Two $\operatorname{ReLU}$ Layers is All You Need

Florestan Brunck, Christoph Hertrich, Kilian Ruess, Jack Stade, Amir Yehudayoff

We prove that every $\operatorname{ReLU}$ network can be exactly simulated by a $\operatorname{ReLU}$ network with two hidden layers. We present two proofs: one that is based on fillings in homological algebra and a direct combinatorial proof.