A Time-Variant Spiking Neuron from a Unified State-Dynamics Perspective

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.

Spiking neural networks (SNNs) are promising for neuromorphic computing, but high-performing models still rely on dense multilayer architectures with substantial communication and state-storage costs. Inspired by autapses, we propose time-delayed autapse SNN (TDA-SNN), a framework that reconstructs SNNs with a single leaky integrate-and-fire neuron and a prototype-learning-based training strategy. By reorganizing internal temporal states, TDA-SNN can realize reservoir, multilayer perceptron, and convolution-like spiking architectures within a unified framework. Experiments on sequential, event-based, and image benchmarks show competitive performance in reservoir and MLP settings, while convolutional results reveal a clear space--time trade-off. Compared with standard SNNs, TDA-SNN greatly reduces neuron count and state memory while increasing per-neuron information capacity, at the cost of additional temporal latency in extreme single-neuron settings. These findings highlight the potential of temporally multiplexed single-neuron models as compact computational units for brain-inspired computing.

Spiking Neural Networks (SNNs) are a promising framework for event-driven temporal processing. Prior work has improved temporal modeling through richer neuron dynamics and network-level mechanisms such as recurrence and delays, but it remains unclear how individual spiking neurons should specialize within a network. In this work, we introduce FiTS, a spiking neuron that factorizes temporal computation within each neuron into Frequency Selectivity (FS) and Temporal Shaping (TS). The FS module parameterizes each neuron's target frequency as the maximizer of its subthreshold magnitude response, while the TS module reshapes when frequency components contribute to membrane voltage accumulation through group-delay modulation. On auditory benchmarks where frequency selectivity and timing are central to the input structure, FiTS consistently improves over a plain Leaky Integrate-and-Fire (LIF) baseline in simple feedforward SNNs without recurrence or network-level delays, while remaining competitive with strong temporal SNN baselines. Beyond accuracy, the learned target frequencies and group-delay shifts provide interpretable neuron-level summaries of the frequency and timing organization learned within the network.