Inference Equivalence Reveals a Scaling Transition in Population Computation

Determining which aspects of neural population variability are necessary to support computation remains a central problem in systems neuroscience. Statistical reductions and surrogate models often simplify trial-to-trial variability by preserving selected response statistics, implicitly assuming that discarded structure is computationally irrelevant. Here we introduce inference equivalence (IE), a criterion stating that a statistical reduction is valid if and only if it preserves inference capacity for a specified task and decoder family. IE therefore provides a direct test of whether simplified statistical descriptions remain computationally sufficient for a neural population. We operationalize IE using controlled surrogate perturbations applied to large-scale recordings from primary visual cortex while systematically increasing stimulus scale. Although many surrogate constructions preserve commonly analyzed response statistics, inference equivalence eventually fails as stimulus diversity increases, revealing a scaling breakdown in population computation. These results show that preserving commonly analyzed response statistics does not guarantee preservation of population-level computational capacity, establishing inference equivalence as a principled criterion for assessing the computational sufficiency of simplified neural representations.