🎨 Welcome to the Activation Zoo

Discover the functions that bring neural networks to lifeβ€”introducing non-linearity for complex pattern learning

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Backpropagation Visualizer

Why Activation Functions?

Without activation functions, neural networks would just be linear transformations. No matter how many layers you stack, the result would be equivalent to a single linear layer.

🎯 The Non-Linearity Problem

Linear transformations can only create straight decision boundaries. Real-world problems need curves, circles, and complex shapes.

y = Wβ‚‚(W₁x + b₁) + bβ‚‚
↓ (equivalent to)
y = Wx + b
πŸ”—

Linear Layers

Perform weighted sums of inputs. Essential for learning, but can't model complex patterns alone.

⚑

Activation Functions

Add non-linearity, enabling networks to learn complex decision boundaries and patterns.

Key Properties

Non-linearity:Enables learning complex patterns
Differentiability:Required for backpropagation
Range:Output bounds affect network behavior
Computational Efficiency:Impacts training speed

Universal Approximation Theorem

Neural networks with at least one hidden layer and non-linear activation functions can approximate any continuous function to arbitrary precision (given enough neurons).

πŸ’‘This theorem justifies the power of deep learning!