Neural Manifold Capacity Captures Representation Geometry, Correlations, and Task-Efficiency Across Species and Behaviors

Abstract

The study of the brain encompasses multiple scales, including temporal, spatial, and functional aspects. To integrate understanding across these different levels and modalities, it requires developing quantification methods and frameworks. Here, we present effective Geometric measures from Correlated Manifold Capacity theory (GCMC) for probing the functional structure in neural representations. We utilize a statistical physics approach to establish analytical connections between neural co-variabilities and downstream read-out efficiency. These effective geometric measures capture both stimulus-driven and behavior-driven structures in neural population activities, while extracting computationally-relevant information from neural data into intuitive and interpretable analysis descriptors. We apply GCMC to a diverse collection of datasets with different recording methods, various model organisms, and multiple task modalities. Specifically, we demonstrate that GCMC enables a wide range of multi-scale data analysis. This includes quantifying the spatial progression of encoding efficiency across brain regions, revealing the temporal dynamics of task-relevant manifold geometry in information processing, and characterizing variances as well as invariances in neural representations throughout learning. Lastly, the effective manifold geometric measures may be viewed as order parameters for phases related to computational efficiency, facilitating data-driven hypothesis generation and latent embedding.