A Gradient-based yet Spike-Timing-Dependent Solution to the Feedback Learning Problem in Neural Microcircuits

Spiking Neural Networks (SNNs) provide a promising framework for energy-efficient and biologically grounded computation; however, scalable learning in deep recurrent architectures with sparse connectivity remains a major challenge. In this work, we propose a structured multi-layer recurrent SNN architecture composed of locally dense recurrent layers augmented with sparse small-world long-range projections to a readout population. The long-range connectivity is largely fixed, preserving routing efficiency and hardware scalability, while synaptic adaptation is performed using strictly local plasticity mechanisms. To enable supervised learning without backpropagation or surrogate gradients, we introduce a biologically motivated learning framework that combines: (i) population-based winner-take-all (WTA) teaching signals at the output layer, (ii) fixed random broadcast alignment feedback pathways, and (iii) low-dimensional modulatory neuron populations that gate synaptic updates through three-factor learning rules with eligibility traces. This design supports deep recurrent computation with sparse global communication and purely local synaptic updates. We analyze the algorithmic properties, computational complexity, and hardware feasibility of the proposed approach, and demonstrate stable learning and competitive performance on benchmark classification tasks. The results highlight the potential of structured recurrence and neuromodulatory learning to enable scalable, hardware-compatible SNN training beyond gradient-based methods.

Spiking neural networks (SNNs) promise low-power event-driven computation for temporally rich tasks, but commonly used neuron models often trade off gradient-based trainability, dynamical richness, and high activity sparsity. These limitations are acute in regression, where approximation error, noise and spike discretization can severely degrade continuous-valued outputs. Indeed, many state-of-the-art (SOTA) SNNs rely on simple phenomenological dynamics trained with surrogate gradients and offer limited control over spiking diversity and sparsity. To overcome such limitations, we introduce multi-timescale conductance spiking networks, a gradient-trainable framework in which neural dynamics emerge from shaping the current-voltage (I-V) curve by tuning fast, slow and ultra-slow conductances. This parametrization allows systematic control over excitability, can be implemented efficiently in analog circuits, and yields rich firing regimes including tonic, phasic and bursting responses within a single model. We derive a discrete-time formulation of these differentiable dynamics, enabling direct backpropagation through time without surrogate-gradient approximations. To probe both trainability and accuracy, we evaluate feedforward networks of these neurons at the predictability limit of Mackey-Glass time-series regression and compare them to baseline LIF and SOTA AdLIF networks. Our model outperforms LIF and AdLIF networks, while exhibiting substantially sparser activity from both communication and computational perspectives. These results highlight multi-timescale conductance spiking neurons as a promising building block for energy-aware temporal processing and neuromorphic implementation.

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.