Information-Theoretic Gradient Flows Reveal Asymmetric Transformations in Mouse Visual Cortex

Neural representations can be modelled as probability distributions that evolve over time.Understanding how these distributions transform among brain regions remains a fundamentalchallenge within computational neuroscience. We introduce a framework that characterizessuch transformations in terms of gradient flows — dynamical trajectories that follow thesteepest ascent of two information-theoretic functionals given by entropy and expectation. Weshow that these two functionals account for orthogonal flows in the case of Gaussiandistributions. Furthermore, the linear combination of entropy and expectation allows for thedecomposition of neural transformations into interpretable components. We first validate thisframework in silico by demonstrating robust recovery of the gradient flows from observablesignal features. We then apply the same framework to two-photon imaging data collected frommurine visual cortex. We identify consistent flow between the rostrolateral area and primaryvisual cortex across all five mice, indicating a bi-directional mapping of the neural activitypatterns between these two cortical regions. Our approach offers a generalizable method thatcan be used to separate information-theoretic flows, not just among brain regions, but alsoacross neuroimaging modalities and observational scales.