Low-power analogue neural networks with trainable nonlinear connections for continuous control

2026-06-21

AI Summary

This work addresses the inefficiency of conventional physical neural networks, which treat nonlinear devices merely as scalar weights and struggle to approximate smooth functions effectively. Inspired by the Kolmogorov–Arnold representation theorem, the authors propose a novel architecture that places trainable nonlinear functions along network connections rather than at nodes, thereby transforming each physical link into a learnable computational unit. This design substantially reduces network size and enhances modeling efficiency for smooth functions, such as those encountered in continuous control tasks, while enabling cross-hardware portability. Implemented using analog bandpass filters based on field-programmable analog arrays, the approach demonstrates architectural generality across both CMOS and memristor platforms. High-accuracy performance is achieved in robotic kinematics, continuous control, and photovoltaic maximum power point tracking with drastically fewer nodes and connections—e.g., only 35,000 connections—than conventional multilayer perceptrons, consuming approximately 30 microwatts when deployed on CMOS hardware.

Abstract

Physical neural networks promise low-power machine learning by computing directly with analogue device physics, but most architectures force nonlinear device responses to act as scalar weights. Inspired by Kolmogorov-Arnold networks, we place trainable nonlinear functions on the connections, making each physical connection a learnable computational element. Realising these functions as analogue band-pass filters on field-programmable analogue arrays, we find that the benefit is task-dependent and follows from the smoothness of the physical basis: the networks represent smooth, continuously valued targets, including robotic kinematics, continuous control, and photovoltaic maximum-power-point tracking, with far fewer nodes and connections than multilayer perceptrons, but offer no parameter-efficiency advantage on classification-like decision boundaries. Trained networks transfer to hardware across approximately 35,000 connections with quantified fidelity, and a dedicated CMOS implementation is projected to operate at approximately 30 microwatts. A memristive realisation reproduces the same behaviour in simulation, indicating that the advantage comes from placing trainable nonlinearity on connections, rather than from a particular device.

Problem

• physical neural networks
• trainable nonlinear connections
• continuous control
• low-power analogue computing
• Kolmogorov-Arnold networks

Innovation

• trainable nonlinear connections
• analogue neural networks
• physical neural networks
• Kolmogorov-Arnold networks
• low-power computing