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FLAMES: A Hybrid Spiking-State Space Model for Adaptive Memory Retention in Event-Based Learning

Biswadeep Chakraborty, Saibal Mukhopadhyay

Abstract

We propose \textbf{FLAMES (Fast Long-range Adaptive Memory for Event-based Systems)}, a novel hybrid framework integrating structured state-space dynamics with event-driven computation. At its core, the \textit{Spike-Aware HiPPO (SA-HiPPO) mechanism} dynamically adjusts memory retention based on inter-spike intervals, preserving both short- and long-range dependencies. To maintain computational efficiency, we introduce a normal-plus-low-rank (NPLR) decomposition, reducing complexity from $\mathcal{O}(N^2)$ to $\mathcal{O}(Nr)$. FLAMES achieves state-of-the-art results on the Long Range Arena benchmark and event datasets like HAR-DVS and Celex-HAR. By bridging neuromorphic computing and structured sequence modeling, FLAMES enables scalable long-range reasoning in event-driven systems.

FLAMES: A Hybrid Spiking-State Space Model for Adaptive Memory Retention in Event-Based Learning

Abstract

We propose \textbf{FLAMES (Fast Long-range Adaptive Memory for Event-based Systems)}, a novel hybrid framework integrating structured state-space dynamics with event-driven computation. At its core, the \textit{Spike-Aware HiPPO (SA-HiPPO) mechanism} dynamically adjusts memory retention based on inter-spike intervals, preserving both short- and long-range dependencies. To maintain computational efficiency, we introduce a normal-plus-low-rank (NPLR) decomposition, reducing complexity from to . FLAMES achieves state-of-the-art results on the Long Range Arena benchmark and event datasets like HAR-DVS and Celex-HAR. By bridging neuromorphic computing and structured sequence modeling, FLAMES enables scalable long-range reasoning in event-driven systems.

Paper Structure

This paper contains 32 sections, 8 theorems, 69 equations, 6 figures, 12 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Methods
  4. Dendrite Attention Layer:
  5. Spatial Pooling Layer
  6. SA-HiPPO Convolution Layer
  7. Theoretical Analysis
  8. Computational Complexity
  9. Long-Range Memory Analysis
  10. Numerical Stability
  11. Efficiency-Memory Trade-offs
  12. Experiments and Results
  13. Conclusion
  14. Supplementary Section A: Detailed Proofs
  15. Computational Complexity of Spike-Driven SSMs
  16. ...and 17 more sections

Key Result

Lemma 1

For the state space model: where $\mathbf{x}(t) \in \mathbb{R}^N$, $\mathbf{A} \in \mathbb{R}^{N \times N}$, and $\mathbf{S}(t) \in \mathbb{R}^M$ represents spike inputs, the computational complexity for state updates at each spike event is $O(N^2)$, and reduces to $O(Nr)$ with our NPLR decomposition, where $r \ll N$.

Figures (6)

  • Figure 1: Block diagram of the proposed model architecture. Input spikes are processed event-by-event
  • Figure 2: Accuracy vs. FLOPS (G) on (a) DVSGesture128 , (b) Celex-HAR and (c) HAR-DVS wang2024hardvs datasets comparing FLAMES variants with other SOTA models. Figure (a) shows the ablation studies showing the impact of removing the Dendrite Attention Layer or replacing SA-HiPPO with standard LIF neurons. Note: There are no spike-based designs for Celex-HAR
  • Figure 3: Figure showing Accuracy vs Inference Latency for different models on the Celex-HAR dataset
  • Figure 4: Comparison of our FLAMES to the state-of-the-art on DVS128-Gestureamir2017low, Spiking Heidelberg digits (SHD) and Spiking Speech Commands (SSC) cramer2020heidelberg datasets
  • Figure 5: Figure showing the Parameters vs Accuracy of different state of the art DNN and SNN models on the Celex-HAR wang2024event dataset wrt the FLAMES models
  • ...and 1 more figures

Theorems & Definitions (12)

  • Lemma 1: Computational Efficiency of Adaptive State Updates
  • Theorem 1: Temporal Dependency Preservation
  • Lemma 2: State Update Stability
  • Theorem 2: Global Stability
  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Lemma 2
  • proof
  • ...and 2 more