这篇论文教你用FFT给特征学习网络做预处理，在数据少时也能提升效果，实验显示NMSE最高降一半，值得搞特征提取的人看看。
该论文证明H-Score目标在无约束函数下对可逆变换不变，但在约束近似类中对输入基旋转敏感。提出用快速傅里叶变换（FFT）作为数据无关的低成本预处理器，将跨协方差奇异值谱集中到少数主模式，从而减少有限宽度截断误差。在8个多元数据集实验中，FFT预处理在资源受限场景下最多降低50%的归一化均方误差（NMSE）。论文还引入基于谱熵和累积依赖能量的无训练指标，可提前评估基的适用性并预测下游推理增益。
Fourier Preconditioning for Neural Feature Learning
Mutual information (MI)-inspired feature learning techniques are capable of generating low-dimensional embeddings that retain nonlinear dependence structures, but direct estimations of MI suffer from noisy probability distribution estimates in the low-data regime. The H-Score objective, computed from second-order statistics, provides a practical proxy metric for training feature extraction networks. We prove that H-Score is invariant to invertible transformations in the unrestricted functional setting, but becomes sensitive to input basis rotations under constrained approximation classes. Consequently, we study unitary preconditioning for H-Score networks and show that selecting an appropriate basis rotation reduces finite-width truncation error by concentrating predictive dependence into fewer dominant modes. We identify the fast Fourier transform (FFT) as an effective data-independent, low-cost preconditioner for approximately stationary processes, where spectral structure induces concentration of the cross-covariance singular value spectrum. We introduce training-free metrics based on spectral entropy and cumulative dependence energy to quantify basis suitability and predict downstream inference gains prior to network training. Experiments across eight multivariate datasets demonstrate that FFT preconditioning is particularly useful in resource-constrained regimes, achieving up to 50% normalized mean squared error (NMSE) reduction, while the proposed metrics correlate with observed performance gains and correctly identify cases where spectral preconditioning is detrimental.