Exactly solvable statistical physics models for large neuronal populations

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>N</a:mi><a:mo>∼</a:mo><a:mn>100</a:mn></a:mrow></a:math> neurons. As <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>N</b:mi></b:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>N</c:mi><c:mo>∼</c:mo><c:mn>1500</c:mn></c:mrow></c:math> neurons in the mouse hippocampus, and we find that the resulting model captures key features of collective activity in the network. Published by the American Physical Society 2025