Scalable Learning in Structured Recurrent Spiking Neural Networks without Backpropagation

Spiking Neural Networks (SNNs) have been proposed as biologically plausible and energy-efficient alternatives to conventional Artificial Neural Networks (ANNs). However, the training of SNN usually relies on surrogate gradients due to the non-differentiability of the spike function, introducing approximation errors that accumulate across layers. To address this challenge, we extend the work on convexification of parallel feedforward threshold networks to parallel recurrent threshold networks, which subsume parallel SNNs as a structured special case. Building on this theoretical framework, we propose a parameter reconstruction algorithm for SNN training that demonstrates consistent and significant advantages across various tasks, both as a standalone method and in combination with surrogate-gradient training. The ablations further demonstrate the data scalability and robustness to model configurations of our training algorithm, pointing toward its potential in large-scale SNN training.

Supervised learning in spiking neural networks (SNNs) typically requires either gradient-based backpropagation, which sacrifices the Hebbian, spike-driven character of biological plasticity, or reward-modulated Spike-Timing-Dependent Plasticity (STDP), in which class supervision enters only as a scalar gate on an otherwise class-agnostic correlation signal. We propose Supervised Spike Agreement-Dependent Plasticity (Supervised SADP), a gradient-free supervised Hebbian learning algorithm in which class information is embedded directly into the Hebbian plasticity computation rather than introduced through reward modulation. SADP trains the output layer via a supervised Hebbian rule that encodes class labels into output spike patterns, then trains the hidden layer by measuring each hidden neuron's chance-corrected temporal agreement, Cohen's kappa, with the correct-class output spike train produced by the forward pass without gradient computation or external reward. A K-shift extension aggregates agreement over temporal offsets, providing robustness to spike-timing jitter at linear computational cost. We evaluate Supervised SADP against reward-modulated STDP across six benchmark and medical imaging datasets, four input encoding strategies, K_shift in {5,25}, and three reward modes (none, binary, margin). Supervised SADP outperforms STDP in a significant majority of comparisons. Under Poisson encoding, SADP achieves 86.46% on MNIST and 76.62% on Fashion-MNIST, outperforming the best STDP configurations by 23.66 and 23.29 percentage points, respectively. Across the encodings tested, including CNN-extracted features, SADP outperforms STDP in the large majority of cells and trains 1.47x faster on average, with up to 2.86x speedup under Poisson inputs. These results position Supervised SADP as a stable, efficient, gradient-free alternative to reward-modulated STDP for supervised SNN learning.

The rapid expansion of spiking neural networks (SNNs) has led to a proliferation of training algorithms that differ widely in biological inspiration, computational structure, and hardware suitability. Despite this progress, the field lacks a unified, fine-grained taxonomy that systematically organizes these approaches and clarifies their conceptual relationships. This survey provides a comprehensive taxonomy of SNN training algorithms, spanning surrogate-gradient backpropagation, local and three-factor learning rules, biologically inspired plasticity mechanisms, ANN-to-SNN conversion pipelines, and non-standard optimization strategies. We analyze each class in terms of its computational principles, learning signals, and locality properties. To support reproducible research, we release NeuroTrain, an open-source snnTorch-based framework that implements a representative set of these algorithms within a unified, modular, and extendable framework, enabling consistent benchmarking across datasets, architectures, and training regimes. By consolidating fragmented literature and providing a reusable benchmarking framework, this survey identifies common patterns, highlights open challenges, and outlines promising directions for future work on scalable, efficient SNN training.