Characterizing neuronal population geometry with AI equation discovery

The visual cortex contains millions of neurons, whose combined activity forms a population code representing visual stimuli. There is, however, a discrepancy between our understanding of this code at the single neuron and population levels: direct measurements suggest that the population code is high-dimensional, but current understanding of single-cell tuning curves implies low dimensionality. To reconcile this discrepancy, we used AI to find a new parsimonious, interpretable equation for tuning curves to oriented stimuli. Candidate equations were expressed as short computer programs, and evolved using Large Language Models (LLMs) to improve their fits to single-cell tuning. This resulted in an equation that not only improved single-cell fits, but also accurately modelled the population code’s high-dimensional structure, even though population dimensionality was not the AI system’s objective. This high-dimensionality occurred because the AI-derived tuning curves were not smooth at their peaks, which we proved is mathematically required for high-dimensional population coding of low-dimensional stimuli. We used the AI-generated tuning equation to demonstrate the advantages of high-dimensional codes in a simulated hyperacuity task, and showed that non-smooth peaks are also present in other brain systems, leading to high-dimensional population coding in head direction cells. These results suggest that the smoothness of neuronal tuning curves has an important role in setting the dimensionality of the population code, and demonstrate how AI equation discovery can accelerate scientific theory building in neuroscience and beyond.