# State-Space Model Inspired Multiple-Input Multiple-Output Spiking Neurons

arXiv: https://arxiv.org/abs/2504.02591 · HTML: https://mlsanity.com/paper/2504.02591/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 31 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Builds on (most cited first, 19 of 19)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [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)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [The Heidelberg spiking datasets for the systematic evaluation of spiking neural networks](https://mlsanity.com/paper/1910.07407/) (2019)
- [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)
- [Ternary Spike: Learning Ternary Spikes for Spiking Neural Networks](https://mlsanity.com/paper/2312.06372/) (2023)
- [Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models](https://mlsanity.com/paper/2404.18508/) (2024)
- [NeuroBench: A Framework for Benchmarking Neuromorphic Computing Algorithms and Systems](https://mlsanity.com/paper/2304.04640/) (2023)
- [Learning Long Sequences in Spiking Neural Networks](https://mlsanity.com/paper/2401.00955/) (2023)
- [SpikingSSMs: Learning Long Sequences with Sparse and Parallel Spiking State Space Models](https://mlsanity.com/paper/2408.14909/) (2024)
- [S7: Selective and Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2410.03464/) (2024)
- [Q-S5: Towards Quantized State Space Models](https://mlsanity.com/paper/2406.09477/) (2024)
- [A Diagonal Structured State Space Model on Loihi 2 for Efficient Streaming Sequence Processing](https://mlsanity.com/paper/2409.15022/) (2024)
- [Accurate Mapping of RNNs on Neuromorphic Hardware with Adaptive Spiking Neurons](https://mlsanity.com/paper/2407.13534/) (2024)

## Built on by (most cited first, 4 of 4)

- [Stochastic Quantum Spiking Neural Networks with Quantum Memory and Local Learning](https://mlsanity.com/paper/2506.21324/) (2025)
- [Low-Bit Data Processing Using Multiple-Output Spiking Neurons with Non-linear Reset Feedback](https://mlsanity.com/paper/2508.06292/) (2025)
- [Delays in Spiking Neural Networks: A State Space Model Approach](https://mlsanity.com/paper/2512.01906/) (2025)
- [Federated Learning of Spiking Neural Networks under Heterogeneous Temporal Resolutions](https://mlsanity.com/paper/2605.15355/) (2026)

## Abstract (arXiv)

In spiking neural networks (SNNs), the main unit of information processing is the neuron with an internal state. The internal state generates an output spike based on its component associated with the membrane potential. This spike is then communicated to other neurons in the network. Here, we propose a general multiple-input multiple-output (MIMO) spiking neuron model that goes beyond this traditional single-input single-output (SISO) model in the SNN literature. Our proposed framework is based on interpreting the neurons as state-space models (SSMs) with linear state evolutions and non-linear spiking activation functions. We illustrate the trade-offs among various parameters of the proposed SSM-inspired neuron model, such as the number of hidden neuron states, the number of input and output channels, including single-input multiple-output (SIMO) and multiple-input single-output (MISO) models. We show that for SNNs with a small number of neurons with large internal state spaces, significant performance gains may be obtained by increasing the number of output channels of a neuron. In particular, a network with spiking neurons with multiple-output channels may achieve the same level of accuracy with the baseline with the continuous-valued communications on the same reference network architecture.