09-feed-forward-neural-network.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config IPCompleter.greedy=True\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn.datasets, sklearn.model_selection\n",
    "from progressbar import progressbar\n",
    "\n",
    "# load the data\n",
    "X, y = sklearn.datasets.fetch_openml('mnist_784', version=1, return_X_y=True, as_frame=False)\n",
    "y, X = y.astype(int), X.reshape(-1, 784)\n",
    "X[X < 128] = 0\n",
    "X[X > 0] = 1\n",
    "train_data, test_data, train_target, test_target = sklearn.model_selection.train_test_split(X, y, test_size=0.3, random_state=47)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, here we are. We will build our first neural network today. I decided to take it the other way around - I will first show you the implementation and I will formalize it, define the concepts, and show the math behind."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementation\n",
    "\n",
    "So let's build our first neural network. Luckily for us, I take into consideration the architecture of the neural network in the last notebook. From the implementation point of view, we will not see anything new today.\n",
    "\n",
    "I exported the code from the previous notebook into separate files. The file [src/utils_09.py](src/utils_09.py) contains definitions of losses, metrics, and optimizers (like `SGD`). The file [src/layers_09.py](src/layers_09.py) contains implementations of layers - `DenseLayer`, `SoftmaxLayer` and so on. Finally, the file [src/sequencemodel_09.py](src/sequencemodel_09.py) contains the definition of `SequenceModel` class - the exact copy of the `MulticlassLogisticRegression` class from the previous notebook. Here is only a subtle difference - we will pass the layers as constructor parameter rather than defining it inside. Let's import the classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from src.utils_09 import SGD, CategoricalCrossEntropyLoss, AccuracyMetric\n",
    "from src.layers_09 import DenseLayer, SoftmaxLayer, SigmoidLayer\n",
    "from src.sequencemodel_09 import SequenceModel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's create and train the neural network. I can tell you right away - the only difference is the number of layers. Remember that logistic regression had one dense layer, the activation layer, and finally loss. The neural network will have one dense layer with $784$ inputs and $100$ outputs, then an activation layer (in this case sigmoid activation), then a dense layer again from $100$ inputs to $10$ outputs (the exact number of classes). The last dense layer follows an activation layer (softmax layer, as we have a classification task in hand) and finally the loss function.\n",
    "\n",
    "Here it is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100% (400 of 400) |######################| Elapsed Time: 2:09:10 Time:  2:09:10\n"
     ]
    }
   ],
   "source": [
    "optimizer = SGD(learning_rate=1e-4)\n",
    "model = SequenceModel(layers=[\n",
    "    DenseLayer(784, 100),\n",
    "    SigmoidLayer(),\n",
    "    DenseLayer(100, 10),\n",
    "    SoftmaxLayer()\n",
    "], loss=CategoricalCrossEntropyLoss(), metrices=[AccuracyMetric()], random_seed=42)\n",
    "result = model.fit(train_data, train_target, optimizer, test_data, test_target, epochs=400, batch_size=128, progress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As usual, let's visualize the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy: 0.9121020408163265, Test accuracy: 0.8897142857142857\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(f\"Train accuracy: {result['train_accuracy'][-1]}, Test accuracy: {result['test_accuracy'][-1]}\")\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(result['train_loss'], label=\"train loss\")\n",
    "plt.plot(result['test_loss'], label=\"test loss\")\n",
    "plt.yscale('log')\n",
    "ticks = [0.16, 0.225, 0.32, 0.45, 0.64, 0.9, 1.28, 1.8, 2.56, 3.6, 5.12]\n",
    "plt.yticks(ticks=ticks, labels=ticks)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(result['train_accuracy'], label=\"train accuracy\")\n",
    "plt.plot(result['test_accuracy'], label=\"test accuracy\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are not so bad, however still worse than one-to-one logistic regression. Nevertheless, the network learned and the predictions are around $88\\%$ accurate. I don't want to dig much deeper into it, as I will discuss activation layers in some of the following notebook, but I can tell you right away, that the sigmoid activation layer is not the best choice. We may replace it with something better - ReLU activation function (rectified linear unit) with formula $max(0, x)$. I already implemented it, so let's see if something changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100% (400 of 400) |######################| Elapsed Time: 2:09:56 Time:  2:09:56\n"
     ]
    }
   ],
   "source": [
    "from src.layers_09 import ReLULayer\n",
    "\n",
    "optimizer = SGD(learning_rate=1e-4)\n",
    "model = SequenceModel(layers=[\n",
    "    DenseLayer(784, 100, random_seed=46),\n",
    "    ReLULayer(),\n",
    "    DenseLayer(100, 10, random_seed=47),\n",
    "    SoftmaxLayer()\n",
    "], loss=CategoricalCrossEntropyLoss(), metrices=[AccuracyMetric()], random_seed=42)\n",
    "result = model.fit(train_data, train_target, optimizer, test_data, test_target, epochs=400, batch_size=128, progress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy: 0.9497959183673469, Test accuracy: 0.9249047619047619\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(f\"Train accuracy: {result['train_accuracy'][-1]}, Test accuracy: {result['test_accuracy'][-1]}\")\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(result['train_loss'], label=\"train loss\")\n",
    "plt.plot(result['test_loss'], label=\"test loss\")\n",
    "plt.yscale('log')\n",
    "ticks = [0.16, 0.225, 0.32, 0.45, 0.64, 0.9, 1.28, 1.8, 2.56, 3.6, 5.12, 7.2, 10.24, 14.4, 20.48]\n",
    "plt.yticks(ticks=ticks, labels=ticks)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(result['train_accuracy'], label=\"train accuracy\")\n",
    "plt.plot(result['test_accuracy'], label=\"test accuracy\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test accuracy is around $92.49\\%$ - the best result we achieved so far. Remember that we had $92.48\\%$ accuracy with one-vs-one logistic regression model. Not a big improvement, but still an improvement nevertheless.\n",
    "\n",
    "You may notice strange behavior around 10th epoch, when the loss decreased unexpectedly. That is probably caused by the weights initialization, but as I want to write about this topic in a separate notebook, I will ignore it for a now.\n",
    "\n",
    "Now we see how the neural networks works - you may want to check the code once again if you are in doubt. Let's formalize it a little bit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feed forward fully connected neural network\n",
    "\n",
    "What we have seen is sometimes called *Feed forward fully connected neural network*. **Feed forward** from the fact, how the network works - it passes the data through layers sequentially. There are no connections from the later layer to the previous layer, no memory. Moreover, each layer is processed at once. The following layer can't start computing it's output unless it has all the outputs from the previous layer.\n",
    "\n",
    "**Fully connected** is from the fact, that each neuron (remember that one neuron is represented as one row in the dense layer weight matrix) is connected with all the neurons from the previous layer. This connection is represented by the `DenseLayer` class, sometimes also called *Fully-connected layer* or shortly just *FC*.\n",
    "\n",
    "The inference is usually called **forward pass** - the inputs pass through all the layers in the network. During the training, the model needs to compute gradients by backpropagation of the error, this is usually called **backward pass** or **backpropagation pass** (shortly **backprop pass**). Finally, the optimizer takes gradients of parameters and update them, this is usually called **update step**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we want to draw a neural network, they are usually shown using this representation:\n",
    "\n",
    "![Colored Neural Network](https://upload.wikimedia.org/wikipedia/commons/4/46/Colored_neural_network.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The circles represent neurons and the arrows connections between them. The red neurons, at the beginning of the network, are called **input neurons** and the whole layer is called **input layer**. Note that these neurons don't have inputs - they represent the input. They have no weights and no activation function. In fact, in our implementation, we don't even see the input layer - the input layer is the data itself. The inputs layer is a nice demonstration of the inputs data, but in reality, this layer is not implemented - the data in the matrix format simulate them.\n",
    "\n",
    "On the other side, the green neurons are the **output neurons** in the **output layer**. The output from these neurons represents output of the network/model. They have weights and activation function - in our case that's the second dense layer and the softmax activation. Notice that the activation is not explicitly mentioned in the picture - it is mandatory that each neuron will have an activation function (expect the input ones), otherwise, there is no reason to have more layers (I will talk about it a little bit more later on). The picture represents more the architecture of the network (number of layers and neuron), rather than details like activation function.\n",
    "\n",
    "All the layers between the input and output layers are called **hidden layers**. In our case, the hidden layer is the first dense layer and the sigmoid resp. the ReLU activation function. Once again, the activation function is not explicitly shown in the picture. Both in the picture and our model have only one hidden layer, but there can be multiple of them with different dimensionality. You need to make sure, the dimensions match. In our case, we have $784$ inputs and reduced it to $100$ outputs in the first hidden layer, the following layer needs to have $100$ inputs and can have an arbitrary number of outputs.\n",
    "\n",
    "The layers are usually indexed - the hidden layer after the input layer is the first hidden layer, the following one layer is the second hidden layer, and so on. It's hard to tell, how many hidden layers you need and how much neurons should each hidden layer have. It depends on the problem at hand and there is no universal recipe - you need to try more options and pick the best one. That means that **number of layers and neurons are hyperparameters of the model**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the visualization above is nice for the introduction, drawing 784 neurons wouldn't be very descriptive. Because of this, you may sometimes see block schemas of the neural networks. For example in our case it would like this:\n",
    "\n",
    "![Dense network block diagram](img/DenseBlock_09.svg)\n",
    "\n",
    "Or a modified version where the author takes into account the dimension of the layer.\n",
    "\n",
    "![Dense network scaled block diagram](img/BlockScaled_09.svg)\n",
    "\n",
    "However, this still doesn't include what activation function neurons use. Sometimes you may see it included as a separate layer - a similar way it is defined in our network.\n",
    "\n",
    "![Dense network scaled block diagram](img/WithActivation_09.svg)\n",
    "\n",
    "We haven't talked about convolution neural networks, but you may see different visualization for them as well.\n",
    "\n",
    "![Convolutional neural networks diagram](https://upload.wikimedia.org/wikipedia/commons/6/63/Typical_cnn.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mathematical definition\n",
    "\n",
    "We may look at the neural network from the mathematical point of view as well. The dense layer represents a linear combination of $\\mathbb{X}\\mathbb{W}+\\mathbb{b}$ and activation layer function. Together we may describe one layer as\n",
    "\n",
    "$$\n",
    "f(\\mathbb{X}\\mathbb{W}+\\mathbb{b})\n",
    "$$\n",
    "\n",
    "As the output of one layer is input to the following layer, we may simply replace $\\mathbb{X}$ with the output of the previous layer. The whole neural network can then be described as\n",
    "\n",
    "$$\n",
    "f_k(f_{k-1}(\\dots f_2(f_1(\\mathbb{X}\\mathbb{W_1}+\\mathbb{b_1})\\cdot\\mathbb{W_2}+\\mathbb{b_2}) \\dots )\\cdot\\mathbb{W_k}+\\mathbb{b_k})\n",
    "$$\n",
    "\n",
    "This is the output of the neural network.\n",
    "\n",
    "Then there is the **backpropagation algorithm**. That is exactly what the layer is doing when we call the `gradient` method on it. The function receives gradient from the following layer. This gradients tell, how each output should change in order to minimalize the loss. The layer may compute the gradient of its weights (in case of the dense layer) and then computes gradient with respect to inputs - how each input should change to minimalize the loss. Once again, we just exploited the chain rule.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial f(g(x))}{\\partial x}=\\frac{\\partial f(g(x))}{\\partial g(x)}\\cdot\\frac{\\partial g(x)}{\\partial x}\n",
    "$$\n",
    "\n",
    "In the end, we want to know the gradients of weights. The error is propagated back through the layers and therefore the **backpropagation algorithm**.\n",
    "\n",
    "We will start from the last, output layer, as it is the first layer in the context of the backpropagation algorithm.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial w_i} = \\frac{\\partial \\mathcal{L}}{\\partial f(\\pmb{x}\\pmb{w}^T)} \\cdot \\frac{\\partial f(\\pmb{x}\\pmb{w}^T)}{\\partial \\pmb{x}\\pmb{w}^T} \\cdot \\frac{\\partial \\pmb{x}\\pmb{w}^T}{\\partial w_i}\n",
    "$$\n",
    "\n",
    "This is the exact equation we had for the logistic regression. Unlike logistic regression, we need to propagate the error backward - in other words, we need a gradient of the loss with respect to the last layer's inputs.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial y_h} = \\frac{\\partial \\mathcal{L}}{\\partial f(y_h w^T)} \\cdot \\frac{\\partial f(y_h w^T)}{\\partial y_h w^T} \\cdot \\frac{\\partial y_h w^T}{\\partial y_h}\n",
    "$$\n",
    "\n",
    "Here $y_1, y_2, \\dots, y_h$ denote outputs of the first hidden layer, second hidden layer up to the last hidden layer.\n",
    "\n",
    "For hidden layers, the equation is a bit more complicated - it needs to receive gradient from the next layer (gradient of the loss with respect to layer's outputs) and after that, it can compute gradients of weights. Formally\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial w_{ij}^l} = \\sum_k \\left( \\frac{\\partial \\mathcal{L}}{\\partial y_{l+1}^k} \\cdot \\frac{\\partial y_{l+1}^k}{\\partial y_l^j} \\right) \\cdot \\frac{\\partial y_l^j}{\\partial y_{l-1} w^T} \\cdot \\frac{\\partial y_{l-1} w^T}{\\partial w_{ij}^l}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we want to obtain gradient of loss in respect to weight from neuron $i$ in layer $l-1$ to neuron $j$ in layer $l$ - denoted as $w_{ij}^l$. We start by iterating over all neurons in the following $l+1$ layer (the $k$ index in the sum), compute the gradient of the loss with respect to the output this neuron followed by the gradient of its output in respect to its $j$ input. In the formula, the term $y_{l+1}^k$ represents *k-th* output of layer $l+1$. Note that the sum part of the equation corresponds to the value we return from the `backward` method call.\n",
    "\n",
    "Finally, the gradient of neuron's input with respect to weight is computed - all we need to apply afterward is to make the update step.\n",
    "\n",
    "Similarly is computed gradient of the loss with respect to the hidden layer's input.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial y_{l-1}} = \\sum_k \\left( \\frac{\\partial \\mathcal{L}}{\\partial y_{l+1}^k} \\cdot \\frac{\\partial y_{l+1}^k}{\\partial y_l^j} \\right) \\cdot \\frac{\\partial y_l^j}{\\partial y_{l-1} w^T} \\cdot \\frac{\\partial y_{l-1} w^T}{\\partial y_{l-1}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You don't need to remember the equations - more important is to understand how the gradient is propagated through layers and how to obtain gradients of loss with respect to weights. Moreover, modern frameworks like PyTorch and TensorFlow can calculate gradients automatically - a topic we will see in the following notebook."
   ]
  }
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