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We introduce a Monte Carlo framework for estimating mutual information in high-dimensional neural populations by fitting a conditionally independent model to single-neuron responses. This approach overcomes the combinatorial explosion of response patterns, enabling accurate estimation and correction of finite-data bias. The method successfully scales to large empirical datasets, revealing an exponential decay of stimulus uncertainty with population size across diverse neural systems.
Stimulus uncertainty in high-dimensional neural codes decays exponentially with population size, revealing a fundamental scaling law for information processing.
Estimating mutual information in large neural populations is limited by the exponential growth of possible neural response patterns. Here we apply a Monte Carlo framework to make this problem tractable by sampling from a conditionally independent population model fit from single-neuron responses. The estimator accurately recovers analytical ground truth, corrects finite-data bias, and scales to empirical recordings containing 100 to 10,000 neurons from visual cortex, hippocampus, and retina. Across systems, stimulus uncertainty decays exponentially with population size, revealing a simple scaling law for high-dimensional neural codes.