[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
...
Bibliographic Explorer
(What is the Explorer?) Connected Papers
(What is Connected Papers?) Litmaps
(What is Litmaps?) scite Smart Citations
(What are Smart Citations?)# Code, Data and Media Associated with this Article alphaXiv
(What is alphaXiv?) CatalyzeX Code Finder for Papers
(What is CatalyzeX?) DagsHub
(What is DagsHub?) Gotit.pub
(What is GotitPub?) Hugging Face
(What is Huggingface?) ScienceCast
(What is ScienceCast?)# Demos Influence Flower
(What are Influence Flowers?) CORE Recommender
(What is CORE?) IArxiv Recommender
(What is IArxiv?)# 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.