Solving constrained minimax problems with spiking neural networks

Authors: Guillermo Martín-Sánchez, William F. Podlaski, Christian K. Machens

Presentation type: Poster at SNUFA 2025 online workshop (5-6 Nov 2025)

Abstract

Spiking neural networks (SNNs) serve as key models of brain function in neuroscience and as energy efficient algorithms in engineering. However, they remain difficult to build and interpret. In this work, we establish a theoretical connection between SNNs and minimax optimization — a broad class of optimization problems with links to decision making under uncertainty, zero-sum games, and optimal control. Building on existing results that link SNNs to convex optimization, we show that the dynamics of certain low-rank SNNs can solve minimax problems with quadratic objectives and linear constraints. We provide geometrical intuitions for how the minimax problem maps onto a network’s latent space, and how the latent dynamics of the spiking networks reaches the optimal solution. With this work, we hope to make a step forward in interpretability and usability of spike-based computation — not only serving as a viable framework to understand biological networks, but also opening avenues for neuromorphic implementations of energy-efficient optimization solvers.