# SPikE-SSM: A Sparse, Precise, and Efficient Spiking State Space Model for Long Sequences Learning

arXiv: https://arxiv.org/abs/2410.17268 · HTML: https://mlsanity.com/paper/2410.17268/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 59 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [Going Deeper With Directly-Trained Larger Spiking Neural Networks](https://mlsanity.com/paper/2011.05280/) (2020)
- [Spikformer: When Spiking Neural Network Meets Transformer](https://mlsanity.com/paper/2209.15425/) (2022)
- [Long Range Language Modeling via Gated State Spaces](https://mlsanity.com/paper/2206.13947/) (2022)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Mixture-of-Depths: Dynamically allocating compute in transformer-based language models](https://mlsanity.com/paper/2404.02258/) (2024)
- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [Spike-driven Transformer V2: Meta Spiking Neural Network Architecture Inspiring the Design of Next-generation Neuromorphic Chips](https://mlsanity.com/paper/2404.03663/) (2024)
- [SpikeGPT: Generative Pre-trained Language Model with Spiking Neural Networks](https://mlsanity.com/paper/2302.13939/) (2023)
- [RecurrentGPT: Interactive Generation of (Arbitrarily) Long Text](https://mlsanity.com/paper/2305.13304/) (2023)
- [Parallel Spiking Neurons with High Efficiency and Ability to Learn Long-term Dependencies](https://mlsanity.com/paper/2304.12760/) (2023)

## Built on by (most cited first, 9 of 9)

- [Efficient Spiking Point Mamba for Point Cloud Analysis](https://mlsanity.com/paper/2504.14371/) (2025)
- [SpikingMamba: Towards Energy-Efficient Large Language Models via Knowledge Distillation from Mamba](https://mlsanity.com/paper/2510.04595/) (2025)
- [Modern Neuromorphic AI: From Intra-Token to Inter-Token Processing](https://mlsanity.com/paper/2601.00245/) (2026)
- [Bullet Trains: Parallelizing Training of Temporally Precise Spiking Neural Networks](https://mlsanity.com/paper/2603.13283/) (2026)
- [FCKT: Fine-Grained Cross-Task Knowledge Transfer with Semantic Contrastive Learning for Targeted Sentiment Analysis](https://mlsanity.com/paper/2505.21040/) (2025)
- [Revisiting Reset Mechanisms in Spiking Neural Networks for Sequential Modeling: Specialized Discretization for Binary Activated RNN](https://mlsanity.com/paper/2504.17751/) (2025)
- [SpikySpace: A Spiking State Space Model for Energy-Efficient Time Series Forecasting](https://mlsanity.com/paper/2601.02411/) (2026)
- [MAR: Efficient Large Language Models via Module-aware Architecture Refinement](https://mlsanity.com/paper/2601.21503/) (2026)
- [LongSpike: Fractional Order Spiking State Space Models for Efficient Long Sequence Learning](https://mlsanity.com/paper/2606.12895/) (2026)

## Abstract (arXiv)

Spiking neural networks (SNNs) provide an energy-efficient solution by utilizing the spike-based and sparse nature of biological systems. Since the advent of Transformers, SNNs have struggled to compete with artificial networks on long sequential tasks, until the recent emergence of state space models (SSMs), which offer superior computational efficiency and modeling capability. However, applying the highly capable SSMs to SNNs for long sequences learning poses three major challenges: (1) The membrane potential is determined by the past spiking history of the neuron, leading to reduced efficiency for sequence modeling in parallel computing scenarios. (2) Complex dynamics of biological spiking neurons are crucial for functionality but challenging to simulate and exploit effectively in large networks. (3) It is arduous to maintain high sparsity while achieving high accuracy for spiking neurons without resorting to dense computing, as utilized in artificial neuron-based SSMs. To address them, we propose a sparse, precise and efficient spiking SSM framework, termed SPikE-SSM. For (1), we propose a boundary compression strategy (PMBC) to accelerate the inference of the spiking neuron model, enabling parallel processing for long sequence learning. For (2), we propose a novel and concise neuron model incorporating reset-refractory mechanism to leverage the inherent temporal dimension for dynamic computing with biological interpretability. For (3), we hierarchically integrate the proposed neuron model to the original SSM block, and enhance the dynamics of SPikE-SSM by incorporating trainable thresholds and refractory magnitudes to balance accuracy and sparsity. Extensive experiments verify the effectiveness and robustness of SPikE-SSM on the long range arena benchmarks and large language dataset WikiText-103, showing the potential of dynamic spiking neurons in efficient long sequence learning.