Taming Binarized Neural Networks and Mixed-Integer Programs

TL;DR

This paper introduces a novel approach to training binarized neural networks by reformulating them as a subadditive dual of a mixed-integer program, enabling implicit differentiation and practical backpropagation.

Contribution

It presents a new formulation of binarized neural networks as a mixed-integer program dual, allowing the use of implicit differentiation for training.

Findings

Enables backpropagation for binarized neural networks

Provides a framework applicable to broader mixed-integer programs

Facilitates explainability of neural networks

Abstract

There has been a great deal of recent interest in binarized neural networks, especially because of their explainability. At the same time, automatic differentiation algorithms such as backpropagation fail for binarized neural networks, which limits their applicability. By reformulating the problem of training binarized neural networks as a subadditive dual of a mixed-integer program, we show that binarized neural networks admit a tame representation. This, in turn, makes it possible to use the framework of Bolte et al. for implicit differentiation, which offers the possibility for practical implementation of backpropagation in the context of binarized neural networks. This approach could also be used for a broader class of mixed-integer programs, beyond the training of binarized neural networks, as encountered in symbolic approaches to AI and beyond.