Temporal Regularized Learning: Self-supervised learning local in space and time

We introduce Temporal Regularized Learning (TRL), a spatially and temporally local learning rule forself-supervised representation learning from sequential input streams. The key idea is that a VICReg-style objective can be reformulated into a per-neuron, online loss with bounded state, making the coreregularizers compatible with strictly local updates and streaming implementations. We also analyzehow this perspective connects modern SSL objectives to classical temporal representation learningrules such as Slow Feature Analysis and trace learning. We present TRL and a simplified variant,TRL-S, and evaluate them on MNIST under controlled temporal orderings. Our method achievescompetitive accuracy compared to backpropagation, Forward-Forward, and Equilibrium Propagation,while learning highly class-separable representations with rich first-layer receptive fields; TRL-Sattains similar performance despite its more restricted design. We further study a scoped recurrentsetting on MNIST-Rows next-row prediction, comparing against a backpropagation-through-timebaseline, and provide quantitative latent-trajectories.