Topologically constrained statistical physics models capture functional aspects of a sensory code

Efficient encoding of sensory information about an organism’s environment arises from the coordinated activity of large populations of neurons, whose complex collective behaviors must be interpreted by downstream brain areas to guide behavior. Recent work has introduced a successful modeling framework based on the minimax entropy principle, providing an analytically tractable description of the activity of large neuronal populations. However, previous analyses using such models have been largely agnostic to the behavioral and cognitive functions of population codes. Here, we evaluate the functional performance of the minimax entropy framework in a sensory context with a clear downstream cognitive task: identification of an external natural environment. We analyze a population of neurons in the retina responding to distinct, behaviorally relevant natural moving visual scenes, inferring a sparse, topologically constrained Ising model that admits only a maximally informative subset of pairwise cell–cell couplings. We find that, beyond accurately reproducing collective firing statistics, these tree-like coupling networks enable rapid and robust scene identification, even in small subpopulations of neurons. We further investigate the scaling of scene identification speed and the critical behavior of the model. Our results demonstrate the functional relevance of topologically constrained, maximally informative coupling networks in sensory codes, offering a computationally efficient and biologically interpretable statistical physics framework for understanding population coding in large neuronal ensembles.