We present experimental results highlighting two key differences resulting from the choice of training algorithm for two-layer neural networks. The spectral bias of neural networks is well known, while the spectral bias dependence on the choice of training algorithm is less studied. Our experiments demonstrate that an adaptive random Fourier features algorithm (ARFF) can yield a spectral bias closer to zero compared to the stochastic gradient descent optimizer (SGD). Additionally, we train two identically structured classifiers, employing SGD and ARFF, to the same accuracy levels and empirically assess their robustness against adversarial noise attacks.

中文翻译：

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比较两层神经网络的谱偏差和鲁棒性：SGD 与自适应随机傅里叶特征

我们提出的实验结果强调了两层神经网络训练算法选择所导致的两个关键差异。神经网络的谱偏差是众所周知的，但对训练算法选择的谱偏差依赖性的研究较少。我们的实验表明，与随机梯度下降优化器 (SGD) 相比，自适应随机傅里叶特征算法 (ARFF) 可以产生接近于零的谱偏差。此外，我们使用 SGD 和 ARFF 训练两个结构相同的分类器达到相同的准确度水平，并根据经验评估它们针对对抗性噪声攻击的鲁棒性。