AI-DISCOVERED TUNING EQUATIONS EXPLAIN HIGH-DIMENSIONAL POPULATION CODES

High-dimensional population codes are a defining feature of sensory cortex, yet existing theory fails to explain how such geometry arises from single-neuron tuning. In mouse primary visual cortex (V1), responses to finely spaced drifting gratings exhibit power-law population eigenspectra. All standard smooth tuning models (Gaussian or von Mises) instead predict exponentially decaying, low-dimensional structure, directly contradicting data. To resolve this discrepancy, we developed an AI-based equation discovery system designed to generate interpretable mechanistic models from neural data. Applied to single-neuron tuning curves alone, the system discovered a previously unconsidered parametric family of angular tuning functions. Crucially, without being trained on population statistics, the AI-discovered equation quantitatively predicted the experimentally observed population eigenspectrum, including its n⁻⁴ decay. The key innovation is a shape parameter controlling peak sharpness, yielding tuning functions of the form exp(−|θ|ᵖ). For p < 2, these non-smooth tuning curves provably generate power-law eigenspectra with analytically predictable exponents. Fits to V1 data clustered near p ≈ 1, providing a direct and quantitative explanation of cortical population geometry. In simulated decoding tasks, the AI-derived tuning enabled accurate linear discrimination of fine angular differences, whereas smooth tuning models failed even with arbitrarily large readout weights. Finally, we show that a stabilized supralinear network can implement the AI-discovered transformation, converting smooth inputs into non-smooth outputs. Across both V1 orientation tuning and thalamic head-direction cells, the AI-derived equation consistently outperformed all classical models. These results demonstrate that AI-driven equation discovery can uncover new computational principles linking single-neuron response properties to population-level representations.