Theory of Intelligence
DEEP LEARNING•Neural Networks•Multilayer Perceptrons•2.4 Depth, Width & Universal Approximation

Introduction

Why a neural network can in principle approximate any function, why deep networks usually beat wide shallow ones, and what representation learning means.

Introduction

How powerful is a neural network, really? And if one hidden layer can already do a lot, why do modern networks have dozens or hundreds of layers?

Imagine building shapes with LEGO. With enough tiny bricks laid side by side in a single flat layer, you can approximate any outline — but you'll need an enormous number of bricks. If you can stack them and build reusable parts (wheels, windows, doors), you can build complex things like a whole town with far fewer bricks. Depth gives neural networks the same advantage: reusable, layered building blocks.

Discuss theoretical concepts, mathematical formulas, and architectural foundations.

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