Multilayer perceptron and activation functions (ReLU and GELU). Explanation.
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Hello everyone! This is the 12th episode of this mini-course on the mathematical foundations of machine learning. Today, we'll learn why conventional linear models fail when faced with simple problems like XOR. In this episode, we'll explore the architecture that has become the foundation of modern deep learning—the multilayer perceptron (MLP). We'll also cover the following topics:
The problem of linearity. Why a single neuron isn't enough and how neural networks manage to "bend" the data space.
The anatomy of MLPs: how hidden layers are structured and what actually happens inside matrix calculations.
The wonders of activation: why activation functions are needed and why without them, any deep network turns into a simple regression.
ReLU vs. GELU: Let's compare the classical approach with the modern standard used in architectures like GPT, and learn how the "smoothness" of a function affects the loss function landscape.
The Universal Approximation Theorem: how simple "folds" and the addition of straight lines give rise to a neural network's ability to describe any complex function in our universe.