Unsupervised and probabilistic learning with Contrastive Local Learning Networks: The Restricted Kirchhoff Machine
Abstract
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.
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BibTeX
@article{guzman2026unsupervised,
title = {{Unsupervised and probabilistic learning with Contrastive Local Learning Networks: The Restricted Kirchhoff Machine}},
author = {Marcelo Guzman and Simone Ciarella and Andrea Liu},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
year = {2026},
month = may,
doi = {10.1073/pnas.2525792123},
eprint = {2509.15842},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05750943v1},
note = {CC BY-NC-ND},
}
RIS
TY - JOUR
TI - Unsupervised and probabilistic learning with Contrastive Local Learning Networks: The Restricted Kirchhoff Machine
AU - Marcelo Guzman
AU - Simone Ciarella
AU - Andrea Liu
PY - 2026
DA - 2026/05/21
JO - Proceedings of the National Academy of Sciences of the United States of America
DO - 10.1073/pnas.2525792123
UR - https://hal.science/hal-05750943v1
AB - 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.
SN - 0027-8424
SN - 1091-6490
ER -