Unsupervised and probabilistic learning with Contrastive Local Learning Networks: The Restricted Kirchhoff Machine - Marcelo Guzman; Simone Ciarella; Andrea J. Liu (Proceedings of the National Academy of Sciences, 2026)
Autonomous physical learning systems modify their internal parameters and solve computational tasks without relying on external computation. Compared to traditional computers, they enjoy distributed and energy-efficient learning due to their physical dynamics. In this paper, we introduce a self-learning resistor network, the Restricted Kirchhoff Machine, capable of solving unsupervised learning tasks akin to the Restricted Boltzmann Machine algorithm. The circuit relies on existing technology based on Contrastive Local Learning Networks, in which two identical networks compare different physical states to implement a contrastive local learning rule. We simulate the training of the machine on a dataset of handwritten digits, providing a proof of concept of its learning capabilities. Finally, we compare the scaling behavior of time, power, and energy per operation as the number of nodes increases to that of a Restricted Boltzmann Machine implemented on central processing unit (CPU) and graphics processing unit (GPU) platforms.