Dynamics-Projected Eligibility Traces for Online Training of Spiking Neural Networks

Spiking neural networks (SNNs) are a promising route to low-power event-driven computing, but their training typically relies on backpropagation through time (BPTT), whose activation memory scales linearly with the number of time steps. Online learning rules avoid this growth by keeping only the current-step computational graph and optionally maintaining fixed-size eligibility traces (ETs) online to approximate weight sensitivities. Existing compact presynaptic ETs use fixed decay or derive it from presynaptic dynamics, although weight sensitivities evolve according to the postsynaptic temporal Jacobian, which varies across layers and training stages. In this work, we propose Dynamics-Projected Eligibility Traces (DPET), which derives trace decay by projecting this Jacobian onto one least-squares coefficient per sample and layer. This scalar projection preserves a single presynaptic ET while adapting its decay to the postsynaptic dynamics. A state-space formulation extends DPET to neurons with richer internal states. In addition, to complement the missing feedback from future time steps in online learning, we introduce an auxiliary objective that uses later-step predictions from completed minibatches as supervision. Experiments across image, event-based, point-cloud, and language classification show gains over existing online methods with substantially lower training memory compared to BPTT. DPET provides a practical solution for memory-constrained SNN training.