Neurons as Detectors of Coherent Sets in Sensory Dynamics
Abstract
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 prior experience, neurons learn coherent sets-regions of stimulus state space whose trajectories evolve cohesively over finite times-and assign membership indices to new stimuli. Coherent sets are identified via spectral clustering of the stochastic Koopman operator (SKO), where the sign pattern of a subdominant singular function partitions the state space into minimally coupled regions. For multivariate Ornstein-Uhlenbeck processes, this singular function reduces to a linear projection onto the dominant singular vector of the whitened state-transition matrix. Encoding this singular vector as a receptive field enables neurons to compute membership indices via the projection sign in a biologically plausible manner. Each neuron detects either a predictive coherent set (stimuli with common futures) or a retrospective coherent set (stimuli with common pasts), suggesting a functional dichotomy among neurons. Since neurons lack access to explicit dynamical equations, the requisite singular vectors must be estimated directly from data, for example, via past-future canonical correlation analysis on lag-vector representations-an approach that naturally extends to nonlinear dynamics. This framework provides a novel account of neuronal temporal filtering, the ubiquity of rectification in neural responses, and known functional dichotomies. Coherent-set clustering thus emerges as a fundamental computation underlying sensory processing and transferable to bio-inspired artificial systems.