch_prediction.argmax()}. The label is {test_label}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "**Listing 2.7: Evaluating the model on new data**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "313/313 [==============================] - 0s 551us/step - loss: 0.0645 - accuracy: 0.9811\n"
     ]
    }
   ],
   "source": [
    "test_loss, test_acc = model.evaluate(test_images_reshaped, test_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Avg. Test Loss: 0.0014046594604544226\n",
      "Test Accuracy: 0.9647\n"
     ]
    }
   ],
   "source": [
    "torchmodel.eval()  # Set the model to evaluation mode\n",
    "\n",
    "test_loss = 0.0\n",
    "correct_predictions = 0\n",
    "total_predictions = 0\n",
    "\n",
    "with torch.no_grad():\n",
    "    for X, y in test_dataloader:\n",
    "        y_hat = torchmodel(X) # Compute the predictions\n",
    "        loss = criterion(y_hat, y) # Compute the loss\n",
    "        test_loss += loss.item() # Accumulate the loss\n",
    "\n",
    "        # For accuracy, we need to count the number of correct predictions\n",
    "        predicted = torch.argmax(y_hat, 1) # Get the predicted class\n",
    "        total_predictions += y.size(0) # Accumulate the number of samples\n",
    "        correct_predictions += (predicted == y).sum().item()\n",
    "\n",
    "test_loss /= len(test_dataloader.dataset)\n",
    "test_accuracy = correct_predictions / total_predictions\n",
    "\n",
    "print(f\"Avg. Test Loss: {test_loss}\")\n",
    "print(f\"Test Accuracy: {test_accuracy}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Evaluating Keras model 'sequential' ====================\n",
      "loss: 0.0644795373082161\n",
      "accuracy: 0.9811000227928162\n",
      "==================== Evaluating PyTorch model 'TorchModel' =================\n",
      "Test loss: 0.1797945648431778 | Test accuracy: 0.9647\n"
     ]
    }
   ],
   "source": [
    "# We can also use the awful tensor_toolbox.py file to do this for us.\n",
    "tensor_toolbox.model_eval(model, test_tuple=(test_images_reshaped, test_labels))\n",
    "tensor_toolbox.model_eval(torchmodel, test_tuple=(test_images_reshaped, test_labels)) # This would also 'work' passing a DataLoader object."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "## 2.2 Data representations for neural networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Scalars (rank-0 tensors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Numpy scalar | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: () | nDims: 0 | dtype: int64\n",
      "Content: 12\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "x = np.array(12)\n",
    "tensor_toolbox.tensor_info(x, \"Numpy scalar\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== PyTorch scalar | tensor_info ====================\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([]) | nDims: 0 | dtype: torch.int64\n",
      "Content: 12\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "x = torch.tensor(12)\n",
    "tensor_toolbox.tensor_info(x, \"PyTorch scalar\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== TensorFlow scalar | tensor_info ====================\n",
      "Type: <class 'tensorflow.python.framework.ops.EagerTensor'>\n",
      "Shape: () | nDims: 0 | dtype: <dtype: 'int32'>\n",
      "Content: 12\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "x = tf.constant(12)\n",
    "tensor_toolbox.tensor_info(x, \"TensorFlow scalar\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Vectors (rank-1 tensors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Numpy vector | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (5,) | nDims: 1 | dtype: int64\n",
      "Content: [12  3  6 14  7]\n",
      "\n",
      "==================== TensorFlow vector | tensor_info ====================\n",
      "Type: <class 'tensorflow.python.framework.ops.EagerTensor'>\n",
      "Shape: (5,) | nDims: 1 | dtype: <dtype: 'int64'>\n",
      "Content: [12  3  6 14  7]\n",
      "\n",
      "==================== PyTorch vector | tensor_info ====================\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([5]) | nDims: 1 | dtype: torch.int64\n",
      "Content: tensor([12,  3,  6, 14,  7])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x = np.array([12, 3, 6, 14, 7])\n",
    "tensor_toolbox.tensor_info(x, \"Numpy vector\")\n",
    "x = tf.constant(x)\n",
    "tensor_toolbox.tensor_info(x, \"TensorFlow vector\")\n",
    "x = torch.tensor(np.array(x))\n",
    "tensor_toolbox.tensor_info(x, \"PyTorch vector\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Matrices (rank-2 tensors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Numpy matrix | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (3, 5) | nDims: 2 | dtype: int64\n",
      "Numpy matrix[0]: [ 5 78  2 34  0]\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIsAAABYCAYAAADFswR+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/H5lhTAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAJRElEQVR4nO3da0gU3R8H8O88m7q66y20NLPMFCkrKgwpytXstiXZjS6ku22a9cIUygrs4oUylTTtImqEmm50WSIoC40yfVVIZgldrNSSNAszky6G63lehPNvn9U6ror/6vd51ZyZM+c303ePM+NsCYwxBkI4/DPcBZDfB4WFcKOwEG4UFsKNwkK4UVgINwoL4UZhIdwoLIQbheUP4+/vD39//yHZd7/Ckp+fD0EQIJVK8fr1a6P1/v7+mDJlyqAV9zdrampCfHw8qqurh7sUkUkzS2dnJ5KTkwe7FvKDpqYmJCQk9DsspaWlKC0tHZKaTArL9OnTcerUKTQ1NQ12PcREnz9/BgCYm5vD3Nx8SMYwKSyxsbHQ6/W/nF0aGhogCALy8/ON1gmCgPj4eHE5Pj4egiCgtrYWISEhsLW1haOjI/bv3w/GGBobGxEcHAwbGxs4OTkhLS3NYH+3b9+GIAg4f/48YmNj4eTkBJlMhuXLl6OxsVHcLi4uDmZmZnj37p1RTREREbCzs8PXr1/7PKZNmzZBLpfj1atXCAoKglwuh4uLC06ePAkAqKmpwfz58yGTyTB+/HicPXvWoP/79+8RExODqVOnQi6Xw8bGBkqlEg8ePDA4llmzZgEANBoNBEEwOI89P+7v3bsHPz8/WFlZITY2Vlz34zWLWq2GVCrF48ePDepYvHgx7O3t+/WBNyksEyZMgEqlGpLZZd26deju7kZycjJ8fX1x8OBBZGRkYOHChXBxcUFKSgo8PDwQExODiooKo/6HDh1CcXEx9uzZg6ioKNy4cQMLFizAly9fAAChoaHo6urC+fPnDfp9+/YNOp0Oq1evhlQq/WmNer0eSqUSrq6uSE1NhZubGyIjI5Gfn48lS5bAx8cHKSkpsLa2hkqlQn19vdi3rq4Oly9fRlBQENLT07Fr1y7U1NRAoVCI53LSpElITEwE8D3AhYWFKCwshJ+fn7if1tZWKJVKTJ8+HRkZGQgICOi11szMTDg6OkKtVkOv1wMAcnJyUFpaiuPHj2PMmDG/+iv5H9YPeXl5DACrrKxkL168YCNGjGBRUVHieoVCwby9vcXl+vp6BoDl5eUZ7QsAi4uLE5fj4uIYABYRESG2dXV1sbFjxzJBEFhycrLY3tbWxiwtLZlarRbbysrKGADm4uLCPn78KLZfuHCBAWCZmZli2+zZs5mvr69BPZcuXWIAWFlZ2U/PgVqtZgBYUlKSUT2CILBz586J7U+ePDE6zq9fvzK9Xm+wz/r6emZhYcESExPFtsrKyj7PnUKhYABYdnZ2r+sUCoVBW0lJCQPADh48yOrq6phcLmcrVqz46XH2xuRbZ3d3d4SGhiI3NxfNzc2m7sZIeHi4+GeJRAIfHx8wxhAWFia229nZwcvLC3V1dUb9VSoVrK2txeU1a9bA2dkZ165dM9jm7t27ePHihdim1Wrh6uoKhULR7zp76pHJZFi7dq3Y7uXlBTs7O4M6LSws8M8/30+7Xq9Ha2sr5HI5vLy8UFVVxTV2z340Gg3XtosWLcLWrVuRmJiIVatWQSqVIicnh3usHgN6zrJv3z50dXUN6p3RuHHjDJZtbW0hlUrh4OBg1N7W1mbU39PT02BZEAR4eHigoaFBbFu3bh0sLCyg1WoBAO3t7bh69So2btwIQRB+WaNUKoWjo6NRPWPHjjXq/986u7u7cfToUXh6esLCwgIODg5wdHTEw4cP0d7e/suxe7i4uPTrQvbIkSMYOXIkqqurcezYMYwaNYq7b48BhcXd3R0hISF9zi59nfien529kUgkXG0AwEx8I9Te3h5BQUFiWHQ6HTo7OxESEsLVv696eOpMSkrCjh074Ofnh6KiIpSUlODGjRvw9vZGd3c39zFYWlpybwsA9+/fx9u3bwF8vwg3xQiTev1g3759KCoqQkpKitE6e3t7AMCHDx8M2l++fDnQYfv07Nkzg2XGGJ4/f45p06YZtKtUKgQHB6OyshJarRYzZsyAt7f3kNXVQ6fTISAgAKdPnzZo//Dhg8HsyTPD8fr06RM0Gg0mT56MOXPmIDU1FStXrhTvuHgN+HH/xIkTERISgpycHLx588ZgnY2NDRwcHIzuWrKysgY6bJ/OnDmDjo4OcVmn06G5uRlKpdJgO6VSCQcHB6SkpKC8vJx7VhkoiURiNCNevHjR6Im4TCYDYPxBM8WePXvw6tUrFBQUID09HW5ublCr1ejs7OzXfgY8swDA3r17UVhYiKdPnxp9OsPDw5GcnIzw8HD4+PigoqICtbW1gzFsr0aOHIm5c+dCo9GgpaUFGRkZ8PDwwJYtWwy2MzMzw/r163HixAlIJBJs2LBhyGr6UVBQEBITE6HRaDBnzhzU1NRAq9XC3d3dYLuJEyfCzs4O2dnZsLa2hkwmg6+vLyZMmNCv8W7duoWsrCzExcVh5syZAIC8vDz4+/tj//79SE1N5d7XoPwi0cPDo89P5oEDBxAWFgadTofdu3dDr9fj+vXrgzFsr2JjY7Fs2TIcPnwYmZmZCAwMxM2bN2FlZWW0rUqlAgAEBgbC2dl5yGr6b307d+5ESUkJoqOjUVVVheLiYri6uhpsZ2ZmhoKCAkgkEmzbtg0bNmxAeXl5v8bq6OjA5s2bMWPGDOzdu1dsnzdvHqKjo5GWloY7d+7w77DfN9v/p3qes1y8eJG7T3V1NQPAzpw5M4SV/Tn+6lcUTp06BblcjlWrVg13Kb+FQblm+d1cuXIFjx49Qm5uLiIjI8WLSfJzf2VYtm/fjpaWFixduhQJCQnDXc5vQ2CMvutM+PzV1yykfygshBuFhXAb1gvcgT7KHj16tMl9f/yVgClyc3NN7hsZGTmgsYcLzSyEG4WFcKOwEG4UFsKNwkK4UVgINwoL4UZhIdwoLIQbhYVwo7AQbhQWwo3CQrhRWAi3YX1F4WffeebR1dX1V47d13eqhxrNLIQbhYVwo7AQbhQWwo3CQrhRWAg3CgvhRmEh3CgshBuFhXCjsBBuFBbCjcJCuFFYCLff+hWF/vzz5YM99kD60ysK5I9HYSHcKCyEG4WFcKOwEG4UFsKNwkK4UVgINwoL4UZhIdwoLIQbhYVwo7AQbhQWwo3CQrjR/2RGuNHMQrhRWAg3CgvhRmEh3CgshBuFhXCjsBBuFBbCjcJCuP0LKMRWLwyhgtQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================== TensorFlow matrix | tensor_info ====================\n",
      "Type: <class 'tensorflow.python.framework.ops.EagerTensor'>\n",
      "Shape: (3, 5) | nDims: 2 | dtype: <dtype: 'int64'>\n",
      "TensorFlow matrix[0]: [ 5 78  2 34  0]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================== PyTorch matrix | tensor_info ====================\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([3, 5]) | nDims: 2 | dtype: torch.int64\n",
      "PyTorch matrix[0]: tensor([ 5, 78,  2, 34,  0])\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[5, 78, 2, 34, 0],\n",
    "              [6, 79, 3, 35, 1],\n",
    "              [7, 80, 4, 36, 2]])\n",
    "tensor_toolbox.tensor_info(x, \"Numpy matrix\")\n",
    "x = tf.constant(x)\n",
    "tensor_toolbox.tensor_info(x, \"TensorFlow matrix\")\n",
    "x = torch.tensor(np.array(x))\n",
    "tensor_toolbox.tensor_info(x, \"PyTorch matrix\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Rank-3 and higher-rank tensors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Numpy tensor | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (3, 3, 5) | nDims: 3 | dtype: int64\n",
      "\n",
      "==================== TensorFlow tensor | tensor_info ====================\n",
      "Type: <class 'tensorflow.python.framework.ops.EagerTensor'>\n",
      "Shape: (3, 3, 5) | nDims: 3 | dtype: <dtype: 'int64'>\n",
      "\n",
      "==================== PyTorch tensor | tensor_info ====================\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([3, 3, 5]) | nDims: 3 | dtype: torch.int64\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]],\n",
    "              [[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]],\n",
    "              [[5, 78, 2, 34, 0],\n",
    "               [6, 79, 3, 35, 1],\n",
    "               [7, 80, 4, 36, 2]]])\n",
    "tensor_toolbox.tensor_info(x, \"Numpy tensor\")\n",
    "x = tf.constant(x)\n",
    "tensor_toolbox.tensor_info(x, \"TensorFlow tensor\")\n",
    "x = torch.tensor(np.array(x))\n",
    "tensor_toolbox.tensor_info(x, \"PyTorch tensor\")\n",
    "# Can't visualize this one, but trust me it's a 3D tensor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Key attributes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "# These are included in tensor_toolbox.tensor_info()!\n",
    "from tensorflow.keras.datasets import mnist\n",
    "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_images.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_images.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('uint8')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_images.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== train_images | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (60000, 28, 28) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "tensor_toolbox.tensor_info(train_images, \"train_images\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "**Listing 2.8: Displaying the fourth digit**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# tensor_toolbox.py is your friend\n",
    "import matplotlib.pyplot as plt\n",
    "digit = train_images[4]\n",
    "plt.imshow(digit, cmap=plt.cm.binary)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tensor_toolbox.draw_image(train_images[4], train_labels[4], size=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Manipulating tensors in NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== my_slice | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (90, 28, 28) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# They are all the same!\n",
    "my_slice = train_images[10:100]\n",
    "my_slice = train_images[10:100, :, :]\n",
    "my_slice = train_images[10:100, 0:28, 0:28]\n",
    "tensor_toolbox.tensor_info(my_slice, \"my_slice\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== my_slice | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (60000, 14, 14) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================== whole picture | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (28, 28) | nDims: 2 | dtype: uint8\n",
      "whole picture[0]: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      "... (showing only the first 20 elements)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "my_slice = train_images[:, 14:, 14:]\n",
    "tensor_toolbox.tensor_info(my_slice, \"my_slice\")\n",
    "tensor_toolbox.tensor_info(train_images[0], \"whole picture\")\n",
    "# You can see that the first 14 pixels are the bottom right corner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== my_slice | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (60000, 14, 14) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "my_slice = train_images[:, 7:-7, 7:-7]\n",
    "tensor_toolbox.tensor_info(my_slice, \"my_slice\")\n",
    "# This 'cuts' the margins"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### The notion of data batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== batch | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (128, 28, 28) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================== batch | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (128, 28, 28) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================== batch | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (128, 28, 28) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "batch = train_images[:128] #First batch\n",
    "tensor_toolbox.tensor_info(batch, \"batch\")\n",
    "batch = train_images[128:256] # Second batch\n",
    "tensor_toolbox.tensor_info(batch, \"batch\")\n",
    "n = 42\n",
    "batch = train_images[128 * n:128 * (n + 1)] # n-th batch\n",
    "tensor_toolbox.tensor_info(batch, \"batch\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== batch | tensor_info ====================\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([128, 1, 28, 28]) | nDims: 4 | dtype: torch.float32\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Using PyTorch DataLoader, batches are automatically implemented.\n",
    "# Retrieve batch n from train_dataloader in a wildly inefficient way:\n",
    "for i, (X, y) in enumerate(train_dataloader):\n",
    "    if i == n:\n",
    "        batch = X\n",
    "        break\n",
    "tensor_toolbox.tensor_info(batch, \"batch\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "## The gears of neural networks: tensor operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Element-wise operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "# These are wild!\n",
    "def naive_relu(x):\n",
    "    assert len(x.shape) == 2\n",
    "    x = x.copy()\n",
    "    for i in range(x.shape[0]):\n",
    "        for j in range(x.shape[1]):\n",
    "            x[i, j] = max(x[i, j], 0)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "def naive_add(x, y):\n",
    "    assert len(x.shape) == 2\n",
    "    assert x.shape == y.shape\n",
    "    x = x.copy()\n",
    "    for i in range(x.shape[0]):\n",
    "        for j in range(x.shape[1]):\n",
    "            x[i, j] += y[i, j]\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "def np_version (x, y, iters):\n",
    "    for _ in range(iters):\n",
    "        z = x + y\n",
    "        z = np.maximum(z, 0.)\n",
    "\n",
    "def tf_version (x, y, iters):\n",
    "    x = tf.convert_to_tensor(x)\n",
    "    y = tf.convert_to_tensor(y)\n",
    "    for _ in range(iters):\n",
    "        z = x + y\n",
    "        z = tf.maximum(z, tf.constant(0., dtype=z.dtype))\n",
    "\n",
    "def torch_version (x, y, iters):\n",
    "    x = torch.tensor(x)\n",
    "    y = torch.tensor(y)\n",
    "    for _ in range(iters):\n",
    "        z = x + y\n",
    "        z = torch.max(z, torch.tensor(0.))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "def naive_version (x, y, iters):\n",
    "    for _ in range(5000):\n",
    "        z = naive_add(x, y)\n",
    "        z = naive_relu(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trying np_version\n",
      "np_version succeeded\n",
      "Took: 0.01100 s\n",
      "\n",
      "Trying tf_version\n",
      "tf_version succeeded\n",
      "Took: 0.23346 s\n",
      "\n",
      "Trying torch_version\n",
      "torch_version succeeded\n",
      "Took: 0.03248 s\n",
      "\n",
      "Trying naive_version\n",
      "naive_version succeeded\n",
      "Took: 4.17032 s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Fun Function:\n",
    "x = np.random.random((20, 100))\n",
    "y = np.random.random((20, 100))\n",
    "tensor_toolbox.function_race([np_version, tf_version, torch_version, naive_version], [x, y, 5000]) \n",
    "# I wouldn't give a lot of value to this results but it's fun."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Broadcasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== X | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (32, 10) | nDims: 2 | dtype: float64\n",
      "X[0]: [0.3250931  0.61506914 0.38978521 0.74487887 0.94132154 0.56439668\n",
      " 0.00359465 0.60419574 0.3071076  0.65458413]\n",
      "... (showing only the first 20 elements)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACwAAAB3CAYAAAB4zaI1AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/H5lhTAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAU8klEQVR4nO2bSWxb19n3f/dyuJwpipMoUbIGu7FleYzjeECRFh2SIEEXdRMgSLprgKJos+iiQNftoqsW7aZAgaJtCjRFixQxkDqb1E4cx3U9qrYkQ7I1mZpIihRnXl5e3vMugntav+8HhEFpfN+Lzw+ghSjp3J8Oz3mG//NQEUII/heZ+n8b4LPaY+BHbY+BH7U9Bn7U9hj4Udv/v8CvvfYaHo+HhYWF//Gzn/zkJyiKwrvvvvufP0j0yLLZrIhEIuKLX/ziQ68vLS0Jr9crzpw505Pn9AxYCCF+9atfCUD89re/la8999xzIhQKibW1tZ48o6fAlmWJ06dPi1gsJra3t8Vbb70lAPGLX/yiZ8/oKbAQQszMzAiXyyVeeuklMTAwII4dOyY6nU7P1u85sBBC/PCHPxSAcDgc4saNGz1d+5G4tVgsBsDg4CBTU1O9Xbyn/74Q4sGDByIQCIipqSkBiB/96Ec9Xb/nwF/72tdEIBAQmUxGvPTSS8Lj8YjFxcWerd9T4L/85S8CED/72c+EEEKsr6+LUCgknnvuuZ49o2fAlUpFpNNpceTIEWGapnz95z//uQDEn/70p548p2fAb7zxhlBVVVy9evWh103TFEePHhWDg4OiUqn8x8/pCfD169eFw+EQ3/3ud/+PP7969apQVVW88cYb//GzFCEe6xKP1B4DP2p7DPyo7THwozZnt7/49ttvY1kW9+/f5/79+wQCAcbHx/F6vczMzDAzM0O9XufBgwfous6hQ4c4cOAAo6OjvPzyy6RSKc6dO8d7771HIBDgwIEDBINBZmdnmZubw7Is/vjHP/YO2DAMOp0OnU4HIQSWZcnvFUXB7Xaj6zoOhwNVVeWXoiiYpkm73abdbmOaplwDQFVVHA5HtxjdA//5z39+6PtGo0Gr1cLtdhMKhXjmmWfY2dnh+vXrlEolBgcHicfjOJ1Opqen0TSNjz/+mGvXrpFIJBgZGUHTNILBIOPj43QbcLsG/tvf/oaiKKTTaQYHB1EUhWKxiMPh4NSpUxw7dox8Pk8+n8fn85FIJIhGo3Q6HRYWFmi1WkxPTzM7O0ulUqFSqdDf34/f78fj8XSL0T1wMplEURSGh4cZGxvDsizq9TqdTgdN0zBNE9M0/7Ww04nH46HT6aDrOqqqEg6HGRoaIhgMsrS0RKlUYnh4mOHhYVS1u/vfNfDU1BQOh4OpqSmmpqZoNptkMhmazSbBYJBWq4VhGFiWhaIoeDwewuEw7XabRqNBp9ORYJVKhQsXLtBsNnnttdd45plncDq7Q+ka2Ol0yguiqioulwu/34/T6cTtdmNZFgCapsm3WNd1DMOg2WzKXQ4EArTbbRRFQQiBoijygvYU+MGDB/IhOzs7hEIhxsfHCQQCiE/yanw+H5OTk+i6TrFY5MKFC7RaLcrlMu12m76+PkKhEH6/n3Q6jdPpZGxsjFwuh6qqXVXYXQOXy2UA3G43pmmSTCbZv38/0WiUer1Oo9HA5XKRTCYxTZNcLsfi4iK6rtNoNLAsC6fTSSwWw+/3MzQ0hNfrxev1UqvVUBSlK46ugc+cOQNAq9Wi1WqhaRorKytsbm5K3+r3+xkbG8Pj8bC6uoqmaYTDYUZHRwkEAvT39xOJROSRUlWVYDBIKBTqFqN74G9/+9t0Oh3m5ua4e/cu1WqVubk5ms0mLpcLp9NJOp3m+PHjJJNJFhYW8Hg8DA0N8fWvf53h4WF5dHRdZ2tri1arRSwWIxqN9n6Hl5eXEUJQr9fxeDxYlkVfXx8ejwdN03C5XPT19eF2u3E4HIRCIVKpFPF4HK/Xi8vlIp/PUygUaDabFAoF2u02Xq+XVCrV9aXruqY7efIkDoeD48ePc+LECZxOJy6XC4fDgaZp8isej+N2u8nlcmSzWTRNI5FI4HA4eOeddzh79iydTgcAl8vFq6++yiuvvCK9zqdZ1zs8NzeHw+Hgc5/7nHRdwWAQp9OJz+fD6/VK99TpdAgEAg+5wna7zdbWFrOzs1iWhdvtxufzUSqV5FHpxj7TpXM4HExOTqJpGrVajenpaRqNBpOTk+zbtw/DMNja2sIwDIaHh0mn0xiGQaFQkFHR3sVQKISmaczPz/O73/0Oh8PB9773vd4BP//88wDyPDYaDW7cuEE2m8XlcjE6Okq1WmVhYYFqtUooFGJycpJGo0Emk6FcLmNZFn6/H1VViUQiaJrG8vIyy8vLAL0FrtVqwCfpoKZpGIZBuVymWCyytbXF6uoqhmFgmiaqqrK8vEyz2aTZbLKxsSF97cGDB+WuNxoNYrEYiUSi915ibW0NRVGwLAtN06jX66yvr7O0tEQwGMSyLDweD/39/bhcLt5//31u3bqFaZoIIVBVlRdeeIHXX3+dTCbDm2++ycbGBocOHeJLX/pS1zlx18CKouBwOGTst+GFELRaLWq1Gp1OB4/Hg8PhYGdnh2w2i6IoeL1ePB6PXMPlchEIBAiFQrhcrs906bp2a+fOnZOVhR3l/vCHP5DJZBgaGmJwcBBd11lZWaHZbNLpdLAsi3g8zsmTJ4lGo6ysrLCyskJ/fz8nT56kr6+PGzducPPmTSzL4sKFC5/K0fUOp9NpAFkW+f1+otEouq7LrE3XdRYXFykWi6TTadLpNENDQ5w4cYJUKsXi4iIffvgh+/fv5/XXX2dycpLbt2/z97///aFcuifAdvLj8/nw+/2EQiHi8TimaVKtVpmfn6dardJut3E6nbTbbSqVikyK7GPhcDgwDIP79+8jhCCVSvHqq6/KYNIzYDsFHBoaIhQK0Wq12LVrF263mytXrnD16lUAeUZbrRaFQoFkMonb7SYYDMow3mw2uXXrFltbW0xNTfHiiy/2Ph+2K2XDMNB1nVarRbvdlhctFotJjwDQ19dHOBwmFothWRbNZhOv18vAwADhcBhN02RYDwQCvQe2F9zZ2aFWq1EsFllfX2dnZ4exsTEmJyep1+vS/x49epQjR47gdrtpNpvcv3+fVCrFN77xDdxuN/F4HJ/PRyQSkd6np8D2zum6Tr1ep1KpyDoumUwyNDREpVKhVCrhdDpJpVLs3r2bTqdDsVik0Wjg8XgYGRlBVVUZMVVVlSVTT4HX19dleVQqlfD5fBw6dAi/3y89R7vdxu1243Q6qVQqrKys4HK50DQNn89HvV6n1WphmibFYhHTNLl16xaVSgUhBD/96U97B7yxsYFlWWQyGTKZDBMTE7z44ouMj4+zsrLC6uqq9AgOh4NKpcKDBw8IBALs2rULj8dDs9mk3W7TbDbJZrM0Gg2uXbsm/XBPgdvttqxy3W43iqJQKpXI5XJUKhUMwwAgGAwC/6r97OI0EAiQy+XI5XIyrDcaDYLBIEePHu19emkYBkIImaS7XC7u3btHNpul3W5LTSKdTtPpdGi1Wui6TjgcJpFI0N/fz507d5ienqZcLrO0tISu6zz//PO88MILvc8lfD4fQgja7Ta6rmNZFo1GQ+YVDodDahbwiVex35FWq0Wj0UDXdfnP2Rf23/WNbqzrXOLq1at0Oh0+/PBDLl68SCAQ4IknnpC1WyqVkv7WVieFEJRKJWZmZiiXyzidThkF7UsHSA/xzjvvfCpH1zv81FNP0W63mZubkyqOfeN9Ph/JZBLLsqhUKrTbbVwul/TBV65cYWlpiSeffJKjR4+iKArRaJR2u83NmzflpevGuga29YdWqyWlqEwmQzabpdVqUalUcLvdspbb3t6mXq+ztrYGfHKk7NBs13PwSTXudDp7D3zv3j2pWIbDYarVKrOzszSbTZaWlkgkEsRiMY4ePUo4HGZpaYnFxUXq9TqAlKm8Xi+hUIjR0VE0TWNhYQFN03qf/LTbbVlVxGIxPB6PFPp8Ph+dTodms0k+n0fXdWq1mryEmqYB4PF48Hg8uFwueX4dDgfhcLj36WW73QZgbGyM0dFR6RmEENy5c4fZ2Vl0Xef8+fOYpsnu3bsZHx+Xulqz2WRoaIjR0VEMw2BpaUl6mSeffLL3R8J+y0KhEMFgEJfLRTgclkr80tIS9Xqdzc1NarUaqVSKYDCIw+GQ59Xr9RIIBGTOYefY0Wi0W4zuge36zE4rhRCsra0hhMDj8XD69GnW1tbIZDLUajXq9TrZbJZOpyMjYz6f59q1a9RqNe7du0ej0XhIT34kwDasruvk83na7TaTk5McOXKE+fl53n//fRRFkcC2e9M0jXw+L9PP9fV1dF0nGo0SiUR6n63lcjmZR9itgGq1iq7rLC8vo+s6hUKBkZER/H6/FFvcbrdMJe2SCWB4eFgK5I9Eqrpx44a8ZNFolFqtxvr6OuVymevXr0vYM2fOMDg4yAcffCAjYiqVIhQKkc1mKRQKJBIJnn32WeLxOLdv3+bOnTu9v3SGYaCqKqZpyqai7da2t7fZ2NggEAgQDAZJJBJ4PB4pfP/3Pobb7SYajZJMJqU20XM//NRTT6GqKqlU6n+UNHZjpt1us7KygmEY5PN5WQc2Gg2cTifxeJxgMEg0GiUUCuF2u0kkEuzZs6dbjO6BJyYmpIqjKMpDwLakalkW2WwWIYR0WXaq2Wq1CAaDsk/n8/lk0BgcHOw9cDKZBJBvr33zNU2TqaHb7Zb1ndPpZHh4GMMwqFarVKtVotEoAwMDKIpCNpsFkMpnz4EnJiZky6Ber6PrOj6fT/ab7Wbi2NgYe/bs4fjx4/h8PlZXV/n973/P5uYm+/btY8+ePZRKJa5cuUKpVOLEiRMcPny46wS+63kJwzBkdevxeGQz0TRNnE6n7L/Z2oX9ez6fj3A4TF9fH5qmIYSQx6TZbFIulykUCmxvb3fF0fUO3717F1VVpWbW6XQolUpsbGwQi8XYvXs3gUCAjY0NKpUKIyMj8vdOnz5Ns9nE4XCQzWYpFotUq1VqtRofffQRly5dAuDXv/5174BLpRKqqjIwMCAzLsMwpN4wMDCA0+mkVqvRbDYJBAKEw2H5NwCFQoFCoYCu67K3l8/n2d7e7toPd10iXbhwASEE9+/fZ3FxUYrUiqLQ6XSkf7aLVVufCIfD7Nu3j1AoRKPRkPkxgGVZXLlyhStXrmBZFtPT05/K0fUOP/300xiGwQcffMAvf/lLRkdH+c53vsP4+PhD6WWpVKLVapHNZslms6TTaTlnYe9NJBKRIkwul+Py5cu9z4dtKTUej3Ps2DH6+vpoNBryzNo7rKoqTqeTvr4+XC4XsVhMNshDoRChUEj2QOwkKR6Pdx3puj4S58+fR1EUGX7X19d599132djYkDcf/qXBDQ0NMTQ0hGEYskK2i9BMJsPbb7/N2tqaVO9VVeXHP/7xp3J8pi6SqqrE43GGh4dlXyOXy8nC0p5CcTqdRCIREokE9XqdQqFAq9XCsiwZETc2NlhZWSEWi9Hf3997udVOC//xj39w/vx5Njc3uXnzJtlsVo4RDA0N8ZWvfIVUKkWtVqNarQIwMDBAp9OhUqlw+fJltra2qFarsl83Pj7ee+XH3qH5+Xnu3r3Lzs6OnNsJBAJ4vV5isRj79+9n7969zMzMMDs7CyAT9Hw+TyaTYWdnB13XURSFUCgkXWJPge1OptPpJJFIEA6H5ayPXR1Ho1Fu377N5uYm5XJZQtnNxr6+PmKxmBQBm80myWSSSqXS+yOxvr4us7UnnngCj8dDIpGQfed6vU4+n+fcuXPs7OzIqtnW2OwRmampKVlimaYp3d8jSeAVRSEcDhOJRKRaYxiGLCRtydWWsGzx0D7/jUYDwzBwOBx4vV6EEKyvr5PP53sPXKlUcDqdTE1Ncfz4cdbW1njrrbfY2Njg2Wef5atf/SqRSITV1dWHCstarcbt27dlX3pzc5NwOMzevXvxer1MT0/z3nvvYVkWP/jBD3oHbCs/Pp+PVCpFsVhkdXWV+fl5Tp8+TX9/P5ZlkUgkZD9aURQ5klAsFgmFQvh8PukaVVUln8+zuLgohZqeAdvBYWFhAdM0MQyDL3/5yzzzzDNMTk7KkGzXcw6HA7fbDUAgEKDRaJBKpdi3bx99fX309/fj8/k4cuSIbPP2FNiOZHNzc/zzn/9kfHycb37zm4yMjMhWQKfTkXM+9q23LItAIEC1WiWdTnPgwAF8Ph/RaBSXy8WJEyfkRewpsF3G2MpPMBiU7QI7RTRNUwraqVSKZDIpI5494ri9vY2mabIwtSsYIQRPP/30p3J0nUvMzMwAyKGNXC7HRx99RC6Xk/0Mu78M8Morr/Dyyy/LCcFcLic7qPYjhRBy0lUIwdmzZz+Vo+sdjkQiwCeCXrPZpFKpsLW1xcrKiqygDcOQkyu2Mt9qtQiFQnL+slqtSmHcNM2HQng31jXwb37zGwD8fj9er1ee20ajwdTUFPv375dNRKfTyeHDhx8aSchkMgwPD3Pq1CkqlYrsewwPD0sVtKfAf/3rX1EUhYGBAZLJJOVyWeYEqVSK06dPEwgESCaTsjVgjxqsr6+zurrKxMQEU1NTci6zUqmQTCbZs2dP70Pz2NgYqqoyMjLCrl27pFBSKpVoNBpcunSJgYEBvvCFLxAKhSgWi+zs7MgOqWmaLC8vc/HiRSzLkmllOp0mFov1fodPnTolI93k5CQ7OzsMDg6Sz+e5dOkSZ8+e5eDBgxw7dozR0VFu3brFxx9/LMENw+Dy5cucO3eOiYkJvvWtbzExMSGH9Lq1roHtcxYMBgkGg5imSX9/P6Zp4na7ZQVdKBTIZrPUajUZDOxpVsuy5BC03XL4945ST4HtYGB//EEIQSwWw+12c/DgQVqtFoqi8Oabb+Jyudi7dy+HDx+mVCrRbrcpFApEo1FGRkbo6+uT4+gHDx5kdHS09wm83++XuprdV/b5fCiKQjKZZNeuXRSLRaanp6nVasTjcQYGBtA0jUgkgmmaeL1eOQFrj40ZhiGFwZ4CFwoFhBDMz8/LRGZychK/30+5XGZ1dZVOp8PExIRM6O/evSt33p61tEd57Q+yrK2tce3aNVRV5fjx470DtsPwxYsXuXjxInv27OH73/8+4XCYnZ0dFhYWiEQifP7znycej1Mul7l165acJQ6HwySTSVmYLi0tUavVWFpaYmNjA0VRegtsXyC7m//fQ6zdELcb4ID82A/8S6a1u/7/vm63Igp8hlzi/xX7X/fxtMfAj9oeAz9qewz8qO0x8KO2/wL41i0wf8BG8wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================== y | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (10,) | nDims: 1 | dtype: float64\n",
      "Content: [0.53939921 0.20033564 0.13357748 0.06324783 0.97126593 0.00783796\n",
      " 0.81031836 0.64067816 0.3447947  0.56354798]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "X = np.random.random((32, 10))\n",
    "y = np.random.random((10,))\n",
    "\n",
    "tensor_toolbox.tensor_info(X, \"X\")\n",
    "tensor_toolbox.tensor_info(y, \"y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== y | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (1, 10) | nDims: 2 | dtype: float64\n",
      "Content: [[0.53939921 0.20033564 0.13357748 0.06324783 0.97126593 0.00783796\n",
      "  0.81031836 0.64067816 0.3447947  0.56354798]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "y_expanded = np.expand_dims(y, axis=0)\n",
    "tensor_toolbox.tensor_info(y_expanded, \"y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Y | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (32, 10) | nDims: 2 | dtype: float64\n",
      "Y[0]: [0.53939921 0.20033564 0.13357748 0.06324783 0.97126593 0.00783796\n",
      " 0.81031836 0.64067816 0.3447947  0.56354798]\n",
      "... (showing only the first 20 elements)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "Y = np.concatenate([y_expanded] * 32, axis=0)\n",
    "tensor_toolbox.tensor_info(Y, \"Y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "def naive_add_matrix_and_vector(x, y):\n",
    "    assert len(x.shape) == 2\n",
    "    assert len(y.shape) == 1\n",
    "    assert x.shape[1] == y.shape[0]\n",
    "    x = x.copy()\n",
    "    for i in range(x.shape[0]):\n",
    "        for j in range(x.shape[1]):\n",
    "            x[i, j] += y[j]\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== z | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (64, 3, 32, 10) | nDims: 4 | dtype: float64\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "x = np.random.random((64, 3, 32, 10))\n",
    "y = np.random.random((32, 10))\n",
    "z = np.maximum(x, y)\n",
    "tensor_toolbox.tensor_info(z, \"z\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Tensor product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "x = np.random.random((32,))\n",
    "y = np.random.random((32,))\n",
    "z = np.dot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "def naive_vector_dot(x, y):\n",
    "    assert len(x.shape) == 1\n",
    "    assert len(y.shape) == 1\n",
    "    assert x.shape[0] == y.shape[0]\n",
    "    z = 0.\n",
    "    for i in range(x.shape[0]):\n",
    "        z += x[i] * y[i]\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "def naive_matrix_vector_dot(x, y):\n",
    "    assert len(x.shape) == 2\n",
    "    assert len(y.shape) == 1\n",
    "    assert x.shape[1] == y.shape[0]\n",
    "    z = np.zeros(x.shape[0])\n",
    "    for i in range(x.shape[0]):\n",
    "        for j in range(x.shape[1]):\n",
    "            z[i] += x[i, j] * y[j]\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "def naive_matrix_vector_dot(x, y):\n",
    "    z = np.zeros(x.shape[0])\n",
    "    for i in range(x.shape[0]):\n",
    "        z[i] = naive_vector_dot(x[i, :], y)\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "def naive_matrix_dot(x, y):\n",
    "    assert len(x.shape) == 2\n",
    "    assert len(y.shape) == 2\n",
    "    assert x.shape[1] == y.shape[0]\n",
    "    z = np.zeros((x.shape[0], y.shape[1]))\n",
    "    for i in range(x.shape[0]):\n",
    "        for j in range(y.shape[1]):\n",
    "            row_x = x[i, :]\n",
    "            column_y = y[:, j]\n",
    "            z[i, j] = naive_vector_dot(row_x, column_y)\n",
    "    return z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Tensor reshaping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Before reshape | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (60000, 28, 28) | nDims: 3 | dtype: uint8\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKoAAAB3CAYAAACT1ttzAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/H5lhTAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAanklEQVR4nO2deWyUx/nHv3vvvnvbe9jGxhivAceYGpwEAnE4Q5tAVCKBpUotRArFVUobmlADUasqQWqFaH8KpTSGChnkpk0BRQpVSziKq5I0LQFKgUCwAV/Ya+/hPd+9d+f3B30nu7YBX5Asno+0Wu/svPO+8/q7884888wzIkIIAYPxFUf8ZV8AgzEcmFAZWQETKiMrYEJlZAVMqIysgAmVkRUwoTKyAiZURlbAhMrICr4yQt25cyemTp0KiUSCqqqqL/tyHhoHDhyASCTCuXPnvuxLuSvt7e0QiUT0deTIkVGVYzAYaBkbN24c0bEjEqpwU9NfFosFixcvxrFjx0Z04nROnDiB+vp6LFiwAI2Njfj5z38+6rIYD44NGzagqakJTz75ZEZ6NBrFli1bUFBQAJVKhblz5+LkyZODjt+3bx+amppGdW7paA566623UFJSAkII+vr6cODAATz//PP485//jJUrV464vNOnT0MsFmP//v2Qy+WjuSTGQ+Cpp57Ct7/97UHpL730Eo4cOYJNmzahrKyM6qG5uRlPP/00zVdbWwsA+M53vjPic49KqM899xwef/xx+vnll1+G1WrFH//4x1EJ1eFwQKVSjZtICSGIRCJQqVTjUt6DLjebOXv2LN577z3s3LkTmzdvBgCsXbsWM2fORH19Pf75z3+Oy3nGpY9qMBigUqkglWbqPpVK4e2330ZFRQWUSiWsVivq6urg8XhoHpFIhMbGRvA8T7sTBw4cAAAkEgls374dpaWlUCgUmDJlCt544w1Eo9GM80yZMgUrV67E8ePH8fjjj0OlUmHv3r0AAK/Xi02bNqGoqAgKhQI2mw07duxAKpW6b73Go9z33nsP1dXV0Gq10Ol0qKysxK5duwadKxqN4rXXXoPZbIZarcaLL74Ip9OZkeeDDz7AihUrUFBQAIVCgdLSUmzfvh3JZDIj36JFizBz5kycP38e8+fPh0qlQklJCRoaGoY8789+9jPYbDYoFAoUFRWhvr5+0D2+G0eOHIFEIsGGDRtomlKpxMsvv4xPPvkEXV1dwyrnvpAR0NjYSACQU6dOEafTSRwOB7ly5Qqpq6sjYrGYnDhxIiP/+vXriVQqJd/97ndJQ0MD2bJlC1Gr1eSJJ54gsViMEEJIU1MTqampIQqFgjQ1NZGmpiZy8+ZNQggh69atIwDI6tWryZ49e8jatWsJALJq1aqM8xQXFxObzUaMRiPZunUraWhoIM3NzYTneTJr1iySm5tL3njjDdLQ0EDWrl1LRCIRefXVV+9b37GWe+LECQKALF26lOzZs4fs2bOHbNy4kaxZs2bQPZ09ezZZsmQJ2b17N3n99deJRCIhtbW1GdezatUqUltbS3bu3EneeecdsmbNGgKAbN68OSPfwoULSUFBAbFYLGTjxo3k17/+NXn66acJALJ//36aL5lMkuXLlxOO48imTZvI3r17ycaNG4lUKiXf/OY3ab62tjYCgDQ2Ng66R8uWLSPl5eWD0k+dOkUAkKNHjw76DgD5/ve/f7/bn3nMSDILN3XgS6FQkAMHDmTkPXPmDAFA3n333Yz0Dz/8cFD6unXriFqtzsh38eJFAoCsX78+I33z5s0EADl9+jRNKy4uJgDIhx9+mJF3+/btRK1Wk5aWloz0rVu3EolEQjo7O+9Z37GW++qrrxKdTkcSicRdzyHc02XLlpFUKkXTf/SjHxGJREK8Xi9NC4VCg46vq6sjHMeRSCRC0xYuXEgAkF/96lc0LRqNkqqqKmKxWDIaCbFYTM6cOZNRZkNDAwFAPv74Y0LIvYVaUVFBlixZMij9s88+IwBIQ0PDoO9GI9RRPfr37NmDkydP4uTJk/j973+PxYsXY/369Xj//fdpnsOHD0Ov1+PZZ5+Fy+Wir+rqamg0GjQ3N9/zHH/9618BAK+99lpG+uuvvw4A+Mtf/pKRXlJSgq9//esZaYcPH0ZNTQ2MRmPGNSxbtgzJZBL/+Mc/7lvXsZRrMBjA8/yQI+CBbNiwASKRiH6uqalBMplER0cHTUvvGwcCAbhcLtTU1CAUCuHzzz/PKE8qlaKuro5+lsvlqKurg8PhwPnz52k9ysvLMWPGjIx6LFmyBADu+z8CgHA4DIVCMShdqVTS78eDUQ2mnnzyyYzB1Le+9S3Mnj0bGzduxMqVKyGXy9Ha2gqfzweLxTJkGQ6H457n6OjogFgshs1my0jPy8uDwWDI+AcCdwQ1kNbWVly6dAlms3lU1zDWcl955RUcOnQIzz33HCZNmoTly5ejtrYW3/jGNwYdM3ny5IzPRqMRADL685999hl+8pOf4PTp0/D7/Rn5fT5fxueCggKo1eqMtGnTpgG4YxedN28eWltbce3atTHdH5VKNWR/NhKJ0O/Hg1EJdSBisRiLFy/Grl270NraioqKCqRSKVgsFrz77rtDHnO3mzOQ9FbmXgx1Q1KpFJ599lnU19cPeYzwj3tQ5VosFly8eBHHjx/HsWPHcOzYMTQ2NmLt2rU4ePBgxjESiWTIssj/Vgp5vV4sXLgQOp0Ob731FkpLS6FUKnHhwgVs2bJlWIPDoepRWVmJ//u//xvy+6KiovuWkZ+fj+7u7kHpdrsdwJ0fzHgwLkIF7ozQASAYDAIASktLcerUKSxYsGBUv6ri4mKkUim0traivLycpvf19cHr9aK4uPi+ZZSWliIYDGLZsmUjPv94lSuXy/HCCy/ghRdeQCqVwiuvvIK9e/fipz/96aCnxb34+9//Drfbjffffx/PPPMMTW9raxsyf09PD3iez2hVW1paANyxZgj1+O9//4ulS5cOu0EYSFVVFZqbm+H3+6HT6Wj6v//9b/r9eDAu5ql4PI4TJ05ALpdTUdXW1iKZTGL79u2D8icSCXi93nuW+fzzzwMA3n777Yx04de/YsWK+15XbW0tPvnkExw/fnzQd16vl/64Rspwy3W73RnficVizJo1CwCGbf4REFpckrYWMxaL4be//e2Q+ROJBDWlCXn37t0Ls9mM6upqWo/u7m787ne/G3R8OBwGz/P3va7Vq1cjmUxi3759NC0ajaKxsRFz584dVqs8HEbVoh47dox23h0OB/7whz+gtbUVW7dupb+qhQsXoq6uDr/4xS9w8eJFLF++HDKZDK2trTh8+DB27dqF1atX3/UcX/va17Bu3Trs27ePPvbOnj2LgwcPYtWqVVi8ePF9r/PHP/4xjh49ipUrV+Kll15CdXU1eJ7H5cuXceTIEbS3t8NkMo24/sMtd/369ejv78eSJUtQWFiIjo4O7N69G1VVVRlPieEwf/58GI1GrFu3Dj/84Q8hEonQ1NSUIdx0CgoKsGPHDrS3t2PatGn405/+hIsXL2Lfvn2QyWQA7swQHTp0CN/73vfQ3NyMBQsWIJlM4vPPP8ehQ4eo/fhezJ07F2vWrMG2bdvgcDhgs9lw8OBBtLe3Y//+/SOq4z0ZiYlgKPOUUqkkVVVV5J133skwrwjs27ePVFdXE5VKRbRaLamsrCT19fWkp6eH5hnKPEUIIfF4nLz55pukpKSEyGQyUlRURLZt25ZhiiHkjhlpxYoVQ15zIBAg27ZtIzabjcjlcmIymcj8+fPJL3/5S2qmuRtjLffIkSNk+fLlxGKxELlcTiZPnkzq6uqI3W4fdE8//fTTjPKbm5sJANLc3EzTPv74YzJv3jyiUqlIQUEBqa+vJ8ePHx+Ub+HChaSiooKcO3eOPPXUU0SpVJLi4mLym9/8ZlA9YrEY2bFjB6moqCAKhYIYjUZSXV1N3nzzTeLz+Qgh9zZPEUJIOBwmmzdvJnl5eUShUJAnnnhikEkvHTxoOyojOxCEOl4IQt29ezdxOp0kGo2Oqhy3202cTufDs6MyJiY/+MEPYDabcfTo0VEdP3Xq1GFbewYybqN+xqNLXl5exqSFMCAcKR988AHi8TiA4Zm+0hERwkL6PGosWrQILpcLV65c+bIvZdxgQmVkBayPysgKmFAZWQETKiMrYEJlZAVMqIysgAmVkRUwoTKyAiZURlbAhMrICphQGVkBEyojK2BCZWQFTKiMrIAJlZEVMKEysgLm4f8VgBAy5Lr6+7kKj3YtfjbChDoOEEKQSqWQSqXuKq5wOAyHw4FwOEzzE0IQjUYRi8Ugl8tRWFgIk8mEYDCI27dvIxgMIhgMwuPxIJlMUmEqFApYrVYYDAao1Wrk5+eD47iHWeWHDhPqGBFC6SQSCUSj0bsKta+vD+fOnYPT6UQymUQ8HkcymYTP54PX66UB5WbNmoXbt2/j1KlTuH37Nm7fvo1r164hHA5DLBZDKpVCq9Vi3rx5KCsrw6RJk1BTU8OEOhEZSmzpraXwd3rLGIvFEAqF7hoDyufzwe12w+l0IpFIIBaLgRACj8cDr9eLWCwGn8+HUCgEv98Ph8OB3t5e9PT0oLOzE+FwGDKZDFKpFHq9Hh6PB8FgEOFweFRxp7INJtQBJJNJRCIRJBKJDDH6/X4EAgHE43F4vV7wPI9UKkVbxv7+ftjtdsRisSHLDQQC6OrqQjAYBCEEyWQy4z0QCODcuXPwer2w2+24fPky7HY7AoEAxGIxFAoFtFotNBoNjEYjCgoKUFRUBIvFMiH2PWBCHUAymQTP84jFYkilUkgmk0gkErDb7bDb7QiFQujs7ITL5UIikUA4HEYymURXVxeuXr1613ig6aIUEIlE4DgOWq0WSqUSEokEnZ2dcLvduHz5MtxuNyQSCSQSCRQKBXQ6HSwWC4xGIwoLC1FUVASDwTBkfNJHDSbU/5FMJqlI+/r6aIuZSCSQTCbR29uLvr4+RCIROJ1O9Pf3035pPB6Hz+dDMBikcUGHg0QigVwup0JVKpWQyWRQKpXQ6/UghEAmk9FXbm4uzGYzDAYD9Ho91Go1FAoFxOJH38rIhIo7IvV4POB5Hh0dHTh27Bi6uroQj8dpyxoKhRAOh5FIJMDzPKLRKJLJJO2j8jw/ouiAIpEIUqkUNpsNc+bMgVKphFarBcdxiEajKC8vRzQahVKphFqthkQigVarpXnKysqQn58PuVzOWtSJgtCSejwedHZ24qOPPsKVK1eQSCQQiUQG7ToyXkgkElgsFlRWVkKpVEIul9OdZQTbqkqlglarhVQqpa2uXC6HyWTKiEf6qMOEii9aN4VCQcUik8lGPZoWyknf4TCVStEWWSwWQywWQyKRQKfTwWw20+2PBkaeViqV4DiOdhOE6xu4VdKjzsSq7V0Qi8X08arX66HRaMBxHAghI94sQSjDZDLRQZBEIgHP8+jq6kIoFKIiVSqVKCwsxOzZs8FxHBX1wGuTSCQQiURU4MIPayIxsWp7F0QiEWQyGQghUCgUdPAilUpHPE0pEomoKUl4XMtkMiraSCQCiURCBajRaGAymR55g/1YYUIFMlooo9GIGTNmQCaTwePxoKenB/F4nPYPY7EYuru74XK5MspQKBQ0T0VFBaqqqiCXy6lQ/X4/bDYb/H4/gsEgXC4XFAoF3XGZcW+YUHFHqHK5HDKZDFarFfPnz0dZWRnsdjtaW1sRjUZhMplgMpng8/nwt7/9bZBQhS00dTodampq8OKLL9L9XaVSKXiep3bYGzdu4MKFC0gkErBYLBPCvDRWmFD/h9A/FFo54M4GDS6XC/F4HGazGWazGXK5HBzHQS6X0wkBwd6pUqmgVqthNBphsVioUIVHvEgkQigUQjAYRG5uLqLRKFQqFWtRhwET6gCUSiUmT54Ms9kMk8mEvLw8JJNJ6HQ66HQ69Pf3o7OzE4lEAoFAAN3d3VR4VVVVyMnJQWFhIe3rCq2lTCaDXq+nfVGO45BMJlFaWnrXPaYYX8CEOgCVSoXCwkLqaCK45Qkmp/7+frS3tyMSicDhcNCJApPJhFmzZsFqtdIdp9NH5oIzCQDk5OSgtLQUAOgUKePeMKEOQXorKDimpE9lptszRSIRCCF0OvVeEwTCI56Jc+Qwod4DwcgOgNovBVOWMEMkiK+/vx+XLl2i8/EVFRXU/skYO0yo92Aow7pIJKIClkqltPX1+/1ob2+H1+ulHvmM8YMJdYRIpVKYTCYUFRWBEIKcnBzwPA+ZTAae5yEWi+H1euHz+RCPx+nInzE2mFBHiEqlQmVlJYqLi3H9+nV0dXVRO2lPTw+kUilu3LiBlpYW6PV6FBUVITc398u+7KyHCXWESCQS5OTkQK/XIxAIICcnBwaDAZFIBMFgECKRiK6DEolEdMkJ66uODSbUESL0UUUiEQwGAyorK2EwGHD16lU4nU5EIhH09PTg008/hU6ng9PphNVqpRMFMpmMekxNNMeSscDu1CiQSqUghMBqtWLRokUIBALgOA6XLl1CLBZDS0sLHA4HOI5DSUkJ8vLyoFarUVBQAI7jUFpaStc/MYYHE+ooEfwD9Ho9nXbVaDR0vZXH40E4HIZWqwUAaLVayGQyaDQaOn0qTK8KlgPWPbg7TKhjQFgeolQqMX36dCxduhROpxO3bt1CW1sb4vE4Ojs74XA4oFAocOvWLchkMvT19QG4M0NlsVhgsVioGyDrDgwNuytjQCqVQqPRgBACm82GxYsXw+Px4Pjx47h58yYikQi8Xi9dKSBMGHg8HigUCphMJjz22GMZzitMqEPD7soYGcrrymKxwGq1gud5+P1+8DxPfQeEhYAulwuEELhcLng8Huq3KpPJqDc/4wuYUMcJg8GAsrIy2vecOnUqvF4vLly4gFu3btFl2KFQCN3d3Thz5gw4jkNvby8cDgcMBgNmzZqF4uJiSKVSuk6KcQcm1HGC4zhwHIdUKkU9sNxuN3ieRygUgtfrRX9/PwDA4/HA4/HQGSuRSERdCs1mM10twIT6BUyo44xgDVCr1UgkEigqKkI4HIbH46GTAT6fD/39/TSUT29vL2KxGNra2qglQVhxwLgDE+o4IxKJoNFooFQqkZOTA47jMHfuXPT39+PatWvweDy4fPkympub4ff70d3dDY/HA5VKBZfLhf/85z+w2WwwGAwTat3+/WBCfQAIgyLBy99qtaK/vx/xeBwejwcOh4P6ugYCAQQCARoRJRwOQ6lUjniZ9qMOE+oDJN1NUKPRoLCwEAaDATdu3KDBJoSQQELEQJFIhL6+PvT19SE3NxcqlQoajWbCWwGYUB8ggpO10LpqtVokEgm0tLRAoVBkzETF43G6tEWtVqOtrQ0qlQpms5k6aU9kmFAfAMLyFQA0ZLpA+kqBgccIztaxWAyJRIJGErxfLP+JABPqOEMIQSgUonP+DocDPp8P0WgUPp8PsVgMZ8+eBc/zGSIUZrk4joPFYkFBQQEKCwuh0WjYbBWYUMed9JmnYDCIq1ev0o0jhPeuri46WyUgFouh1WphMBgyhCrEm5roMKGOgfQY/vF4nIZUdzgcNBiww+GA0+lEMBhEf38/QqEQQqHQoDVVwrSpMMgaKrLfRIYJdQwkEgn4/X7EYjH09PTgxo0bCAaD6OjoQEdHB8LhMHp7e+kjPxwO0/f0oL+CM7ZKpYJOp4NaraZ9WcYdmFDHgBB9OhwOo7u7GxcvXoTX60VLSwtu3LiBaDSKYDCIUCh01zLSw0kKU6fpAX0Zd2B3Y5gIcaaE6NTRaBSBQACdnZ0IBAJoa2tDd3c3/H4/vF4v3ehsqGXTQhALIZCv0IqWlpYiPz8fJSUlUKlUX0Itv7owoQ4TIQpKKBRCa2sr9Xq6cOECtX/a7XaaLxKJ0M0qBsJxHMxmMziOw8yZMzFz5kxoNBqUl5dj0qRJUKlUsFgsX0Itv7owoQ6D9JA94XAYbrcbPT096O7uxvXr19Hb24tQKASPx3PfDSfSnVa0Wi0KCgpQVlYGvV6PGTNmYNKkSQ+pVtkFE+oAhBF8KpVCLBZDJBJBPB5HW1sbOjs7EQwGcf36ddjtdni9XrjdboRCIUQikUGGeYlEQrfY4TgOVquVvk+ZMgVqtRo2mw3FxcU0Vj9jaJhQB5BMJhEOhxGPx+H3++FyuRAKhXDmzBl89NFH1C1PWGIibOOTPrMkIJVKYTQaYTQakZeXh/nz58NqtaKwsBDTp08Hx3F0ACVMtzKGhgkVXzzahc10g8EgFarX60UwGITT6URvby+1h/r9/owy0tf7p4/idTodDAYDcnNzYbFYkJ+fj7y8POTl5bEgviNgQgtVmE8PhUK4evUqenp6aB80EonA7/fD6XQiGo3i5s2bcDgciMViiEajg8riOA4GgwEymQyFhYV0DX9JSQksFgv0ej2mTp0KvV4PnU5H10YxhseEF2okEoHH48G5c+dw/vx5BINB2O128DyPQCAAj8dDd+8TXkM5iQhz9FqtFnPmzMGcOXOg0+lgs9mQn59P97FKb3UZw2dCCFV4tAu7QQv9Sp7n6Y59DocDbrcb4XAYPp8P4XCYGvOHGskLvqZKpRJisRg5OTnIz8+HVquFxWJBTk4ONBoNNBoNVCoVxGIxa0XHwIQQajQapSIUTEo8z8PtdtNRe0tLC+x2O51tEkb9QxnshbioRqMR06dPh9FohM1mQ3V1Nd0B2mKxQCaT0QgpQ7n2MYbPhBBqIpGAz+dDIBDArVu38K9//Qterxd2ux29vb10lonn+fuWlT5Y0mg0mDp1KvLy8lBZWYlnnnkGer2ezjwxxo8JIVRhm3KPxwOXywW32w2v14tAIEA9noTHe7rnkhCBLz02lEQiQW5uLjQaDcxmM2w2G93aR+iDsv7n+DMhhBoKhXDz5k10d3fj6tWruHTpEvx+P+LxOOLxeIYNVLB9ChucFRcX02UjwgrTqqoqTJkyJWOpCMdx0Ol0LG7/A2JCCFXYE0oI/OD1egfZQYEv1jgJG5sZDAbk5+dTBxHBieSxxx5DeXk5pFIpVCoV8xt9CEwIoarVakybNg25ubmwWq0oKChAJBIZMq9cLodWq4VCoUBOTg7y8vIyFuIJDiWC9xNrPR8OIjIBVo4J06KJRIKap+5W7fTBkkQiGWRSEmachOlOJtSHw4QQKiP7YcNTRlbAhMrICphQGVkBEyojK2BCZWQFTKiMrIAJlZEVMKEysgImVEZWwITKyAqYUBlZARMqIytgQmVkBUyojKyACZWRFTChMrKC/wd5fVfj2F0iUwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================== After reshape | tensor_info ====================\n",
      "Type: <class 'numpy.ndarray'>\n",
      "Shape: (60000, 784) | nDims: 2 | dtype: uint8\n",
      "After reshape[0]: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      "... (showing only the first 20 elements)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "tensor_toolbox.tensor_info(train_images, \"Before reshape\")\n",
    "train_images_reshaped = train_images.reshape((60000, 28 * 28))\n",
    "tensor_toolbox.tensor_info(train_images_reshaped, \"After reshape\", image=False) \n",
    "# The previous one only displays the first image. I could do the same but it doesn't make a lot of sense\n",
    "# as the images are now mono-dimensional. This image would be 60000*784, each digit being one row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[0., 1.],\n",
    "             [2., 3.],\n",
    "             [4., 5.]])\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.],\n",
       "       [1.],\n",
       "       [2.],\n",
       "       [3.],\n",
       "       [4.],\n",
       "       [5.]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = x.reshape((6, 1))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 300)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.zeros((300, 20))\n",
    "x = np.transpose(x)\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "## The engine of neural networks: gradient-based optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "#### The gradient tape in TensorFlow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== x | tensor_info ====================\n",
      "Type: <class 'tensorflow.python.ops.resource_variable_ops.ResourceVariable'>\n",
      "Shape: () | dtype: <dtype: 'float32'>\n",
      "Content: 0.0\n",
      "\n",
      "==================== Gradient of y wrt x | tensor_info ====================\n",
      "Type: <class 'tensorflow.python.framework.ops.EagerTensor'>\n",
      "Shape: () | nDims: 0 | dtype: <dtype: 'float32'>\n",
      "Content: 2.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "# In TensorFlow, we use Gradient Tape to compute gradients.\n",
    "x = tf.Variable(0.) # Variable to compute the gradient\n",
    "with tf.GradientTape() as tape: # Gradient tape context\n",
    "    # Every operation inside the context is recorded on the tape\n",
    "    y = 2 * x + 3\n",
    "grad_of_y_wrt_x = tape.gradient(y, x)\n",
    "tensor_toolbox.tensor_info(grad_of_y_wrt_x, \"Gradient of y wrt x\")\n",
    "# Honestly, this is unbelievably cool."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== x | tensor_info ====================\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([]) | nDims: 0 | dtype: torch.float32\n",
      "Content: 0.0\n",
      "-- Gradient:\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([]) | nDims: 0 | dtype: torch.float32\n",
      "Content: 2.0\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "# In PyTorch, we use the requires_grad attribute to compute gradients.\n",
    "x = torch.tensor(0., requires_grad=True) # Variable to compute the gradient\n",
    "y = 2 * x + 3\n",
    "y.backward() # Compute the gradient of y wrt x\n",
    "tensor_toolbox.tensor_info(x, \"x\")\n",
    "# From a math point of view it is just incredible that this\n",
    "# is even possible. Sooooo beautiful."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Gradient of y wrt x | tensor_info ====================\n",
      "Type: <class 'tensorflow.python.framework.ops.EagerTensor'>\n",
      "Shape: (2, 2) | nDims: 2 | dtype: <dtype: 'float32'>\n",
      "Gradient of y wrt x[0]: [2. 2.]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x = tf.Variable(tf.random.uniform((2, 2))) # 2x2 matrix\n",
    "with tf.GradientTape() as tape:\n",
    "    y = 2 * x + 3\n",
    "grad_of_y_wrt_x = tape.gradient(y, x)\n",
    "tensor_toolbox.tensor_info(grad_of_y_wrt_x, \"Gradient of y wrt x\", image=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Gradient of y wrt x | tensor_info ====================\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([2, 2]) | nDims: 2 | dtype: torch.float32\n",
      "Gradient of y wrt x[0]: tensor([2., 2.])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# In PyTorch:\n",
    "x = torch.rand((2, 2), requires_grad=True) # 2x2 matrix\n",
    "y = 2 * x + 3\n",
    "y.backward(torch.ones_like(y)) # Compute the gradient of y wrt x\n",
    "# The argument ones_like(y) is a tensor of ones with the same shape as y.\n",
    "# It is necessary because y is not a scalar, so we need to provide the gradient \n",
    "# of the output with respect to itself.\n",
    "grad_of_y_wrt_x = x.grad\n",
    "tensor_toolbox.tensor_info(grad_of_y_wrt_x, \"Gradient of y wrt x\", image=False)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== Gradient of y wrt W | tensor_info ====================\n",
      "Type: <class 'tensorflow.python.framework.ops.EagerTensor'>\n",
      "Shape: (2, 2) | nDims: 2 | dtype: <dtype: 'float32'>\n",
      "Gradient of y wrt W[0]: [0.54304206 0.54304206]\n",
      "\n",
      "==================== Gradient of y wrt b | tensor_info ====================\n",
      "Type: <class 'tensorflow.python.framework.ops.EagerTensor'>\n",
      "Shape: (2,) | nDims: 1 | dtype: <dtype: 'float32'>\n",
      "Content: [2. 2.]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "W = tf.Variable(tf.random.uniform((2, 2)))\n",
    "b = tf.Variable(tf.zeros((2,)))\n",
    "x = tf.random.uniform((2, 2))\n",
    "with tf.GradientTape() as tape:\n",
    "    y = tf.matmul(x, W) + b\n",
    "\n",
    "grad_of_y_wrt_W_and_b = tape.gradient(y, [W, b])\n",
    "tensor_toolbox.tensor_info(grad_of_y_wrt_W_and_b[0], \"Gradient of y wrt W\", image=False)\n",
    "tensor_toolbox.tensor_info(grad_of_y_wrt_W_and_b[1], \"Gradient of y wrt b\", image=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================== W | tensor_info ====================\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([2, 2]) | nDims: 2 | dtype: torch.float32\n",
      "W[0]: tensor([0.6129, 0.3994], grad_fn=<SliceBackward0>)\n",
      "-- Gradient:\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([2, 2]) | nDims: 2 | dtype: torch.float32\n",
      "gradient[0]: tensor([0.9144, 0.9144])\n",
      "\n",
      "\n",
      "==================== b | tensor_info ====================\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([2]) | nDims: 1 | dtype: torch.float32\n",
      "Content: tensor([0., 0.], grad_fn=<SliceBackward0>)\n",
      "-- Gradient:\n",
      "Type: <class 'torch.Tensor'>\n",
      "Shape: torch.Size([2]) | nDims: 1 | dtype: torch.float32\n",
      "Content: tensor([2., 2.])\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "W = torch.rand((2, 2), requires_grad=True)\n",
    "b = torch.zeros((2,), requires_grad=True)\n",
    "x = torch.rand((2, 2))\n",
    "y = torch.matmul(x, W) + b\n",
    "y.backward(torch.ones_like(y))\n",
    "grad_of_y_wrt_W = W.grad\n",
    "grad_of_y_wrt_b = b.grad\n",
    "tensor_toolbox.tensor_info(W, \"W\", image=False)\n",
    "tensor_toolbox.tensor_info(b, \"b\", image=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "## Looking back at our first example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
    "train_images = train_images.reshape((60000, 28 * 28))\n",
    "train_images = train_images.astype(\"float32\") / 255\n",
    "test_images = test_images.reshape((10000, 28 * 28))\n",
    "test_images = test_images.astype(\"float32\") / 255"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "model = keras.Sequential([\n",
    "    layers.Dense(512, activation=\"relu\"),\n",
    "    layers.Dense(10, activation=\"softmax\")\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "model.compile(optimizer=\"rmsprop\",\n",
    "              loss=\"sparse_categorical_crossentropy\",\n",
    "              metrics=[\"accuracy\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/5\n",
      "469/469 [==============================] - 2s 3ms/step - loss: 0.2584 - accuracy: 0.9242\n",
      "Epoch 2/5\n",
      "469/469 [==============================] - 1s 3ms/step - loss: 0.1041 - accuracy: 0.9685\n",
      "Epoch 3/5\n",
      "469/469 [==============================] - 1s 3ms/step - loss: 0.0676 - accuracy: 0.9797\n",
      "Epoch 4/5\n",
      "469/469 [==============================] - 1s 3ms/step - loss: 0.0497 - accuracy: 0.9849\n",
      "Epoch 5/5\n",
      "469/469 [==============================] - 1s 3ms/step - loss: 0.0376 - accuracy: 0.9886\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.src.callbacks.History at 0x3219a5c10>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(train_images, train_labels, epochs=5, batch_size=128)\n",
    "# Honestly, it's impressive how Keras manages to obtain the data,\n",
    "# build a neural network and train it in just a few lines of code.\n",
    "# However, it's probably good to look a bit further to get a better understanding."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Reimplementing our first example from scratch in TensorFlow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "#### A simple Dense class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "\n",
    "class NaiveDense:\n",
    "    def __init__(self, input_size, output_size, activation):\n",
    "        self.activation = activation\n",
    "\n",
    "        w_shape = (input_size, output_size)\n",
    "        w_initial_value = tf.random.uniform(w_shape, minval=0, maxval=1e-1)\n",
    "        self.W = tf.Variable(w_initial_value)\n",
    "\n",
    "        b_shape = (output_size,)\n",
    "        b_initial_value = tf.zeros(b_shape)\n",
    "        self.b = tf.Variable(b_initial_value)\n",
    "\n",
    "    def __call__(self, inputs):\n",
    "        return self.activation(tf.matmul(inputs, self.W) + self.b)\n",
    "\n",
    "    @property\n",
    "    def weights(self):\n",
    "        return [self.W, self.b]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "#### A simple Sequential class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "class NaiveSequential:\n",
    "    def __init__(self, layers):\n",
    "        self.layers = layers\n",
    "\n",
    "    def __call__(self, inputs):\n",
    "        x = inputs\n",
    "        for layer in self.layers:\n",
    "           x = layer(x)\n",
    "        return x\n",
    "\n",
    "    @property\n",
    "    def weights(self):\n",
    "       weights = []\n",
    "       for layer in self.layers:\n",
    "           weights += layer.weights\n",
    "       return weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "model = NaiveSequential([\n",
    "    NaiveDense(input_size=28 * 28, output_size=512, activation=tf.nn.relu),\n",
    "    NaiveDense(input_size=512, output_size=10, activation=tf.nn.softmax)\n",
    "])\n",
    "assert len(model.weights) == 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "#### A batch generator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "class BatchGenerator:\n",
    "    def __init__(self, images, labels, batch_size=128):\n",
    "        assert len(images) == len(labels)\n",
    "        self.index = 0\n",
    "        self.images = images\n",
    "        self.labels = labels\n",
    "        self.batch_size = batch_size\n",
    "        self.num_batches = math.ceil(len(images) / batch_size)\n",
    "\n",
    "    def next(self):\n",
    "        images = self.images[self.index : self.index + self.batch_size]\n",
    "        labels = self.labels[self.index : self.index + self.batch_size]\n",
    "        self.index += self.batch_size\n",
    "        return images, labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Running one training step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "def one_training_step(model, images_batch, labels_batch):\n",
    "    with tf.GradientTape() as tape:\n",
    "        predictions = model(images_batch)\n",
    "        per_sample_losses = tf.keras.losses.sparse_categorical_crossentropy(\n",
    "            labels_batch, predictions)\n",
    "        average_loss = tf.reduce_mean(per_sample_losses)\n",
    "    gradients = tape.gradient(average_loss, model.weights)\n",
    "    update_weights(gradients, model.weights)\n",
    "    return average_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "learning_rate = 1e-3\n",
    "\n",
    "def update_weights(gradients, weights):\n",
    "    for g, w in zip(gradients, weights):\n",
    "        w.assign_sub(g * learning_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "from tensorflow.keras import optimizers\n",
    "\n",
    "optimizer = optimizers.legacy.SGD(learning_rate=1e-3)\n",
    "\n",
    "def update_weights(gradients, weights):\n",
    "    optimizer.apply_gradients(zip(gradients, weights))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### The full training loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [],
   "source": [
    "def fit(model, images, labels, epochs, batch_size=128):\n",
    "    for epoch_counter in range(epochs):\n",
    "        print(f\"Epoch {epoch_counter}\")\n",
    "        batch_generator = BatchGenerator(images, labels)\n",
    "        for batch_counter in range(batch_generator.num_batches):\n",
    "            images_batch, labels_batch = batch_generator.next()\n",
    "            loss = one_training_step(model, images_batch, labels_batch)\n",
    "            if batch_counter % 100 == 0:\n",
    "                print(f\"loss at batch {batch_counter}: {loss:.2f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0\n",
      "loss at batch 0: 6.21\n",
      "loss at batch 100: 2.25\n",
      "loss at batch 200: 2.24\n",
      "loss at batch 300: 2.12\n",
      "loss at batch 400: 2.25\n",
      "Epoch 1\n",
      "loss at batch 0: 1.93\n",
      "loss at batch 100: 1.89\n",
      "loss at batch 200: 1.87\n",
      "loss at batch 300: 1.74\n",
      "loss at batch 400: 1.85\n",
      "Epoch 2\n",
      "loss at batch 0: 1.60\n",
      "loss at batch 100: 1.59\n",
      "loss at batch 200: 1.54\n",
      "loss at batch 300: 1.44\n",
      "loss at batch 400: 1.52\n",
      "Epoch 3\n",
      "loss at batch 0: 1.34\n",
      "loss at batch 100: 1.36\n",
      "loss at batch 200: 1.27\n",
      "loss at batch 300: 1.22\n",
      "loss at batch 400: 1.28\n",
      "Epoch 4\n",
      "loss at batch 0: 1.14\n",
      "loss at batch 100: 1.17\n",
      "loss at batch 200: 1.07\n",
      "loss at batch 300: 1.06\n",
      "loss at batch 400: 1.11\n",
      "Epoch 5\n",
      "loss at batch 0: 0.99\n",
      "loss at batch 100: 1.03\n",
      "loss at batch 200: 0.92\n",
      "loss at batch 300: 0.94\n",
      "loss at batch 400: 0.99\n",
      "Epoch 6\n",
      "loss at batch 0: 0.88\n",
      "loss at batch 100: 0.92\n",
      "loss at batch 200: 0.82\n",
      "loss at batch 300: 0.84\n",
      "loss at batch 400: 0.90\n",
      "Epoch 7\n",
      "loss at batch 0: 0.79\n",
      "loss at batch 100: 0.84\n",
      "loss at batch 200: 0.73\n",
      "loss at batch 300: 0.77\n",
      "loss at batch 400: 0.83\n",
      "Epoch 8\n",
      "loss at batch 0: 0.73\n",
      "loss at batch 100: 0.77\n",
      "loss at batch 200: 0.67\n",
      "loss at batch 300: 0.72\n",
      "loss at batch 400: 0.78\n",
      "Epoch 9\n",
      "loss at batch 0: 0.68\n",
      "loss at batch 100: 0.71\n",
      "loss at batch 200: 0.62\n",
      "loss at batch 300: 0.67\n",
      "loss at batch 400: 0.74\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.keras.datasets import mnist\n",
    "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
    "\n",
    "train_images = train_images.reshape((60000, 28 * 28))\n",
    "train_images = train_images.astype(\"float32\") / 255\n",
    "test_images = test_images.reshape((10000, 28 * 28))\n",
    "test_images = test_images.astype(\"float32\") / 255\n",
    "\n",
    "fit(model, train_images, train_labels, epochs=10, batch_size=128)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text"
   },
   "source": [
    "### Evaluating the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "colab_type": "code"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy: 0.82\n"
     ]
    }
   ],
   "source": [
    "predictions = model(test_images)\n",
    "predictions = predictions.numpy()\n",
    "predicted_labels = np.argmax(predictions, axis=1)\n",
    "matches = predicted_labels == test_labels\n",
    "print(f\"accuracy: {matches.mean():.2f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Big TODO: PyTorch implementation done before is already quite similar.\n",
    "# However, I want to go line by line over the tf implementation.\n",
    "# Also also, I did a numpy version that worked kind of ok-ish in MNIST digits.\n",
    "# I could try to find it and add it here, with algebraic notation."
   ]
  }
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