Multilayer Perceptrons › Summary

Multilayer perceptrons extend single neurons into networks capable of learning complex, non-linear functions. By stacking layers with non-linear activations, MLPs can approximate virtually any function, a property formalized in the universal approximation theorem.

Key takeaways from this chapter:

• Hidden layers transform inputs into new representations where patterns become easier to detect, as demonstrated by the XOR problem
• Weight matrices connect layers, with shape $(n^{[l]}, n^{[l-1]})$ for the matrix connecting layer $l-1$ to layer $l$
• Forward pass propagates information through linear transformations and activations: $\mathbf{a}^{[l]} = \sigma(\mathbf{W}^{[l]} \mathbf{a}^{[l-1]} + \mathbf{b}^{[l]})$
• Batch processing uses matrix operations for efficiency, stacking examples as columns of shape $(n^{[0]}, m)$
• Classification uses sigmoid (binary) or softmax (multiclass) output activations with cross-entropy loss
• Regression uses identity (no) output activation with MSE loss
• Architecture design involves balancing depth, width, activation functions, and regularization

The next chapter explores backpropagation in detail, examining how gradients flow backward through the network to update weights. Backpropagation explains how MLPs learn from data.