Self-Supervised Learning of Local Predictive Directions as a Neural Computation

Natural sensory dynamics are globally nonlinear but often exhibit simple local geometry, with nearby trajectories evolving preferentially along a small number of predictive directions. We ask how neural circuits could discover this geometry directly from temporal experience. We introduce Local Predictive Directions (LPD), a self-supervised framework that learns local directions whose projections maximally predict near-future trajectory evolution. LPD applies past–future canonical correlation analysis to temporal differences, making the learned representation invariant to translations of the underlying state while avoiding estimation of equilibria or a global dynamical model. To represent systems containing multiple predictive regimes, we introduce a non-negative similarity-matching objective that partitions trajectory segments into predictive domains, each associated with a distinct local predictive direction. We derive both offline and online algorithms for optimizing this objective. The online algorithm admits a natural neural-network interpretation: the resulting activities provide soft domain assignments, while synaptic weights encode the corresponding local predictive filters. On stochastic nonlinear dynamical systems, LPD recovers the local predictive geometry and partitions trajectories into distinct dynamical regimes. On naturalistic sensory streams, the online algorithm produces center–surround spatial receptive fields and ON/OFF sustained and transient temporal filters resembling those of early visual neurons. Our results suggest that predictive learning can provide a self-supervised mechanism by which neural circuits discover the local geometry of environmental dynamics and represent it through specialized receptive fields.