Regime Mapping of Oscillatory States in Balanced Spiking Networks with Multiple Time Scales

Human cognition emerges from coordinated spiking dynamics in distributed neural circuits, where information is encoded via both firing rates and precise spike timing determined by brain rhythms. Inspired by this notion, we propose a brain-inspired learning primitive in which cognition-level neural synchrony emerges through iterative bottom-up and top-down interactions between micro-scale dynamics of spiking neurons and a macro-scale mechanism of oscillatory synchronization. Specifically, we model each parcel (e.g., a cortical region or an image pixel) in the target system as a spiking neuron embedded in a predefined connectivity scaffold. Low-level information is encoded in a spatiotemporal domain, where neurons are selectively grouped and fire spontaneously over time through self-organized dynamics. In the bottom-up route, oscillatory synchronization is formed from past spiking activity accumulated over a finite memory window. Since brain dynamics operate in a regime of partial and transient synchronization rather than global phase locking, we model oscillatory coordination using a time-delayed synchronization formulation, which enables a top-down modulation of heterogeneous neural spiking for a large-scale distributed system. Together, we devise a spiking-by-synchronization neural network (S2-Net) that uses rhythmic timing as a control mechanism for efficient information processing. Promising results have been achieved across a broad range of tasks, including neural activity decoding, energy-efficient signal processing, temporal binding and semantic reasoning.

Biological organisms minimize free energy by balancing two competing demands on their internal world model: it must be accurate enough to predict sensory input, yet simple enough to generalize beyond it. Two mechanisms regulate this balance offline: sleep reduces complexity through gradual synaptic downscaling, while stochastic noise attenuates precision, relaxing the constraint sensory input imposes on synaptic reorganization. Engineered Spiking Neural Networks (SNNs) leave this balance unaddressed, favoring instantaneous, noiseless weight normalization instead. This paper investigates the hypothesis that a biologically inspired micro-sleep paradigm, napping -- combining proportional weight scaling with continuous stochastic membrane activity -- can replicate the stability of normalization while shedding model complexity. We evaluate this in an unsupervised recurrent SNN trained via trace-based spike-timing-dependent plasticity (STDP) on Gabor-preprocessed MNIST. We tune napping across three regularization regimes by sweeping its duration and membrane noise level, then compare the best configuration against weight normalization. Across all three regimes, well-tuned napping matches the accuracy of normalization: accuracy peaks at brief durations and low noise, then declines monotonically as either grows. Clustering diverges, with the strongest geometric separation arising at longer durations and higher noise -- the two terms of free energy pulling apart, accuracy rewarding data fit and structure rewarding the simpler representation that gradual, noisy downscaling induces. This gain carries a simulation cost normalization avoids, so napping is most compelling where representational structure, rather than raw classification efficiency, is the priority.

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.