# Balanced Resonate-and-Fire Neurons

arXiv: https://arxiv.org/abs/2402.14603 · HTML: https://mlsanity.com/paper/2402.14603/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 44 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks](https://mlsanity.com/paper/2007.05785/) (2020)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [The Heidelberg spiking datasets for the systematic evaluation of spiking neural networks](https://mlsanity.com/paper/1910.07407/) (2019)
- [Accurate and efficient time-domain classification with adaptive spiking recurrent neural networks](https://mlsanity.com/paper/2103.12593/) (2021)
- [Learning Delays in Spiking Neural Networks using Dilated Convolutions with Learnable Spacings](https://mlsanity.com/paper/2306.17670/) (2023)
- [Efficient Video and Audio processing with Loihi 2](https://mlsanity.com/paper/2310.03251/) (2023)
- [Noise-Robust Deep Spiking Neural Networks with Temporal Information](https://mlsanity.com/paper/2104.11169/) (2021)
- [Deep Spiking Neural Networks with Resonate-and-Fire Neurons](https://mlsanity.com/paper/2109.08234/) (2021)
- [Long Short-term Memory with Two-Compartment Spiking Neuron](https://mlsanity.com/paper/2307.07231/) (2023)

## Built on by (most cited first, 12 of 12)

- [The Resurrection of the ReLU](https://mlsanity.com/paper/2505.22074/) (2025)
- [Detection of Fast-Moving Objects with Neuromorphic Hardware](https://mlsanity.com/paper/2403.10677/) (2024)
- [Dendritic Resonate-and-Fire Neuron for Effective and Efficient Long Sequence Modeling](https://mlsanity.com/paper/2509.17186/) (2025)
- [A Complete Pipeline for deploying SNNs with Synaptic Delays on Loihi 2](https://mlsanity.com/paper/2510.13757/) (2025)
- [Modern Neuromorphic AI: From Intra-Token to Inter-Token Processing](https://mlsanity.com/paper/2601.00245/) (2026)
- [Understanding the Convergence in Balanced Resonate-and-Fire Neurons](https://mlsanity.com/paper/2406.00389/) (2024)
- [A Scalable Hybrid Training Approach for Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2506.14464/) (2025)
- [Neuromorphic Wireless Split Computing with Resonate-and-Fire Neurons](https://mlsanity.com/paper/2506.20015/) (2025)
- [Optimization of Low-Latency Spiking Neural Networks Utilizing Historical Dynamics of Refractory Periods](https://mlsanity.com/paper/2507.02960/) (2025)
- [ASecond-Order SpikingSSM for Wearables](https://mlsanity.com/paper/2510.14386/) (2025)
- [Efficient Sparse Selective-Update RNNs for Long-Range Sequence Modeling](https://mlsanity.com/paper/2603.02226/) (2026)
- [REACT: A Fully Spiking State-Space Model for Real-Time Event-Driven Temporal Perception](https://mlsanity.com/paper/2609.19204/) (2026)

## Abstract (arXiv)

The resonate-and-fire (RF) neuron, introduced over two decades ago, is a simple, efficient, yet biologically plausible spiking neuron model, which can extract frequency patterns within the time domain due to its resonating membrane dynamics. However, previous RF formulations suffer from intrinsic shortcomings that limit effective learning and prevent exploiting the principled advantage of RF neurons. Here, we introduce the balanced RF (BRF) neuron, which alleviates some of the intrinsic limitations of vanilla RF neurons and demonstrates its effectiveness within recurrent spiking neural networks (RSNNs) on various sequence learning tasks. We show that networks of BRF neurons achieve overall higher task performance, produce only a fraction of the spikes, and require significantly fewer parameters as compared to modern RSNNs. Moreover, BRF-RSNN consistently provide much faster and more stable training convergence, even when bridging many hundreds of time steps during backpropagation through time (BPTT). These results underscore that our BRF-RSNN is a strong candidate for future large-scale RSNN architectures, further lines of research in SNN methodology, and more efficient hardware implementations.