提出频谱能量中心度量，提升隐式神经表示的频率建模能力
Spectral Energy Centroid: a Metric for Improving Performance and Analyzing Spectral Bias in Implicit Neural Representations
- 用频谱能量中心度量分析隐式神经表示的频率偏置
- 新方法在不同深度模型下均优于传统超参数调优策略
- 适用于图像建模、复杂度评估与跨架构频谱对齐
隐式神经表示（INRs）利用多层感知机（MLPs）建模连续信号，实现数据在多个领域的紧凑、可微且高保真表示。然而，由于MLP存在低频偏好，难以有效学习细节信息，需通过嵌入层精细调节模型频率。以往研究虽提出基于目标信号的预调参方法，但未考虑模型深度的影响，表明我们对频率与INR性能关系的理解仍不充分。为此，本文引入频谱能量中心（SEC）度量，用于量化目标图像的频率特性和INR模型的频谱偏置。实验表明，SEC在三个任务中具有广泛适用性：（1）提出一种数据驱动的超参数选择策略（SEC-Conf），显著优于现有启发式方法，且对模型深度鲁棒；（2）作为信号复杂度的可靠代理指标；（3）有效实现多种INR架构间的频谱偏置对齐。
原文摘要 · Abstract (English)
Implicit Neural Representations (INRs) model continuous signals using multilayer perceptrons (MLPs), enabling compact, differentiable, and high-fidelity representations of data across diverse domains. However, due to the low-frequency bias of MLPs that prevents effective learning of small details, the model's frequency must be carefully tuned through the embedding layer. Prior work established that this tuning can be performed before training based on the target signal, but it did not account for the significant effect of model depth, indicating that our understanding of the relationship between frequency and INR performance remains limited. To gain insights into this relationship, we utilize the Spectral Energy Centroid (SEC) metric that quantifies the frequency of target images and the spectral bias of INR models. We show that SEC is a versatile tool for INR analysis, demonstrating its utility across three tasks: (1) a data-driven strategy (SEC-Conf) for hyperparameter selection that outperforms existing heuristics and is robust to model depth, (2) a reliable proxy for signal complexity, and (3) effective alignment of spectral biases across diverse INR architectures.
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