Neural Population Geometry across model scale: A tool for cross-species functional comparison of visual brain regions

Breakthrough in-vivo recording techniques and computational tools allow quantitative characterization of the population geometry from large-scale neural recordings. Activity covariance from such recordings exhibits striking statistical properties, namely a characteristic power law in the eigenspectrum: the decay coefficient of the eigenspectrum α≈1 for mouse and monkey V1 population responses. Concurrently, studies in self-supervised deep neural networks (DNNs) also demonstrate a similar property, i.e., α is close to 1 in their final layers of visual information processing. However, these models are typically overparameterized, and the network size significantly impacts α of emergent representations. This observation begs the question: how does the neural population geometry vary with the "size" of a biological neural network? Furthermore, could α be used to compare functional properties of brain areas across species?
We show that well-trained DNNs of sufficient width and depth optimized with self-supervised objectives on natural images exhibit α similar to mammalian V1. However, shallower networks do not exhibit the same behavior, raising questions about neural population geometry across the scale of model capacity. Moreover, we present results of how α varies with depth in DNN with canonical architectures, i.e. convolutional neural networks and vision transformers. These observations suggest a vast hypothesis space for observed α given the overall network size and depth of the representation in the information processing hierarchy.
Cross-species functional comparison presents several challenges, including normalizing for size, diversity in behavioral repertoire, and information-processing hierarchy. Our work presents a framework for scale-adjusted comparison by providing an extensive characterization of the relationship between α, network size, and information-processing hierarchy. In particular, given neural responses from a brain's visual region, we could compute α and then determine its functional analog in other organisms. Overall, we believe our work contributes to establishing the cross-species homology of visual processing regions in the brain.