Quadratic integrate-and-fire neurons exhibit less fragmented loss landscapes and outperform leaky integrate-and-fire neurons in spike-based gradient descent

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.

Continuous-time spiking neural networks (SNNs) provide an event-driven framework for temporal computation, computational neuroscience, and neuromorphic hardware. However, training deep continuous-time SNNs is severely constrained by the memory required for exact spike-time computation, which evaluates and retains candidate firing times over intervals determined by presynaptic spike ordering. Here we introduce a memory-efficient training framework based on differentiable spike-time discretization (DSTD) for leaky integrate-and-fire neurons with general membrane and synaptic time constants. DSTD maps irregular presynaptic spikes onto differentiable weighted events at fixed time points, replacing the input-dependent candidate dimension with $M$ fixed time intervals while accurately approximating continuous-time membrane-potential dynamics. This reduces candidate-related activation memory from $O(N_{\mathrm{out}}N_{\mathrm{in}})$ to $O(N_{\mathrm{out}}M)$ in the case of time-to-first-spike (TTFS) coding, where $N_{\mathrm{in}}$ and $N_{\mathrm{out}}$ denote the numbers of presynaptic and postsynaptic neurons, respectively. We further introduce synfire-chain-inspired temporal regularization that organizes layer-wise firing windows, mitigates dead-neuron failures, and enables pipeline-like processing. In dense LIF layers, DSTD reduced peak memory consumption by up to approximately 100-fold and training time by up to approximately 20-fold compared with exact spike-time computation. Together, these methods allowed us to train 9-layer convolutional SNNs on CIFAR-10 and 20-layer convolutional SNNs on Fashion-MNIST on a single GPU.

Binary spike coding enables sparse and event-driven computation in spiking neural networks (SNNs), yet its 1-bit-per-timestep representation fundamentally limits information throughput. This bottleneck becomes increasingly restrictive in deep architectures under short simulation horizons. We propose the Quantized Burst-LIF (QB-LIF) neuron, which reformulates burst spiking as a saturated uniform quantization of membrane potentials with a learnable scale. Instead of relying on predefined multi-threshold structures, QB-LIF treats the quantization scale as a trainable parameter, allowing each layer to autonomously adapt its spiking resolution to the underlying membrane-potential statistics. To preserve hardware efficiency, we introduce an absorbable scale strategy that folds the learned quantized scale into synaptic weights during inference, maintaining a strict accumulate-only (AC) execution paradigm. To enable stable optimization in the discrete multi-level space, we further design ReLSG-ET, a rectified-linear surrogate gradient with exponential tails that sustains gradient flow across burst intervals. Extensive experiments on static (CIFAR-10/100, ImageNet) and event-driven (CIFAR10-DVS, DVS128-Gesture) benchmarks demonstrate that QB-LIF consistently outperforms binary and fixed-burst SNNs, achieving higher accuracy under ultra-low latency while preserving neuromorphic compatibility.