Hidden Monotonicity: Explaining Deep Neural Networks via their DC Decomposition

TL;DR

This paper introduces methods leveraging monotonicity in neural networks, including a decomposition technique and training as a difference of monotone models, to enhance explainability and improve saliency methods on ImageNet.

Contribution

It proposes a novel decomposition of trained networks into monotone and convex parts and a new training paradigm as the difference of two monotone networks for better explainability.

Findings

SplitCAM and SplitLRP outperform state-of-the-art saliency methods on ImageNet.

Decomposition overcomes numerical issues in monotone neural network approximation.

Training as a difference of monotone networks yields inherently interpretable models.

Abstract

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 adaptation of the decomposition of a trained ReLU network into two monotone and convex parts, thereby overcoming numerical obstacles from an inherent blowup of the weights in this procedure. Our proposed saliency methods - SplitCAM and SplitLRP - improve on state of the art results on both VGG16 and Resnet18 networks on ImageNet-S across all Quantus saliency metric categories. Second, we exhibit that training a model as the difference between two monotone neural networks results in a system with strong self-explainability properties.