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Facilitating online learning in spiking neural networks (SNNs) is a key stepin developing event-based models that can adapt to changing environments andlearn from continuous data streams in real-time. Although forward-modedifferentiation enables online learning, its computational requirementsrestrict scalability. This is typically addressed through approximations thatlimit learning in deep models. In this study, we propose Online Training withPostsynaptic Estimates (OTPE) for training feed-forward SNNs, whichapproximates Real-Time Recurrent Learning (RTRL) by incorporating temporaldynamics not captured by current approximations, such as Online TrainingThrough Time (OTTT) and Online Spatio-Temporal Learning (OSTL). We showimproved scaling for multi-layer networks using a novel approximation oftemporal effects on the subsequent layer's activity. This approximation incursminimal overhead in the time and space complexity compared to similaralgorithms, and the calculation of temporal effects remains local to eachlayer. We characterize the learning performance of our proposed algorithms onmultiple SNN model configurations for rate-based and time-based encoding. OTPEexhibits the highest directional alignment to exact gradients, calculated withbackpropagation through time (BPTT), in deep networks and, on time-basedencoding, outperforms other approximate methods. We also observe sizeable gainsin average performance over similar algorithms in offline training of SpikingHeidelberg Digits with equivalent hyper-parameters (OTTT/OSTL - 70.5%; OTPE -75.2%; BPTT - 78.1%).

Estimating Post-Synaptic Effects for Online Training of Feed-Forward SNNs