Thursday, December 26, 2024
12/26/2024
Project Summary / Abstract We do not fully understand how the cortex adapts its limited resources to optimally represent sensory information in time-varying environments. The proposed studies aim to mathematically characterize adaptation in populations of cortical neurons by applying novel geometric analyses and developing a normative theory that accounts for the experimental data. In Aim 1, we will test two hypothetical properties of adaptation. Direction invariance posits that the direction of the population response to a given stimulus is approximately invariant to changes in its prior probability of being observed. A power law relationship postulates that the ratio of the magnitudes of population response to a fixed stimulus across two statistical environments is a power of the ratio between its prior probabilities. An empirical confirmation of these findings will deliver the first mathematical characterization of adaptation capable of predicting population responses in a new environment from the population responses in a known one. In Aim 2, we will develop a normative theory for the power law property. We will consider the hypothesis that a power law emerges as a tradeoff between discrimination performance and the metabolic cost of cortical representation. We will tackle this question using two synergistic approaches: (a) the analysis of simple, analytically tractable models of adaptation and (b) a larger class of auto-encoder models, which provide a flexible way to study the problem numerically. The proposed studies are significant because they fill a major gap in the field by taking a rigorous look at cortical adaptation at the population level, gathering critical data not yet available to the community, and analyzing them using innovative geometric analyses and theoretical modeling. These rigorous studies rely on solid concepts from representational geometry and efficient coding. Solid, preliminary findings show the work has a good chance of transforming our conceptual view of adaptation at the level of neural populations, generating ideas readily applicable to other sensory modalities and systems.
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