arXiv Machine Learning By Alexei V. Tkachenko

Thermodynamic cost of inference and learning in physical neural networks

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The paper investigates the thermodynamic cost of inference and learning in physical neural networks. It shows that quasi‑static inference requires no work, while finite‑speed inference incurs work bounded by the Wasserstein‑2 distance between thermal states, roughly $k_B T$ per dimension of the widest layer. Learning, however, has an irreducible cost of a few $k_B T$ per parameter, independent of speed, indicating that memory dominates the thermodynamic price.

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