用阻尼振荡器建模神经元,让网络自动适应信号频谱。
Spectral Gating via Damped Oscillations for Adaptive Implicit Neural Representations

- 将神经元激活视为受迫阻尼振荡器的稳态响应,控制频谱选择性。
- 无需调参即可实现从低频到高频的渐进式学习,重建精度领先。
- 适合需要自适应频谱表征的连续信号建模任务。
隐式神经表示(INRs)通过基于坐标的网络编码连续信号,但面临频谱困境:周期性激活能捕捉细节却易记忆噪声,空间紧凑激活虽正则化强却存在低频偏差。现有方法引入计算开销或调参脆弱性。本文将每个神经元激活建模为正弦强迫阻尼谐振子的稳态响应,其振幅自然调控训练过程中的频谱选择性。联合优化振子参数与网络权重,使模型自适应目标信号的频谱内容,无需显式正则化。初始设置在阻带,网络呈现由粗到细的学习课程,先捕获低频结构,仅当重构目标要求时才拓展至高频细节。大量实验表明,本方法在主流INRs上持续达到或超越当前最优结果,且无需任何任务特定超参数调优。
原文摘要 · Abstract (English)
Implicit Neural Representations (INRs) have been proven successful in encoding continuous signals through coordinate-based networks, yet facing a spectral dilemma: periodic activations capture fine details but act as all-pass filters that memorise noise, while spatially compact activations regularise effectively but suffer from low-frequency bias. Existing attempts to resolve this trade-off introduce computational overhead or tuning frailty. We propose to model each neuron's activation as the steady-state response of a sinusoidally-forced damped harmonic oscillator, whose amplitude naturally governs the network's spectral selectivity during training. By jointly optimising the oscillator parameters alongside the network weights, our method adapts to the target signal's spectral content without explicit regularisation. Initialised in the stopband, the network exhibits a coarse-to-fine learning curriculum that progressively expands its spectral gate, capturing low-frequency structures first and high-frequency details only when justified by the reconstruction objective. Comprehensive experiments show that our approach consistently achieves state-of-the-art or competitive results against established INRs, while requiring no task-specific tuning of any hyperparameters.
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