Arvind Murugan

Authored papers (1)

• Learning without neurons in physical systems2022

  Physical systems — elastic networks, flow networks, molecular assemblies, and creased sheets — can autonomously learn desired input-output behaviors through purely local learning rules, without any computer or centralized optimizer, a framework Stern and Murugan term 'physical learning.' The core theoretical advance is demonstrating that local rules of the form dw[x,t]/dt ∼ h(s(f;{w})[x,t]) can collectively minimize a global cost function because the physical response s encodes global information locally, bridging the apparent gap between locality and global optimization. Contrastive learning in resistor networks (Dillavou et al. 2021) successfully classifies the 4-feature Iris dataset with accuracy reaching 97% by step 300, and learning capacity in 2D molecular self-assembly systems scales as the square root of the number of distinct molecular species. A Hebbian molecular learning rule — dwij/dt ∼ si(x,t)sj(x,t) — enables self-assembling systems built from 2,500 molecular species to perform pattern recognition on 2,500-pixel images through stochastic nucleation dynamics. Physical learning also leaves diagnostic signatures in its substrates: trained systems develop spatial heterogeneity in elastic moduli, prune unused network edges, generate anomalously few energy minima relative to random disordered systems, and acquire soft modes that reduce response dimensionality. The paper argues these findings imply that physical learning provides a principled, model-free route to inverse-problem solving in materials, that local rules are not fundamentally inferior to global gradient descent, and that the physical signatures of learning — heterogeneity, soft modes, reduced landscape complexity — may serve as empirical markers for identifying naturally evolved or learned physical systems in biology and materials science.

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• The collective intelligence of evolution and development2× refs

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  stern-2022-learning.md