通过尼奎斯特原理优化频率分配，减少神经网络冗余，提升多维度信号重建效果。
FM-SIREN & FM-FINER: Implicit Neural Representation Using Nyquist-based Orthogonality
- 为每个神经元分配独特频率倍数，基于尼奎斯特准则避免频段重叠。
- 特征冗余降低近50%，在音频、图像、3D形状和视频任务中均表现更优。
- 无需调参或加深网络，适用于多模态隐式表示场景。
现有的基于周期激活函数的隐式神经表示（INR）网络（如 SIREN 和 FINER）存在隐藏特征冗余问题，即同一层内神经元捕捉到重叠的频率成分，原因在于使用固定的频率倍数。本文受离散正弦变换（DST）等经典信号处理方法启发，提出 FM-SIREN 与 FM-FINER，为周期激活函数中的神经元分配基于尼奎斯特准则的、各不相同的频率倍数。与现有方法不同，该设计在不增加超参数调优或网络深度的前提下引入频率多样性。该简单而严谨的方法使特征冗余减少近50%，并持续提升多种 INR 任务的信号重建性能，包括一维音频、二维图像、三维形状及视频建模，显著优于其基线模型，同时保持高效性。
原文摘要 · Abstract (English)
Existing periodic activation-based implicit neural representation (INR) networks, such as SIREN and FINER, suffer from hidden feature redundancy, where neurons within a layer capture overlapping frequency components due to the use of a fixed frequency multiplier. This redundancy limits the expressive capacity of multilayer perceptrons (MLPs). Drawing inspiration from classical signal processing methods such as the Discrete Sine Transform (DST), in this paper, we propose FM-SIREN and FM-FINER, which assign Nyquist-informed, neuron-specific frequency multipliers to periodic activations. Contrary to existing approaches, our design introduces frequency diversity without requiring hyperparameter tuning or additional network depth. This simple yet principled approach reduces the redundancy of features by nearly 50% and consistently improves signal reconstruction across diverse INR tasks, such as fitting 1D audio, 2D image and 3D shape, and video, outperforming their baseline counterparts while maintaining efficiency.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。