How network anatomy shapes learning in resistive circuits

Machine learning (ML) and biological learning have been connected from the beginning, but many ML approaches lack constraints ubiquitous in biological learning, such as locality and tight energy budgets. Contrastive Local Learning Networks (CLLNs), or resistive circuits trained by local rules such as coupled learning [1], offer an appealing middle path because they admit good "ground truth" microscopic models like ML, yet their learning is subject to many of the same constraints faced by biological learners. Here we study how network architecture, nonlinear tunable conductances and learning rule affect the performance of tunable resistive networks on the MNIST digit classification task. Beginning with linear networks, in which each learning degree of freedom is an adjustable Ohmic resistor, we observe and explain why circuits with higher connectivity classify better. Then, we examine how to choose learning rate, nudging, and batch size to avoid failure. Finally, we touch on how our results in the linear case can be extended to nonlinear networks, which can provide even better performance.

[1]: M Stern et al, “Supervised Learning in Physical Networks: From Machine Learning to Learning Machines,” PRX, 2021.

[2]: M Stern et al, “Physical networks become what they learn,” PRL, 2025.