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Balanced Resonate-and-Fire Neurons
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Proposes balanced resonate-and-fire (BRF) and balanced harmonic RF (BHRF) spiking neurons with a refractory period, smooth reset, and analytically derived divergence boundary, used in recurrent SNNs that train faster and spike far less than ALIF networks.
Problem
Vanilla resonate-and-fire neurons diverge and spike excessively in discrete-time simulation and reset mechanisms disrupt their oscillation, hindering effective training of recurrent spiking networks; RSNNs also converge slowly under BPTT.
Approach
Adds a refractory-period-based adaptive threshold, a smooth reset that increases dampening after spikes, and a divergence boundary constraining the dampening parameter to a stable range derived from the Euler-discretized RF dynamics, yielding stable resonant neurons for RSNNs.
Key results
- BRF reaches 99.0% on S-MNIST and 95.0% on PS-MNIST with 68,874 parameters, versus 98.7% and 94.3% for ALIF-RSNN with 156,126 parameters.
- On SHD, BRF achieves 91.7% vs 90.4% for ALIF while spiking only about 14% as much (14.01 SOPs/step vs 98.76).
- BRF reaches 95% of final S-MNIST accuracy in 3 epochs versus 105 for ALIF.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace vanilla RF with BRF (refractory period, smooth reset, and divergence boundary) | RF-RSNN · PS-MNIST test | accuracy: 9.9\pm 0.8\,\% -> 95.0\pm 0.2\,\% | Helped |
| Replace vanilla RF with BRF (refractory period, smooth reset, and divergence boundary) | RF-RSNN · S-MNIST test | accuracy: 98.0\pm 0.4 \, \% -> 99.0\pm 0.1\,\% | Helped |
| Replace vanilla RF with BRF (refractory period, smooth reset, and divergence boundary) | RF-RSNN · SHD test | accuracy: 89.2\pm 0.6\,\% -> 91.7\pm 0.8\,\% | Helped |
| Replace vanilla RF with BRF (refractory period, smooth reset, and divergence boundary) | RF-RSNN · ECG test | accuracy: 85.5\pm 0.7\,\% -> 85.8\pm 0.7\,\% | Mixed |
| Add a refractory period and smooth reset (ablation) | RF neuron · RF neuron simulation | SOPs | Helped |
| Add the divergence boundary (ablation) | RF-RSNN · PS-MNIST | stability | Helped |
| Replace smooth reset with traditional soft or hard reset (ablation) | RF-RSNN · ECG and SHD | convergence | Hurt |
| Remove recurrent weights by pruning (ablation) | BRF-RSNN · S-MNIST and PS-MNIST | accuracy | No clear effect |
| Remove recurrent weights by pruning (ablation) | ALIF-RSNN · S-MNIST and PS-MNIST | accuracy | Hurt |
| Use BRF instead of ALIF with full BPTT rather than ALIF TBPTT | RSNN · S-MNIST | epochs to 95% of final accuracy: 105 -> 3 | Helped |
| Use BRF instead of ALIF with full BPTT rather than ALIF TBPTT | RSNN · PS-MNIST | epochs to 95% of final accuracy: 143 -> 10 | Helped |
| Combine TorchScript with forward gradient injection (ablation) | BRF-RSNN · S-MNIST training | training speedup: 2.3\times | Helped |
Surprising findings
- Vanilla RF without reset stays at chance (9.9%) on PS-MNIST, while the balanced variant reaches 95%.
- BRF networks remain accurate when recurrent weights are pruned fully, whereas ALIF networks degrade poorly.
Limitations
- Performance depends on initialization of angular frequencies and dampening offset.
- Evaluated only on single-hidden-layer networks and four relatively small benchmarks; scaling not demonstrated.
- BHRF remained preliminary and BRF is sensitive to input frequencies far from its initialization.
Experimental setup
Datasets: S-MNIST PS-MNIST ECG QT database Spiking Heidelberg Digits (SHD)
Benchmarks: S-MNIST PS-MNIST ECG SHD
Metrics: test accuracy number of parameters spiking operations (SOPs) epochs to reach 95% of final accuracy noise robustness
Baselines: ALIF-RSNN vanilla RF-RSNN DCLS-Delays RadLIF
Builds on: resonate-and-fire neuron adaptive leaky integrate-and-fire (ALIF) multi-Gaussian surrogate gradient e-prop
Closest papers by meaning
- Dendritic Resonate-and-Fire Neuron for Effective and Efficient Long Sequence Modeling (NeurIPS 2025 · similarity 0.91)
- Spiking Neural Networks Need High-Frequency Information (NeurIPS 2025 · similarity 0.89)
- Sparse Spiking Neural Network: Exploiting Heterogeneity in Timescales for Pruning Recurrent SNN (ICLR 2024 · similarity 0.87)
- FiTS: Interpretable Spiking Neurons via Frequency Selectivity and Temporal Shaping (NeurIPS 2026 · similarity 0.87)
- CLIF: Complementary Leaky Integrate-and-Fire Neuron for Spiking Neural Networks (ICML 2024 · similarity 0.87)
- SpikingSSMs: Learning Long Sequences with Sparse and Parallel Spiking State Space Models (AAAI 2025 · similarity 0.87)
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