Layer-local self-supervised objectives remove the backward pass between layers, but almost all still compute their loss over a batch of samples and are therefore local in space but not in time. We introduce Temporal Regularized Learning (TeReL), a spatially and temporally local learning rule for self-supervised representation learning from sequential input streams. The key idea is to instantiate a VICReg-style objective with temporally adjacent positives and non-differentiated running population statistics, yielding a per-neuron online loss with bounded state. The objective is a soft form of Slow Feature Analysis, and its gradient is a Hebbian update of the feedforward weights and an anti-Hebbian update of one lateral matrix per layer. The aim of the experiments is to show that the rule works in a small network, not to compete with backpropagation. On a class-chunked MNIST stream, a two-layer fully connected network trained with batch size one outperforms random features (96.48% versus 95.09% linear-probe accuracy) and classical SFA, and a variant that relaxes both locality constraints is comparable to supervised backpropagation. Because training and inference use the same computation, the network can keep learning from unlabeled data during inference without loss of accuracy.

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