A modular platform for decentralized unsupervised learning: the Restricted Kirchoff Machine

The physical learning paradigm takes advantage of energy minimization and local learning rules to develop materials that can learn new computational tasks without the need for a central processor. The Restricted Boltzmann Machine is a type of physics-informed neural network modeled after a spin-glass system that can perform unsupervised learning tasks on sets of input data [1]. An analogous system, the Restricted Kirchoff Machine, treats resistors as coupling terms between spins, and involves binarization of node voltages via an analog-to-digital conversion that is mediated by a random comparator signal, modeling a Boltzmann temperature, T. Here we present an experimental realization of the Restricted Kirchoff Machine. The modular structure of the electronic device provides a pathway for scaling to large-N systems. We also demonstrate the successful training of simple tasks on minimal network structures, and show that increasing the ``temperature,” or randomness of the system, leads to poorer reconstruction of the training data, in accordance with expectations from theory.

[1]: Guzman, Marcelo, Simone Ciarella, and Andrea J. Liu. "Unsupervised and probabilistic learning with Contrastive Local Learning Networks: The Restricted Kirchhoff Machine." arXiv preprint arXiv:2509.15842 (2025).