NLT-prop: Nonlocal Temporal Credit Assignment for Online Learning in Spiking Neural Networks

Spiking neural networks (SNNs), inspired by biological neural networks, communicate through discrete spikes and offer the potential for energy-efficient information processing. They are commonly trained using backpropagation through time (BPTT) with surrogate gradients. However, BPTT requires propagating gradients backward in time, making it biologically implausible and incompatible with strictly online learning. Real-time recurrent learning (RTRL) enables online gradient computation, but maintaining full eligibility traces in recurrent networks requires memory that grows cubically with network width and incurs substantial computational costs. Many existing online methods reduce these costs by simplifying temporal dependencies between neurons, limiting their ability to capture nonlocal temporal influences. We propose NLT-prop, an online learning method that efficiently approximates nonlocal temporal credit assignment through recurrent connections. Starting from the forward recursion for eligibility traces, NLT-prop decomposes the temporal Jacobian into diagonal and off-diagonal components, separating local neuronal dynamics from interactions between neurons. It organizes temporal paths by their number of nonlocal transitions and uses structured low-rank approximations to propagate the retained contributions forward in time. For a fixed retained order, the memory required for eligibility traces scales linearly with network width. This formulation explicitly incorporates nonlocal temporal influences without storing the full activity history or introducing additional eligibility-trace decay parameters. Experiments on SHD, N-MNIST, CIFAR10-DVS, DVS Gesture, and DMTS demonstrate that NLT-prop achieves performance comparable to BPTT while supporting fully online learning.