Advancing Spatiotemporal Representations in Spiking Neural Networks via Parametric Invertible Transformation

Spiking Neural Networks (SNNs) are regarded as energy-efficient neural architectures due to their event-driven, spike-based computation paradigm. However, existing SNNs suffer from two fundamental limitations: (1) the constrained representational space imposed by binary spike firing mechanisms, which restricts the network's capacity to encode complex spatiotemporal patterns, and (2) the ineffective design of surrogate gradient functions that leads to gradient mismatch issues and suboptimal learning dynamics. To address these challenges, we propose the Parametric Invertible Transformation (PIT), which operates in a conjugate manner with neuronal dynamics to achieve adaptive modulation and augmented spike representations simultaneously. Second, we design an auxiliary gradient correction term to mitigate the gradient mismatch issue and oscillation phenomena during training. Moreover, we introduce a theoretical framework for analyzing the spatiotemporal representation space of SNNs. Extensive experiments on both static and neuromorphic datasets demonstrate state-of-the-art performance with our proposed method. This approach lays the theoretical foundation for expanding the spatiotemporal representations of SNNs, offering a viable pathway for developing low-latency and high-performance neuromorphic processing systems in resource-constrained environments. The code is available at https://github.com/YinsongYan/ICLR26.