Backpropagation through space, time, and the brain
How to achieve efficient credit assignment under spatiotemporal locality constraints in physical neural networks remains a fundamental challenge in neuromorphic computing. This paper introduces the Generalized Latent Equilibrium (GLE) framework, which for the first time couples energy minimization with neuron-level local mismatch dynamics to derive biologically plausible forward and backward continuous-time dynamics. By incorporating dendritic morphology modeling and membrane potential phase modulation, GLE implements spatiotemporal convolution and temporal reversal of feedback signals. Crucially, GLE relies exclusively on local synaptic plasticity—requiring no global timing coordination or external error broadcasting. Experiments demonstrate that, under strict locality constraints, GLE approximates the performance of backpropagation through time (BPTT), enables real-time online learning, incurs minimal memory overhead, and provides an interpretable, biologically realistic credit assignment mechanism for deep cortical networks.