# A simple geometric proof for the benefit of depth in ReLU networks

@article{Amrami2019ASG, title={A simple geometric proof for the benefit of depth in ReLU networks}, author={Asaf Amrami and Yoav Goldberg}, journal={ArXiv}, year={2019}, volume={abs/2101.07126} }

We present a simple proof for the benefit of depth in multi-layer feedforward network with rectified activation (“depth separation”). Specifically we present a sequence of classification problems indexed by m such that (a) for any fixed depth rectified network there exist an m above which classifying problem m correctly requires exponential number of parameters (in m); and (b) for any problem in the sequence, we present a concrete neural network with linear depth (inm) and small constant width…

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