The specific problem that arises, when trying to implement the feedforward neural network, is that we are trying to transform from 784 nodes all the way down to 10 nodes. To really understand how and why the following approach works, you need a grasp of linear algebra, specifically dimensionality when using the dot product operation. The initialization of weights in the neural network is kind of hard to think about. X_train, x_val, y_train, y_val = train_test_split(x, y, test_size=0.15, random_state=42) x, y = fetch_openml('mnist_784', version=1, return_X_y=True) We also choose to load our inputs as flattened arrays of 28 * 28 = 784 elements, since that is what the input layer requires. We choose to go with one-hot encoded labels, since we can more easily subtract these labels from the output of the neural network. We do normalization by dividing all images by 255, and make it such that all images have values between 0 and 1, since this removes some of the numerical stability issues with activation functions later on. Now we have to load the dataset and preprocess it, so that we can use it in NumPy. from sklearn.datasets import fetch_openmlįrom _utils import to_categoricalįrom sklearn.model_selection import train_test_split Note that we use other libraries than NumPy to more easily load the dataset, but they are not used for any of the actual neural network. Imports And Datasetįor the whole NumPy part, I specifically wanted to share the imports used. In most real-life scenarios, you would want to optimize these parameters by brute force or good guesses – usually by Grid Search or Random Search, but this is outside the scope of this article. Though, the specific number of nodes chosen for this article were just chosen at random, although decreasing to avoid overfitting. This is based on empirical observations that this yields better results, since we are not overfitting nor underfitting, but trying to get just the right number of nodes. You might realize that the number of nodes in each layer decreases from 784 nodes, to 128 nodes, to 64 nodes and then to 10 nodes. This label is received in the form of an array with 10 elements, where one of the elements is 1, while the rest is 0. Output layer: In this layer, we are reducing the 64 nodes to a total of 10 nodes, so that we can evaluate the nodes against the label.This is no new challenge, since we already reduced the number in the first layer. Hidden layer 2: In this layer, we have decided to go with 64 nodes, from the 128 nodes in the first hidden layer.This brings a challenge when we are going forward in the neural network (explained later). Hidden layer 1: In this layer, we have decided to reduce the number of nodes from 784 in the input layer to 128 nodes.This means our input layer will have 784 nodes. We flatten these images into one array with $28 \times 28 = 784$ elements. ![]() Input layer: In this layer, we input our dataset, consisting of 28x28 images.To be able to classify digits, we must end up with the probabilities of an image belonging to a certain class, after running the neural network, because then we can quantify how well our neural network performed. Let's try to define the layers in an exact way. 10 examples of the digits from the MNIST dataset, scaled up 2x.įor training the neural network, we will use stochastic gradient descent which means we put one image through the neural network at a time. ![]() We say that there are 10 classes, since we have 10 labels. ![]() The dataset contains one label for each image, specifying the digit we are seeing in each image. We are making this neural network, because we are trying to classify digits from 0 to 9, using a dataset called MNIST, that consists of 70000 images that are 28 by 28 pixels. We are building a basic deep neural network with 4 layers in total: 1 input layer, 2 hidden layers and 1 output layer.
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