Redefining spiking neural networks through the lens of dynamical superspace

The convergence of neuroscience and artificial intelligence has positioned Spiking Neural Networks (SNNs) as one of the pivotal paradigms for future computing. However, the field faces a theoretical challenge: reconciling the mathematical clarity of static deep learning with the rich, non-equilibrium dynamics of biological circuits. We introduce the dynamical superspace, a framework that reimagines neural computing as a continuous hierarchy defined by temporal density and state-space complexity. We suggest that while current synchronous SNNs successfully optimize rate-based equilibria, they often neglect the intrinsic power of biological time. The true neuromorphic advantage emerges by ascending to asynchronous timing, where information is decoupled from clock cycles, and to complex non-equilibrium dynamics, where heterogeneity and criticality drive computation through transient trajectories. We propose a roadmap to bridge global optimization with local execution, leveraging evolutionary priors to support innate learning. By identifying native applications, from ultra-low-latency event perception to infinite-context memory for AGI, this perspective invites the community to view SNNs not merely as efficient quantization, but as dynamical systems capable of stable transience, offering a physical bridge to the next generation of intelligence.