Kartikay Agrawal, Abhijeet Vikram, Vedant Sharma et al.
In recent years, with the emergence of large models, there has been a significant interest in spiking neural networks (SNNs) primarily due to their energy efficiency, multiplication-free, and sparse event-based deep learning. Similarly, state space models (SSMs) in varying designs have evolved as a powerful alternative to transformers for target modeling in long sequences, thereby overcoming the quadratic dependence on sequence length of a transformer. Inspired by this progress, we here design SHaRe-SSM (Spiking Harmonic Resonate and Fire State Space Model), for target variable modeling (including both classification and regression) for very-long-range sequences. Our second-order spiking SSM, on average, performs better than transformers or first-order SSMs while circumventing multiplication operations, making it ideal for resource-constrained applications. The proposed block consumes $73 \times$ less energy than second-order ANN-based SSMs for an 18k sequence, while retaining performance. To ensure learnability over the long-range sequences, we propose exploiting the stable and efficient implementation of the dynamical system using parallel scans. Moreover, for the first time, we propose a kernel-based spiking regressor using resonate and fire neurons for very long-range sequences. Our network shows superior performance on even a 50k sequence while being significantly energy-efficient. In addition, we conducted a systematic analysis of the impact of heterogeneity, dissipation, and conservation in resonate-and-fire SSMs.