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

arXiv: https://arxiv.org/abs/2506.06374 · HTML: https://mlsanity.com/paper/2506.06374/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Core SSM architectures for language, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 4 Jun 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Core SSM architectures for language](https://mlsanity.com/ssm/core-ssm-architectures-for-language/)

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

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Training Deep Spiking Neural Networks using Backpropagation](https://mlsanity.com/paper/1608.08782/) (2016)
- [SuperSpike: Supervised learning in multi-layer spiking neural networks](https://mlsanity.com/paper/1705.11146/) (2017)
- [The Heidelberg spiking datasets for the systematic evaluation of spiking neural networks](https://mlsanity.com/paper/1910.07407/) (2019)
- [Optimal ANN-SNN Conversion for High-accuracy and Ultra-low-latency Spiking Neural Networks](https://mlsanity.com/paper/2303.04347/) (2023)
- [Accurate and efficient time-domain classification with adaptive spiking recurrent neural networks](https://mlsanity.com/paper/2103.12593/) (2021)
- [State Space Models for Event Cameras](https://mlsanity.com/paper/2402.15584/) (2024)
- [Learning Delays in Spiking Neural Networks using Dilated Convolutions with Learnable Spacings](https://mlsanity.com/paper/2306.17670/) (2023)
- [Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models](https://mlsanity.com/paper/2404.18508/) (2024)
- [Recurrent neural networks: vanishing and exploding gradients are not the end of the story](https://mlsanity.com/paper/2405.21064/) (2024)
- [Dilated convolution with learnable spacings](https://mlsanity.com/paper/2112.03740/) (2021)
- [SpikingSSMs: Learning Long Sequences with Sparse and Parallel Spiking State Space Models](https://mlsanity.com/paper/2408.14909/) (2024)
- [Co-learning synaptic delays, weights and adaptation in spiking neural networks](https://mlsanity.com/paper/2311.16112/) (2023)
- [P-SpikeSSM: Harnessing Probabilistic Spiking State Space Models for Long-Range Dependency Tasks](https://mlsanity.com/paper/2406.02923/) (2024)
- [Low-power event-based face detection with asynchronous neuromorphic hardware](https://mlsanity.com/paper/2312.14261/) (2023)
- [Provable Benefits of Complex Parameterizations for Structured State Space Models](https://mlsanity.com/paper/2410.14067/) (2024)
- [Zero-Shot Temporal Resolution Domain Adaptation for Spiking Neural Networks](https://mlsanity.com/paper/2411.04760/) (2024)
- [Deep Spiking Neural Networks with Resonate-and-Fire Neurons](https://mlsanity.com/paper/2109.08234/) (2021)
- [Scaling Up Resonate-and-Fire Networks for Fast Deep Learning](https://mlsanity.com/paper/2504.00719/) (2025)
- [Stabilizing Spiking Neuron Training](https://mlsanity.com/paper/2202.00282/) (2022)

## Built on by (most cited first, 3 of 3)

- [Conjoint Audio-to-Spikes Encoding and Processing for Efficient Neuromorphic Speech Recognition](https://mlsanity.com/paper/2608.30792/) (2026)
- [REACT: A Fully Spiking State-Space Model for Real-Time Event-Driven Temporal Perception](https://mlsanity.com/paper/2609.19204/) (2026)
- [ADPTNet: Adaptive with Prescriptive Timescales Non-Linear SSM for Sequence Modelling](https://mlsanity.com/paper/2609.34034/) (2026)

## Abstract (arXiv)

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.