Physical networks become what they learn

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.

6 pages, 2 figures

References in corpus (21)

• A high-bias, low-variance introduction to Machine Learning for physicists
• Parameter Space Compression Underlies Emergent Theories and Predictive Models
• Designing allostery-inspired response in mechanical networks
• Low-frequency vibrations of soft colloidal glasses
• Self-sustained lift and low friction via soft lubrication
• The Sense of Place: Grid Cells in the Brain and the Transcendental Number e
• Learning without neurons in physical systems
• Protein sectors: statistical coupling analysis versus conservation
• Directed aging, memory and Nature's greed
• Demonstration of Decentralized, Physics-Driven Learning
• The limits of multifunctionality in tunable networks
• Supervised learning in a mechanical system
• Supervised learning in physical networks: From machine learning to learning machines
• Physical model of the genotype-to-phenotype map of proteins
• Machine Learning Without a Processor: Emergent Learning in a Nonlinear Electronic Metamaterial
• The hidden topological structure of flow network functionality
• Desynchronous Learning in a Physics-Driven Learning Network
• Self-learning Machines based on Hamiltonian Echo Backpropagation
• Revealing structure-function relationships in functional flow networks via persistent homology
• The Physical Effects of Learning
• Learning to self-fold at a bifurcation