Neurons as Detectors of Coherent Sets in Sensory Dynamics
Dmitri Chklovskii, Xuehao Ding, Charles Epstein, Philip Greengard, Jason J. Moore, Joshua L Pughe-Sanford, Anirvan Sengupta
We model sensory streams as observations from high-dimensional stochastic dynamical systems and conceptualize sensory neurons as self-supervised learners of compact representations of such dynamics. From previously encountered stimuli, neurons learn \emph{coherent sets}—regions of stimulus state space whose trajectories evolve cohesively over finite times—and compute membership indices for new stimuli. Coherent sets are discovered via spectral clustering of the \emph{stochastic Koopman operator (SKO)}, where the sign pattern of the subdominant singular function partitions the state space into minimally coupled regions. For multivariate Ornstein–Uhlenbeck processes, the subdominant singular function reduces to a linear projection of inputs onto the dominant singular vector of the whitened state-transition matrix, enabling neurons to compute membership indices through a simple filter-and-rectify operation. These indices support near-future prediction in contracting coherent sets and retrospection-enhanced representations in expanding coherent sets, suggesting a functional dichotomy between prospective and retrospective neuron types. We extend this approach to nonlinear dynamics via Galerkin projections of the SKO followed by past-future canonical correlation analysis, providing a biologically plausible, data-driven route to the requisite singular vectors. This framework accounts for neuronal temporal receptive fields, the ubiquity of rectification in neuronal responses, and the predictive versus retrospective specialization seen in tufted versus mitral cells and non-lagged versus lagged cells. Coherent set detection thus emerges as a fundamental neural computation for modeling biological sensory processing and designing artificial systems.