ml-recall

#linear-regions

3 questions from Neural Network Basics

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hardAI-checkedNeural Network Basics

Keep the width $k$ of a scalar-input ReLU network fixed and add layers. How can the largest possible number of non-differentiable points (kinks) of the output grow with the number of layers $l$ ?

Exponentially in $l$ 1
Linearly in $l$ , adding at most $k$ kinks per layer2
Polynomially in $l$ , like $l^k$ 3
It stays at most $k$ , whatever the depth4

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