用重采样稳定随机傅里叶特征训练，提升图像回归效果。
Adaptive Random Fourier Features Training Stabilized By Resampling With Applications in Image Regression
- 引入粒子滤波式重采样，降低对超参数敏感度
- 可省去马尔可夫测试，减少每轮计算开销
- 适用于函数回归与图像重建，支持自动频率采样
本文提出一种改进的自适应随机傅里叶特征（ARFF）训练算法，用于浅层神经网络。该方法基于粒子滤波式的重采样技术，稳定训练过程并降低对超参数的敏感性。当使用重采样时，可省略马尔可夫测试，减少一个超参数，并相比原ARFF方法降低每轮迭代的计算成本。通过大量数值实验，验证了该算法在函数回归任务中的有效性，既可作为独立方法使用，也可作为梯度优化前的预训练步骤（结合Adam优化器）。进一步将该算法应用于简单图像回归问题，实现对坐标基多层感知机中随机傅里叶特征（RFF）层参数的自动化频率采样。
原文摘要 · Abstract (English)
This paper presents an enhanced adaptive random Fourier features (ARFF) training algorithm for shallow neural networks, building upon the work introduced in "Adaptive Random Fourier Features with Metropolis Sampling", Kammonen et al., \emph{Foundations of Data Science}, 2(3):309--332, 2020. This improved method uses a particle filter-type resampling technique to stabilize the training process and reduce the sensitivity to parameter choices. The Metropolis test can also be omitted when resampling is used, reducing the number of hyperparameters by one and reducing the computational cost per iteration compared to the ARFF method. We present comprehensive numerical experiments demonstrating the efficacy of the proposed algorithm in function regression tasks as a stand-alone method and as a pretraining step before gradient-based optimization, using the Adam optimizer. Furthermore, we apply the proposed algorithm to a simple image regression problem, illustrating its utility in sampling frequencies for the random Fourier features (RFF) layer of coordinate-based multilayer perceptrons. In this context, we use the proposed algorithm to sample the parameters of the RFF layer in an automated manner.
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