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  • Letter
  • Open Access

Exactly solvable statistical physics models for large neuronal populations

Christopher W. Lynn1,2,3,*, Qiwei Yu4, Rich Pang5, William Bialek3,4,6, and Stephanie E. Palmer7,8

  • *Contact author: christopher.lynn@yale.edu
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Phys. Rev. Research 7, L022039 – Published 19 May, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022039

Abstract

Maximum-entropy methods provide a principled path connecting measurements of neural activity directly to statistical physics models, and this approach has been successful for populations of N∼100 neurons. As N increases in new experiments, we enter an undersampled regime where we have to choose which observables should be constrained in the maximum-entropy construction. The best choice is the one that provides the greatest reduction in entropy, defining a “minimax entropy” principle. This principle becomes tractable if we restrict attention to correlations among pairs of neurons that link together into a tree; we can find the best tree efficiently, and the underlying statistical physics models are exactly solved. We use this approach to analyze experiments on N∼1500 neurons in the mouse hippocampus, and we find that the resulting model captures key features of collective activity in the network.

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Exact minimax entropy models of large-scale neuronal activity

Christopher W. Lynn, Qiwei Yu, Rich Pang, Stephanie E. Palmer, and William Bialek
Phys. Rev. E 111, 054411 (2025)

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Outline

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Phys. Rev. Research 7, L022039– Published 19 May, 2025
  • Received 18 December 2023
  • Revised 27 June 2024
  • Accepted 28 March 2025
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