Exact and Trainable Growth of Stateful Spiking Neural Networks

Spiking neural networks (SNNs) typically rely on fixed architectures whose ca- pacity is chosen before training. Insufficient width limits representation, whereas excessive width introduces unnecessary parameters and computation. This problem is especially challenging in SNNs because structural changes can disrupt their temporal dynamics. We introduce an exact and trainable growth mechanism for stateful SNNs. The proposed paired basis adds new neurons to a partially trained network while preserving the downstream temporal computation and output logits at every simulation step. Unlike conventional zero readout, which preserves the current output but blocks the immediate task gradient to the incoming parameters of newborn neurons, our construction uses identical neuron pairs whose forward contributions cancel exactly while their backward signals remain nonzero and opposing. Growth is implemented as an atomic transaction that expands the model, migrates Adam state, verifies the required invariants, and resumes surrogate gradi- ent training. We establish temporal function preservation, conditional immediate trainability, preservation of the optimizer state for existing parameters, and layer- wise composition, providing a principled mechanism for expanding stateful SNNs without discarding their learned temporal computation.