Exploiting Subgradient Sparsity in Max-Plus Neural Networks

TL;DR

This paper introduces a Max-Plus neural network architecture that leverages algebraic sparsity in subgradients to improve training efficiency, combining interpretability with scalable learning.

Contribution

It proposes a sparse subgradient algorithm tailored for Max-Plus networks, exploiting natural algebraic sparsity for more efficient training with theoretical guarantees.

Findings

Achieves more efficient updates in Max-Plus neural networks.

Exploits subgradient sparsity to reduce unnecessary computations.

Provides a principled approach linking algebraic structure and scalable learning.

Abstract

Deep Neural Networks are powerful tools for solving machine learning problems, but their training often involves dense and costly parameter updates. In this work, we use a novel Max-Plus neural architecture in which classical addition and multiplication are replaced with maximum and summation operations respectively. This is a promising architecture in terms of interpretability, but its training is challenging. A particular feature is that this algebraic structure naturally induces sparsity in the subgradients, as only neurons that contribute to the maximum affect the loss. However, standard backpropagation fails to exploit this sparsity, leading to unnecessary computations. In this work, we focus on the minimization of the worst sample loss which transfers this sparsity to the optimization loss. To address this, we propose a sparse subgradient algorithm that explicitly exploits the algebraic sparsity. By tailoring the optimization procedure to the non-smooth nature of Max-Plus models, our method achieves more efficient updates while retaining theoretical guarantees. This highlights a principled path toward bridging algebraic structure and scalable learning.