# LMUFormer: Low Complexity Yet Powerful Spiking Model With Legendre Memory Units

arXiv: https://arxiv.org/abs/2402.04882 · HTML: https://mlsanity.com/paper/2402.04882/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 49 references that are in the map.
- First posted on arXiv 20 Jan 2024.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [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)
- [Conformer: Convolution-augmented Transformer for Speech Recognition](https://mlsanity.com/paper/2005.08100/) (2020)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [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)
- [AST: Audio Spectrogram Transformer](https://mlsanity.com/paper/2104.01778/) (2021)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [Early Convolutions Help Transformers See Better](https://mlsanity.com/paper/2106.14881/) (2021)
- [Deep Residual Learning in Spiking Neural Networks](https://mlsanity.com/paper/2102.04159/) (2021)
- [Spikformer: When Spiking Neural Network Meets Transformer](https://mlsanity.com/paper/2209.15425/) (2022)
- [Direct Training for Spiking Neural Networks: Faster, Larger, Better](https://mlsanity.com/paper/1809.05793/) (2018)
- [Training Deep Spiking Neural Networks using Backpropagation](https://mlsanity.com/paper/1608.08782/) (2016)
- [Spiking-YOLO: Spiking Neural Network for Energy-Efficient Object Detection](https://mlsanity.com/paper/1903.06530/) (2019)
- [Spike-driven Transformer](https://mlsanity.com/paper/2307.01694/) (2023)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [Enabling Spike-based Backpropagation for Training Deep Neural Network Architectures](https://mlsanity.com/paper/1903.06379/) (2019)

## Built on by (most cited first, 11 of 11)

- [SpikingSSMs: Learning Long Sequences with Sparse and Parallel Spiking State Space Models](https://mlsanity.com/paper/2408.14909/) (2024)
- [SPikE-SSM: A Sparse, Precise, and Efficient Spiking State Space Model for Long Sequences Learning](https://mlsanity.com/paper/2410.17268/) (2024)
- [Scaling Up Resonate-and-Fire Networks for Fast Deep Learning](https://mlsanity.com/paper/2504.00719/) (2025)
- [Edge Intelligence with Spiking Neural Networks](https://mlsanity.com/paper/2507.14069/) (2025)
- [Dendritic Resonate-and-Fire Neuron for Effective and Efficient Long Sequence Modeling](https://mlsanity.com/paper/2509.17186/) (2025)
- [SpikCommander: A High-performance Spiking Transformer with Multi-view Learning for Efficient Speech Command Recognition](https://mlsanity.com/paper/2511.07883/) (2025)
- [Numerical Analysis of HiPPO-LegS ODE for Deep State Space Models](https://mlsanity.com/paper/2412.08595/) (2024)
- [FLAMES: A Hybrid Spiking-State Space Model for Adaptive Memory Retention in Event-Based Learning](https://mlsanity.com/paper/2504.01257/) (2025)
- [Towards Green Wearable Computing: A Physics-Aware Spiking Neural Network for Energy-Efficient IMU-based Human Activity Recognition](https://mlsanity.com/paper/2604.10458/) (2026)
- [LongSpike: Fractional Order Spiking State Space Models for Efficient Long Sequence Learning](https://mlsanity.com/paper/2606.12895/) (2026)
- [Latency and accuracy tradeoffs in Spiking Neural Networks](https://mlsanity.com/paper/2609.35260/) (2026)

## Abstract (arXiv)

Transformer models have demonstrated high accuracy in numerous applications but have high complexity and lack sequential processing capability making them ill-suited for many streaming applications at the edge where devices are heavily resource-constrained. Thus motivated, many researchers have proposed reformulating the transformer models as RNN modules which modify the self-attention computation with explicit states. However, these approaches often incur significant performance degradation. The ultimate goal is to develop a model that has the following properties: parallel training, streaming and low-cost inference, and SOTA performance. In this paper, we propose a new direction to achieve this goal. We show how architectural modifications to a recurrent model can help push its performance toward Transformer models while retaining its sequential processing capability. Specifically, inspired by the recent success of Legendre Memory Units (LMU) in sequence learning tasks, we propose LMUFormer, which augments the LMU with convolutional patch embedding and convolutional channel mixer. Moreover, we present a spiking version of this architecture, which introduces the benefit of states within the patch embedding and channel mixer modules while simultaneously reducing the computing complexity. We evaluated our architectures on multiple sequence datasets. In comparison to SOTA transformer-based models within the ANN domain on the SCv2 dataset, our LMUFormer demonstrates comparable performance while necessitating a remarkable 53 times reduction in parameters and a substantial 65 times decrement in FLOPs. Additionally, owing to our model's proficiency in real-time data processing, we can achieve a 32.03% reduction in sequence length, all while incurring an inconsequential decline in performance. Our code is publicly available at https://github.com/zeyuliu1037/LMUFormer.git.