3 accepted papers
It has been demonstrated in various contexts that monotonicity leads to better explainability in neural networks. However, not every function can be well approximated by a monotone neural network.We demonstrate that monotonicity can still be used in two ways to boost explainability. First, we use an
We contribute towards resolving the open question of how many hidden layers are required in ReLU networks for exactly representing all continuous and piecewise linear functions on $\mathbb{R}^d$. While the question has been resolved in special cases, the best known lower bound in general is still 2…
We prove that the set of functions representable by ReLU neural networks with integer weights strictly increases with the network depth while allowing arbitrary width. More precisely, we show that $\lceil\log_2(n)\rceil$ hidden layers are indeed necessary to compute the maximum of $n$ numbers, match…