Physical networks become what they learn

A study submitted to arXiv on 14 Jun 2024 and revised on 10 Apr 2025 shows that physical networks of nodes connected by resistive edges can learn diverse functions by adapting edge conductances to lower a cost function, while also minimizing power dissipation. The research, led by Menachem Stern, reveals that this double optimization process couples the cost landscape and the physical landscape, suggesting that the physical response of networks to perturbations holds significant information about their adapted functions.

Condensed Matter Disordered Systems and Neural Networks Submitted on 14 Jun 2024 v1 https://arxiv.org/abs/2406.09689v1 , last revised 10 Apr 2025 this version, v2 Title:Physical networks become what they learn View PDF /pdf/2406.09689 HTML experimental https://arxiv.org/html/2406.09689v2 Abstract:Physical networks can develop diverse responses, or functions, by design, evolution or learning. We focus on electrical networks of nodes connected by resistive edges. Such networks can learn by adapting edge conductances to lower a cost function that penalizes deviations from a desired response. The network must also satisfy Kirchhoff's law, balancing currents at nodes, or, equivalently, minimizing total power dissipation by adjusting node voltages. The adaptation is thus a double optimization process, in which a cost function is minimized with respect to conductances, while dissipated power is minimized with respect to node voltages. Here we study how this physical adaptation couples the cost landscape, the landscape of the cost function in the high-dimensional space of edge conductances, to the physical landscape, the dissipated power in the high-dimensional space of node voltages. We show how adaptation links the physical and cost Hessian matrices, suggesting that the physical response of networks to perturbations holds significant information about the functions to which they are adapted. Submission history From: Menachem Stern view email /show-email/2d577250/2406.09689 Fri, 14 Jun 2024 03:20:41 UTC 840 KB v1 /abs/2406.09689v1 v2 Thu, 10 Apr 2025 06:37:08 UTC 630 KB Current browse context: cond-mat.dis-nn Change to browse by: References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender IArxiv Recommender What is IArxiv? https://iarxiv.org/about arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .