发表机构
Technion – Israel Institute of Technology; NVIDIA; Institute of Science and Technology Austria (ISTA)（以色列理工学院; 英伟达; 奥地利科学技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出可学习的频谱激活函数（LSA），用残差截断傅里叶级数替代固定非线性，通过独立梯度解耦特征选择与频谱整形，在音频、图像、神经辐射场等任务中提升重建质量。
AI 中文摘要
隐式神经表示（INRs）受其输入编码和激活函数所引入的频谱结构影响。现有方法主要通过坐标编码或周期性非线性来修改网络可用的频率，从而改善拟合效果。然而，频率访问并非唯一的瓶颈：具有局部化或空间变化结构的信号要求网络高效地将频率组合成多谐波内部响应。我们引入了可学习的频谱激活函数（LSA），它用残差截断傅里叶级数替换固定的神经元级非线性，该级数的谐波幅度在训练过程中学习。LSA 并不扩展渐近函数类。相反，它改变了表示的因式分解：线性权重选择特征，而激活系数控制频谱整形，两者通过独立的梯度进行更新。由于给定固定预激活时，激活输出关于系数是仿射的，频谱调谐成为一个更直接的子问题，相比于将其与特征选择纠缠在一起的架构。实验上，这种因式分解将更多目标信号能量集中到神经正切核的主特征模态中，这与优化行为的改善一致。在音频、图像、神经辐射场和神经声场任务中，LSA 也提高了重建质量。
英文摘要
Implicit neural representations (INRs) are shaped by the spectral structure induced by their input encodings and activation functions. Existing methods improve fitting primarily by modifying which frequencies are available to the network, through coordinate encodings or periodic nonlinearities. However, frequency access is not the only bottleneck: signals with localized or spatially varying structure require the network to efficiently compose frequencies into multi-harmonic internal responses. We introduce learnable spectral activations (LSA), which replace fixed neuron-level nonlinearities with a residual truncated Fourier series whose harmonic amplitudes are learned during training. LSA does not expand the asymptotic function class. Instead, it changes the factorization of the representation: linear weights select features while activation coefficients control spectral shaping, and the two are updated by separate gradients. Because the activation output is affine in the coefficients given fixed pre-activations, spectral tuning becomes a more direct subproblem compared to architectures where it is entangled with feature selection. Empirically, this factorization concentrates more target-signal energy in the leading eigenmodes of the neural tangent kernel, consistent with improved optimization behavior. Across audio, image, neural radiance field, and neural acoustic field tasks, LSA also improves reconstruction quality.
