SiLIF: Structured State Space Model Dynamics and Parametrization for Spiking Neural Networks

TL;DR

Two SSM-inspired Leaky Integrate-and-Fire neuron models are introduced that achieve new state-of-the-art performance among spiking neuron models on both event-based and raw-audio speech recognition datasets and demonstrate a favorable performance-efficiency trade-off compared to SSMs.

Abstract

Multi-state spiking neurons combine sparse binary activations with rich second-order nonlinear recurrent dynamics, making them a promising alternative to standard deep learning models. However, gradient propagation through these dynamics often leads to instabilities that hinder scalability and performance. Inspired by the stable training and strong performance of state space models (SSMs) on long sequences, we introduce two SSM-inspired Leaky Integrate-and-Fire (SiLIF) neuron models. The first extends a two-state neuron with a learnable discretization timestep and logarithmic reparametrization, while the second additionally incorporates the initialization scheme and structure of complex-state SSMs, enabling oscillatory regimes. Our two SiLIF models achieve new state-of-the-art performance among spiking neuron models on both event-based and raw-audio speech recognition datasets. We further demonstrate a favorable performance-efficiency trade-off compared to SSMs, even surpassing them while using half the computational cost through the use of synaptic delays. Our code is available at https://github.com/Maxtimer97/SSM-inspired-LIF.

Figures (6)

• Figure 1: Our proposed method distills features from modern structured state space models (SSMs) to build novel high-performing spiking neural networks (SNNs). The SiLIF model is an enhancement of the adaptive LIF (AdLIF) neuron, achieved by reparametrizing its state transition matrix according to the S4 model. The C-SiLIF additionally exploits the complex representation and specific initialization of the S4D model, drawing a parallel with the resonate-and-fire (RF) neuron. The right part of the figure illustrates the similar structure of SSMs and SNNs, plus the SNN-exclusive reset mechanism.
• Figure 2: Scatter plot and histogram of state transition matrix eigenvalues for different pre-trained neuron models on the SSC dataset. (a) depicts the full unit circle, while (b) shows a zoomed view with a logarithmic range histogram of the eigenvalues. The range of covered eigenvalues, especially out of the real axis, corresponds to different accessible neuronal dynamics regimes.
• Figure 3: Test accuracy and synaptic operations (SOP) with standard deviation for different models on the 3 audio datasets SHD, SSC, and GSC from left to right. Our models are shown in bold.
• Figure 4: Test accuracy per synaptic operations (SOPs) on the GSC dataset for our SiLIF model and SOTA SSM models at different scales. The standard deviation is represented as a shaded area.
• Figure 5: Neuronal dynamics of the (a) cAdLIF and (b) SiLIF models pre-trained on the SSC task. Each dot corresponds to the obtained training parameters for one neuron of the model. The position of each dot directly correlates to the corresponding neuron's regime.