Principled Weight Initialisation for Input-Convex Neural Networks

TL;DR

This paper introduces a new weight initialization method for Input-Convex Neural Networks (ICNNs) that improves training efficiency and generalization, enabling effective application in real-world tasks like drug discovery.

Contribution

We derive a principled weight initialization for ICNNs by extending signal propagation theory to non-negative weights, enhancing training and application performance.

Findings

Initialization accelerates learning in ICNNs.

Proper initialization allows training without skip-connections.

ICNNs improve molecular space exploration in drug discovery.

Abstract

Input-Convex Neural Networks (ICNNs) are networks that guarantee convexity in their input-output mapping. These networks have been successfully applied for energy-based modelling, optimal transport problems and learning invariances. The convexity of ICNNs is achieved by using non-decreasing convex activation functions and non-negative weights. Because of these peculiarities, previous initialisation strategies, which implicitly assume centred weights, are not effective for ICNNs. By studying signal propagation through layers with non-negative weights, we are able to derive a principled weight initialisation for ICNNs. Concretely, we generalise signal propagation theory by removing the assumption that weights are sampled from a centred distribution. In a set of experiments, we demonstrate that our principled initialisation effectively accelerates learning in ICNNs and leads to better generalisation. Moreover, we find that, in contrast to common belief, ICNNs can be trained without skip-connections when initialised correctly. Finally, we apply ICNNs to a real-world drug discovery task and show that they allow for more effective molecular latent space exploration.