Frequency Matching in Spiking Neural Networks for mmWave Sensing

Conference: ICML 2026
arXiv: 2605.09983
Code: GitHub
Area: Edge Sensing / Spiking Neural Networks (SNN) / Wireless Sensing
Keywords: LIF neuron, IIR low-pass filtering, mmWave sensing, discriminative spectrum, neural dynamics-data alignment

TL;DR

This work proves from a "mechanism-data alignment" perspective that LIF spiking neurons are equivalent to first-order IIR low-pass filters. It proposes setting the membrane decay coefficient \(\beta\) according to the discriminative spectrum of mmWave signals, enabling the SNN to achieve an average accuracy improvement of 6.22% and a theoretical energy reduction of 3.64× compared to ANNs across four common mmWave datasets.

Background & Motivation

Background: mmWave radar is a crucial sensor for edge-side posture, gesture, and activity recognition due to its privacy-friendly nature, light resistance, and penetration capabilities. Mainstream solutions utilize ANNs like CNNs or Transformers, relying on increased depth and handcrafted pre-processing for robustness at the cost of high energy consumption and latency.

Limitations of Prior Work: mmWave signals are inherently sparse, irregular, and heavily contaminated by high-frequency noise from multi-path effects and phase jitter. ANNs lack an inherent temporal filtering bias, necessitating either handcrafted low-pass pre-processing (which may discard useful high-frequency discriminative information) or deeper networks for brute-force fitting, leading to unsustainable energy and latency.

Key Challenge: Discriminative information is often distributed in the "low-to-medium frequency bands," while noise is concentrated in high frequencies. Existing ANNs and low-pass pre-processing fail to distinguish between "useful high-frequency discriminative components" and "true high-frequency noise." Although existing SNN works demonstrate energy efficiency advantages, they rely on empirical hyperparameter tuning without clarifying "when and why SNNs outperform ANNs."

Goal: To answer two questions from a signal processing perspective: (1) What is the mechanism behind the SNN's advantage in mmWave sensing? (2) How should the key hyperparameter, membrane decay coefficient \(\beta\), be selected based on the data spectrum?

Key Insight: By linearizing the discrete dynamics of LIF neurons into first-order IIR low-pass filters and quantifying the overlap between their cutoff frequencies and the discriminative spectrum of the dataset, selecting \(\beta\) is transformed into a frequency-domain alignment problem.

Core Idea: Aligning the effective bandwidth \(B_{\text{eff}}(\beta)\) of the LIF neuron with the discriminative spectrum \(\Omega^\star\) of the mmWave data. "Frequency matching" is identified as the fundamental mechanism for SNN superiority in such tasks and serves as the physical criterion for selecting \(\beta\).

Method

Overall Architecture

The paper maintains the network structure but equips "LIF neurons + LeNet-style SNN" with a set of frequency-domain analysis tools to address the empirical selection of \(\beta\). The approach involves comparing both data and neurons in the frequency domain: first, measuring where discriminative information resides in each mmWave dataset using DFT; then, linearizing the LIF neuron into a low-pass filter whose bandwidth is controlled by \(\beta\); and finally, using an alignment score to measure the overlap between the "filtered spectrum" and the "discriminative spectrum," categorizing the range of \(\beta\) into three interpretable segments.

graph TD
    subgraph D1["Discriminative Spectrum DI_norm"]
        direction TB
        A["mmWave Samples → 1D Time Series + DFT Magnitude Spectrum"] --> B["Inter-class / Intra-class Scatter → DI_norm"]
    end
    subgraph D2["LIF Low-pass Template (β as Inverse Bandwidth)"]
        direction TB
        E["LIF Neuron → 1st-order IIR + DC Normalized Template"] --> F["Half-power Point Defines Effective Bandwidth B_eff(β)"]
    end
    B --> H["FMS Alignment Score<br/>Inner Product of DI_norm and Template"]
    F --> H
    H --> I["β† Max Deviation Rule<br/>Furthest Point from Diagonal of logτ vs FMS"]
    I --> J["Tri-segment Division<br/>under-filter / stability window / over-low-pass"]
    J -->|Select β in stability window| K["Train SpikingLeNet"]

Key Designs

1. Discriminative Spectrum \(\mathrm{DI}_{\text{norm}}\): Measuring where discriminative information resides

To discuss "frequency matching," a metric is required to define the frequency distribution of discriminative information in mmWave data. For each sample \(\mathbf{X}_i\in\mathbb{R}^L\times C\times H\times W\), the non-temporal dimensions are averaged into a 1D time series \(\mathbf{s}_i\in\mathbb{R}^L\). After sample-wise mean subtraction and one-sided DFT to obtain the magnitude spectrum \(A_i[k]\), the inter-class scatter \(S_B[k]=\sum_c\pi_c(\mu_c[k]-\bar\mu[k])^2\) and intra-class scatter \(S_W[k]=\sum_c\pi_c\,\mathrm{Var}_c[k]\) are estimated per frequency band. The Discriminative Index is defined as \(\mathrm{DI}(\omega_k)=S_B[k]/(S_W[k]+\varepsilon)\) and normalized in the frequency domain as a probability distribution \(\mathrm{DI}_{\text{norm}}\). This Fisher-style linear separability statistic reflects both energy distribution and class separability, serving as the intermediary between data truth and neuronal mechanisms.

2. LIF Low-pass Template: Turning \(\beta\) into a clean "inverse bandwidth" knob

Beyond the data spectrum, the LIF neuron's nature as a filter must be defined. By writing the LIF dynamics as \(u_{t+1}=\beta u_t+(1-\beta)I_t-v_{\text{th}}O_t\) and ignoring the reset term, it functions as a first-order IIR filter with a frequency response \(H(\omega_k;\beta)=(1-\beta e^{-j\omega_k})^{-1}\). To eliminate global magnitude differences and compare "shape" only, a DC-normalized power template is defined: \(\tilde H(\omega_k;\beta)=(1-\beta)^2/[(1-\beta)^2+2\beta(1-\cos\omega_k)]\). Lemma 3.2 proves that \(\tilde H\in(0,1]\), \(\tilde H(0;\beta)=1\), and it is non-increasing with respect to both \(\omega_k\) and \(\beta\)—meaning a larger \(\beta\) results in a narrower passband. Using the half-power point \(\tilde H(\omega_c;\beta)=1/2\) to define the effective bandwidth \(B_{\text{eff}}(\beta)=\omega_c\), \(\beta\) is transformed from a heuristic hyperparameter into a physical control for bandwidth.

3. FMS Alignment Score and \(\beta^\dagger\) Max Deviation Rule: Segmenting \(\beta\) without training

With the data spectrum and LIF template, "frequency matching" can be quantified by the inner product, yielding the alignment score \(\mathrm{FMS}_{\text{avg}}(\beta)=\sum_{\omega_k}\mathrm{DI}_{\text{norm}}(\omega_k)\tilde H(\omega_k;\beta)\in[0,1]\). This score represents the "quality of discriminative spectrum preserved by the LIF at a given \(\beta\)." A critical issue is that if \(\beta\) is too large, the passband becomes too narrow, discarding useful high-frequency discriminative components. A geometric rule is used to locate this critical point: let \(\tau=(1-\beta)^{-1}\), apply min-max normalization to both \(\log\tau\) and \(\mathrm{FMS}_{\text{avg}}\) to obtain \((\phi_r,\psi_r)\), and connect the endpoints to form a reference diagonal \(\hat L\). The furthest point from this line is defined as \(\beta^\dagger=\arg\max_r|\hat L(\phi_r)-\psi_r|\). Proposition 3.5 divides \(\beta\) into: under-filter (\(\beta\to 0\), noise not suppressed), stability window (\(0<\beta<\beta^\dagger\), where accuracy peaks typically reside), and over-low-pass (\(\beta\geq\beta^\dagger\), discriminative information discarded). Notably, \(\beta^\dagger\) is determined solely by data spectrum and neural dynamics, independent of label accuracy, allowing practitioners to avoid expensive dataset-specific accuracy sweeps.

Mechanism

Taking the AOPHand gesture dataset as an example: First, DFT is applied to all samples, revealing that discriminative energy is concentrated in the low-to-medium frequency bands while high frequencies are dominated by noise, yielding \(\mathrm{DI}_{\text{norm}}\). Then, a range of candidate \(\beta\) values is swept to calculate the LIF's normalized bandwidth \(B_{\text{eff}}(\beta)\) and alignment score \(\mathrm{FMS}_{\text{avg}}(\beta)\). By plotting \(\mathrm{FMS}_{\text{avg}}\) against \(\log\tau\) and finding the point of maximum deviation from the diagonal, the critical \(\beta^\dagger\) is identified. Selecting \(\beta\) within the stability window before \(\beta^\dagger\) for training SpikingLeNet results in an optimal accuracy corresponding to a \(\beta^\ast\) located to the left of \(\beta^\dagger\), improving accuracy from LeNet's 60.86% to 83.70%. The entire process avoids accuracy-based scanning for \(\beta\) selection.

Loss & Training

Standard SNN training with surrogate gradients is employed. The backbone is a simple LeNet-style SpikingLeNet (≈4.19M parameters). The only additional step is pre-selecting \(\beta\) for each dataset using the aforementioned frequency matching method.

Key Experimental Results

Main Results: Accuracy across 4 mmWave Datasets (%, mean of 3 seeds)

Model	AOPHand	mmFiT	Pantomime	MMActivity	#Params (M)
LeNet	60.86	62.36	61.83	59.17	4.19
VGG9	74.39	69.36	72.63	70.00	31.6
ResNet50	72.54	71.84	73.90	61.67	23.5
GRU	67.52	14.11	75.45	47.50	0.075
CNN-GRU	61.98	67.80	72.77	65.00	0.46
ViT	21.39	36.40	42.16	65.83	2.18
SpikingLeNet	83.70	73.67	78.31	75.00	4.19

Main Results: Theoretical Energy Consumption per Sample (μJ)

Model	AOPHand	mmFiT	Pantomime	MMActivity
LeNet	251.08	251.08	251.10	251.08
VGG16	6017.25	6017.26	6017.34	6017.24
RNN	7.35	7.35	7.36	7.35
SpikingLeNet	2.53	2.04	2.44	1.45

Ablation Study

Setup	Key Observation	Background
Explicit LPF + LeNet vs SpikingLeNet	LeNet improves with filter but still lags behind	Hard frequency truncation suppresses noise but kills high-f discriminative info; LIF's "soft" LPF is superior
\(\beta\) sweep (Fig 4)	Accuracy rises then falls; peak \(\beta^\ast < \beta^\dagger\)	Directly validates the stability window prediction of Proposition 3.5
\(T\) sweep	Small \(T\) increase \(\rightarrow\) Accuracy gains then saturates	Moderate time steps stabilize predictions; primary driver is \(\beta\)
t-SNE (Fig 3)	SNN features show clearer inter-class separation	Noise suppression via frequency matching makes feature space more discriminative
Multi-platform Latency	~4× slower than LeNet on Jetson GPU; nearly matches on Darwin3	Current GPUs treat spikes as dense kernels; neuromorphic hardware realizes sparsity benefits

Key Findings

• SpikingLeNet with the same LeNet backbone outperforms the strongest ANN by 6.22% on average across 4 datasets with identical parameter counts, indicating the performance gain stems from the temporal frequency bias provided by LIF, not capacity.
• SpikingLeNet's energy consumption is ~3.64× lower than the next most efficient model (RNN) and orders of magnitude lower than VGG/ResNet. This is highly suitable for always-on edge sensing equipment with hardware support.
• The optimal \(\beta^\ast\) consistently appears before the theoretically derived \(\beta^\dagger\), and \(\mathrm{FMS}_{\text{avg}}\) is highly correlated with accuracy, confirming the "frequency matching" hypothesis across all datasets.
• Current latency bottlenecks of SNNs on GPUs are primarily systems-level artifacts. Deploying the workflow on neuromorphic chips like Darwin3 realizes the "event-driven + sparse" hardware advantage.

Highlights & Insights

• Elevates the explanation of "why SNNs outperform ANNs on mmWave" from empirical observation to frequency-domain mechanisms, supplemented by provable lemmas and propositions.
• Translates \(\beta\) as "inverse bandwidth" and provides a graphic selection rule for \(\beta^\dagger\), allowing practitioners to achieve near-optimal \(\beta\) without expensive sweeps. This mechanism-based tuning can be extended to other tasks with distinct frequency structures (EEG, inertial sensing, radar tracking).
• Introducing the discriminative spectrum \(\mathrm{DI}_{\text{norm}}\) as a "data spectrum profiling" tool provides a lightweight yet universal method to inspect whether the "frequency bias" of various networks matches the target data, offering a new perspective for model design.

Limitations & Future Work

• The framework is entirely built on "LIF + ignoring reset" IIR linearization. For neurons with hard reset, adaptive thresholds, or multi-state spiking, frequency analysis must be revisited.
• Experiments were conducted on a small LeNet-style backbone; whether "frequency matching" remains the primary bottleneck or is diluted by hierarchical interactions in deeper/multi-branch SNNs requires validation.
• \(\beta^\dagger\) is a geometric choice based on a discrete candidate set and depends on sweep density; the optimal \(\beta^\ast\) still requires post-training confirmation, as an analytical solution for the optimal \(\beta\) without training was not provided.
• Latency is attributed to "system-level artifacts," but actual deployment requires quantifiable hardware-algorithm co-design paths; a single case on Darwin3 is insufficient.

Related Work & Insights

• vs Fang et al. (2025): Advances the conclusion that "LIF ≈ IIR Low-pass" into a "spectrum-data alignment" framework, providing a directly applicable criterion for parameter tuning.
• vs Arsalan et al. 2022/2023, Hu et al. 2025, etc.: Previous works emphasized energy efficiency or engineering improvements; this work explains the mechanism and provides reusable design principles.
• vs Classic Low-pass Pre-processing: Traditional hard frequency truncation discards high-frequency discriminative information; LIF's soft low-pass suppression of noise while retaining discriminative components provides experimental evidence for "Frequency Matching > Hard Truncation."

Rating

• Novelty: ⭐⭐⭐⭐ Explaining SNN advantages in mmWave via frequency mechanisms and providing calculable \(\beta\) selection rules is a novel perspective.
• Experimental Thoroughness: ⭐⭐⭐⭐ Covers 4 common datasets and multi-platform latency, though limited to LeNet backbones.
• Writing Quality: ⭐⭐⭐⭐ Clear lemmas and propositions with a complete mechanistic narrative.
• Value: ⭐⭐⭐⭐ Provides direct tuning guidance for edge SNN deployment and a template for "mechanism-data alignment" research.

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