The provided text is a technical article covering the implementation and explanation of a multilayer neural network from scratch. It discusses the foundations, implementation, training, hyperparameter tuning, and conclusions about the network, along with sections on activation, loss function, backpropagation, and dataset. It also includes code for implementation and examples of mathematical notation and equations used in the article. The article seems to serve as a valuable educational resource for understanding and implementing neural networks.
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Setting the foundations right
Photo by Konta Ferenc on Unsplash
What is a multilayer neural network?
This section introduces the architecture of a generalised, feedforward, fully-connected multilayer neural network. The network accepts a vector of features as input and produces a vector as an output, where each element lies in the range [0, 1]. The article covers the mathematical notation used for describing mathematically neural networks, the role of various matrices with weights and biases, and the formulas for updating the weights and biases to minimize the loss function.
Activation
Enabling the neural network to solve complex problems requires introducing some form of nonlinearity. The article introduces the sigmoid (logistic) activation function and its visual representation.
Loss function
The loss function used for adaline was the mean square error. In practice, a multiclass classification problem would use a multiclass cross-entropy loss. The article explains the mean square error loss function and its role in the context of a multilayer neural network.
Backpropagation
The article delves into the backpropagation process, which involves the successive application of the chain differentiation rule from the right to the left. It covers the derivatives of the loss function with respect to the weights and bias terms used for computing the net input of each layer.
Implementation
This section provides the implementation of a generalised, feedforward, multilayer neural network, drawing analogies to specialised deep learning libraries such as PyTorch. It includes utility functions for activation and one-hot encoding, along with methods for forward and backward propagation.
Dataset
The article introduces the MNIST handwritten digits dataset, explains its features, and visualizes sample images for each digit.
Training the model
The article details the process of splitting the dataset, using mini-batches, and monitoring the loss and accuracy during training. It provides code for iterating over epochs and mini-batches to update the model parameters and monitor the training and test set performance.
Hyperparameter tuning
This section covers the process of basic hyperparameter tuning by varying the number of hidden layers, the number of nodes in the hidden layers, and the learning rate. It employs cross-validation to find the optimal hyperparameters and retrain the model with the selected parameters.
Conclusions
The article concludes by summarizing the educational value of the implementation and outlines potential improvements for practical use. It also provides guidance for further study in the form of a recommended book.
LaTeX code of equations used in the article
The article provides a link to the LaTeX code of equations used in the gist below.
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