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 filter, mmWave sensing, discriminative spectrum, neural dynamics-data alignment

TL;DR

From a "mechanism-data alignment" perspective, this work proves that LIF spiking neurons are equivalent to a first-order IIR low-pass filter, and proposes setting the membrane decay coefficient \(\beta\) according to the discriminative spectrum of mmWave signals. This enables SNNs to achieve an average of 6.22% higher accuracy and 3.64× lower theoretical energy consumption than ANNs on four standard mmWave datasets.

Background & Motivation

Background: mmWave radar is an important sensor for edge-side posture, gesture, and activity recognition due to its privacy-friendliness, robustness to lighting, and penetration capability. Mainstream solutions use CNNs/Transformers and other ANNs, relying on deep stacking and manual preprocessing for robustness, but at the cost of high energy and latency.

Limitations of Prior Work: mmWave signals are inherently sparse, irregular, and heavily contaminated by high-frequency noise from multipath and phase jitter. ANNs lack built-in temporal filtering bias: either manual low-pass preprocessing is applied (which also removes useful high-frequency discriminative information), or deeper networks are used to fit the data, resulting in high energy and latency.

Key Challenge: Discriminative information is often distributed in the "low-to-mid frequency band," while noise is concentrated in the high-frequency band. Existing ANN/low-pass preprocessing cannot distinguish "useful high-frequency discriminative components" from "true high-frequency noise." Prior SNN work has shown energy efficiency advantages, but hyperparameter tuning is empirical, and there is no clear explanation of "when and why SNNs outperform ANNs."

Goal: From a signal processing perspective, answer two questions—(1) What is the mechanism behind SNNs' advantage on mmWave tasks? (2) How should the key hyperparameter, membrane decay coefficient \(\beta\), be selected based on the data spectrum?

Key Insight: Linearize the discrete dynamics of the LIF neuron as a first-order IIR low-pass filter, directly quantify the overlap between its cutoff frequency and the dataset's discriminative spectrum, and thus turn "setting \(\beta\)" into a frequency-domain alignment problem.

Core Idea: Match the effective bandwidth \(B_{\text{eff}}(\beta)\) of the LIF neuron to the discriminative spectrum \(\Omega^\star\) of mmWave data—"frequency matching" is the fundamental mechanism for SNNs' superiority over ANNs in such tasks, and provides a physical criterion for selecting \(\beta\).

Method

Overall Architecture

No new network structure is introduced; instead, a frequency-domain mechanism analysis and hyperparameter selection method is provided for "LIF neuron + LeNet-style SNN." The approach consists of three steps: (1) Use DFT along the temporal dimension to analyze each mmWave dataset, define a Fisher-style discriminative index \(\mathrm{DI}(\omega_k)\) and normalize it to a probability distribution \(\mathrm{DI}_{\text{norm}}\); (2) Express LIF as \(u_{t+1}=\beta u_t+(1-\beta)I_t-v_{\text{th}}O_t\), ignore the reset term, yielding an equivalent first-order IIR filter \(H(\omega_k;\beta)=(1-\beta e^{-j\omega_k})^{-1}\), define the DC-normalized power template \(\tilde H(\omega_k;\beta)\) and half-power cutoff \(B_{\text{eff}}(\beta)\); (3) Use the dot product \(\mathrm{FMS}_{\text{avg}}(\beta)=\sum_{\omega_k}\mathrm{DI}_{\text{norm}}(\omega_k)\tilde H(\omega_k;\beta)\) to measure mechanism-data alignment, then apply the "maximum deviation from reference diagonal" rule to identify the over-low-pass threshold \(\beta^\dagger\), partitioning \(\beta\) into "under-filter / stability window / over-low-pass" regions.

Key Designs

1. Data Side: Discriminative Spectrum \(\mathrm{DI}_{\text{norm}}(\omega_k)\):

   • Function: Objectively quantifies the "density of class-discriminative information at each frequency," serving as the "ground truth" for subsequent mechanism matching.
   • Mechanism: For each sample \(\mathbf{X}_i\in\mathbb{R}^{L\times C\times H\times W}\), average over non-temporal dimensions to obtain a 1D sequence \(\mathbf{s}_i\in\mathbb{R}^L\), perform sample-wise mean removal and one-sided DFT to get amplitude spectrum \(A_i[k]\); estimate inter-class scatter \(S_B[k]=\sum_c\pi_c(\mu_c[k]-\bar\mu[k])^2\) and intra-class scatter \(S_W[k]=\sum_c\pi_c\,\mathrm{Var}_c[k]\) per frequency, define \(\mathrm{DI}(\omega_k)=S_B[k]/(S_W[k]+\varepsilon)\) and normalize in the frequency domain.
   • Design Motivation: Directly applies Fisher-style statistics for linear separability, reflecting both "signal energy distribution" and "class separability," serving as a bridge between "data" and "mechanism."

2. Mechanism Side: LIF Low-Pass Template and Monotonic Bandwidth Control (Lemma 3.2):

   • Function: Translates the temporal integration behavior of spiking neurons into "a low-pass filter with bandwidth monotonically controlled by \(\beta\)," enabling direct frequency-domain alignment with the data spectrum.
   • Mechanism: LIF without reset is a first-order IIR with frequency response \(H(\omega_k;\beta)=(1-\beta e^{-j\omega_k})^{-1}\); to eliminate overall amplitude differences, define the DC-normalized power template \(\tilde H(\omega_k;\beta)=(1-\beta)^2/[(1-\beta)^2+2\beta(1-\cos\omega_k)]\). Lemma 3.2 proves: \(\tilde H\in(0,1]\), \(\tilde H(0;\beta)=1\), non-increasing in both \(\omega_k\) and \(\beta\). The half-power point \(\tilde H(\omega_c;\beta)=1/2\) defines the effective bandwidth \(B_{\text{eff}}(\beta)=\omega_c\), making \(\beta\) a clean "inverse bandwidth" knob.
   • Design Motivation: Assigns a clear physical meaning (bandwidth control) to the hyperparameter \(\beta\), turning "tuning" into "bandwidth-data spectrum alignment" rather than empirical guesswork.

3. Alignment Side: FMS Score and \(\beta^\dagger\) Maximum Deviation Rule:

   • Function: Provides a "starting point for over-low-pass" \(\beta^\dagger\) that depends only on data spectrum and neural dynamics, not label accuracy, thus quantitatively partitioning the tunable range of \(\beta\).
   • Mechanism: Take the inner product of the template and data spectrum to obtain \(\mathrm{FMS}_{\text{avg}}(\beta)=\sum_{\omega_k}\mathrm{DI}_{\text{norm}}(\omega_k)\tilde H(\omega_k;\beta)\in[0,1]\), interpreted as "the quality of discriminative spectrum retained by LIF at current \(\beta\)." Let \(\tau=(1-\beta)^{-1}\), min-max normalize both \(\log\tau\) and \(\mathrm{FMS}_{\text{avg}}\) to \((\phi_r,\psi_r)\), connect endpoints to form reference diagonal \(\hat L\), and select the point of maximum deviation \(\beta^\dagger=\arg\max_r|\hat L(\phi_r)-\psi_r|\). Proposition 3.5 thus defines three regions: under-filter (\(\beta\to 0\), noise not suppressed), stability window (\(0<\beta<\beta^\dagger\), accuracy typically peaks here), over-low-pass (\(\beta\geq\beta^\dagger\), discriminative information also suppressed).
   • Design Motivation: Traditional \(\beta\) tuning requires dataset-specific accuracy sweeps, which are costly and lack mechanistic explanation; defining \(\beta^\dagger\) via frequency-domain geometry turns "tuning" into "drawing a line on the spectrum," highly meaningful for edge SNN deployment.

Loss & Training

Standard SNN training with surrogate gradients is used (details in the appendix), with a simple LeNet-style SpikingLeNet (≈4.19M parameters); the only extra step is to pre-select \(\beta\) for each dataset as described above.

Key Experimental Results

Main Results: Accuracy (%) on 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 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 & Diagnostics

Setting	Key Observation	Note
Explicit low-pass preprocessing + LeNet vs SpikingLeNet	Adding filter improves LeNet but still lags behind SpikingLeNet	Hard frequency truncation suppresses noise but also removes high-frequency discriminative information; LIF provides superior "soft low-pass"
\(\beta\) sweep (Fig. 4)	Accuracy rises then falls with \(\beta\), peak at \(\beta^\ast<\beta^\dagger\)	Directly validates the stability window prediction of Proposition 3.5
\(T\) sweep	Slight increase in \(T\) → accuracy improves then saturates	Moderate time steps mainly stabilize prediction; main driver is \(\beta\)
t-SNE (Fig. 3)	SNN features show much clearer inter-class separation than ANN	Frequency matching suppresses high-frequency noise, making feature space more discriminative
Multi-platform latency	~4× slower than LeNet on Jetson GPU, nearly matches on Darwin3	Current GPUs run spikes as dense kernels; neuromorphic hardware is needed to realize sparsity advantage

Key Findings

• SpikingLeNet with the same LeNet backbone outperforms the strongest ANN by an average of 6.22% across four datasets, with identical parameter count—indicating the performance gain comes from the temporal-frequency bias of LIF, not model capacity.
• In terms of energy, SpikingLeNet is ~3.64× more efficient than the next best (RNN), and two to three orders of magnitude lower than VGG/ResNet; with hardware support, this approach is highly suitable for always-on edge sensing devices.
• The optimal \(\beta^\ast\) always appears before the theoretically predicted \(\beta^\dagger\), and \(\mathrm{FMS}_{\text{avg}}\) is highly correlated with accuracy, confirming the "frequency matching" hypothesis on all four datasets.
• The apparent "slowness" of SNNs on GPUs is mainly a system-level artifact; deploying on neuromorphic chips like Darwin3 realizes the "event-driven + sparsity" hardware advantage.

Highlights & Insights

• Elevates the explanation for "why SNNs outperform ANNs on mmWave" from empirical observation to frequency-domain mechanism, with provable lemmas and propositions, filling the explanatory gap in existing SNN-mmWave work without algorithmic novelty.
• Translates \(\beta\) into "inverse bandwidth" and provides a graphical selection rule for \(\beta^\dagger\), enabling practitioners to obtain near-optimal \(\beta\) without expensive sweeps; this mechanism-based tuning method can be extended to other "LIF + frequency-structured" tasks (EEG, inertial sensing, radar tracking).
• Introducing the discriminative spectrum \(\mathrm{DI}_{\text{norm}}\) as a "data spectrum profile" is a lightweight yet general tool, allowing inspection of whether a network's "frequency bias" matches the target data—a new perspective for model design/selection.

Limitations & Future Work

• The framework is entirely based on the IIR linearization of "LIF + ignoring reset"; for hard reset, adaptive threshold, or multi-state spiking neurons, frequency-domain analysis needs to be redone.
• All experiments are conducted on small LeNet models; it remains to be verified on deeper/multi-branch SNNs whether "frequency matching" is still the key bottleneck or diluted by higher-level interactions.
• \(\beta^\dagger\) is a geometric selection from a discrete candidate set, dependent on sweep density; the optimal \(\beta^\ast\) still requires post-training determination, and the paper does not provide an analytic solution for "best \(\beta\) without any training samples."
• The paper attributes latency issues to "system-level artifacts," but real-world deployment often requires quantifiable hardware-algorithm co-design paths; providing only a Darwin3 case is insufficient.

Related Work & Insights

• vs Fang et al. (2025): This work advances Fang et al.'s "LIF ≈ IIR low-pass" result from formulaic to a "spectrum-data alignment" framework, providing the first directly applicable criterion for hyperparameter tuning.
• vs Arsalan et al. 2022/2023, Hu et al. 2025 and other SNN-mmWave works: Previous studies emphasized energy efficiency or engineering improvements; this work explains "why SNNs suit mmWave" from a frequency-domain mechanism and offers reusable design principles.
• vs Classical Low-Pass Preprocessing: Traditional hard frequency truncation also removes high-frequency discriminative information; LIF's soft low-pass suppresses noise while retaining discriminative components, providing experimental evidence that "frequency matching > hard truncation."

Rating

• Novelty: ⭐⭐⭐⭐ Explains SNN's advantage on mmWave from a frequency-domain mechanism and provides a computable \(\beta\) selection rule; novel perspective.
• Experimental Thoroughness: ⭐⭐⭐⭐ Covers 4 standard mmWave datasets + multi-platform latency tests, but limited to LeNet backbone.
• Writing Quality: ⭐⭐⭐⭐ Lemmas and propositions are clear, mechanism narrative is complete.
• Value: ⭐⭐⭐⭐ Directly guides SNN deployment on edge devices, and provides a template for "mechanism-data alignment" research paradigm.

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