ReLIF: Exploiting Temporal Parallelism through Finite-Time Coalescence in Spiking Neural Networks

Spiking neural networks carry recurrent neuronal states across time, making exact temporal execution serial even when the surrounding network is highly parallel. We introduce ReLIF, which rectifies the recurrent state before integration. Under a shared input sequence, sufficiently negative inputs erase the carried state through rectification, while sufficiently positive inputs trigger a common hard reset, allowing executions from different incoming membrane states to converge to the same zero state. We formalize this event as finite-time state coalescence and develop Coalescent Chunking, an exact execution scheme that precomputes boundary-independent suffixes in the forward pass and composes independent gradient intervals in the backward pass. ReLIF matches LIF accuracy across vision backbones and shows better performance in language modeling. In kernel-level measurements, parallel ReLIF reaches up to $38.07\times$ forward and $17.71\times$ backward speedup over SpikingJelly CuPy LIF. Across three SpikeTransformer++ scales, the complete stack reaches $2.92\times$–$3.20\times$ inference and $1.95\times$–$2.14\times$ training throughput over paired SpikingJelly CuPy LIF.