We study the eigenvalue distributions of the Conjugate Kernel and Neural
Tangent Kernel associated to multi-layer feedforward neural networks. In an
asymptotic regime where network width is increasing linearly in sample size,
under random initialization of the weights, and for input samples satisfying a
notion of approximate pairwise orthogonality, we show that the eigenvalue
distributions of the CK and NTK converge to deterministic limits. The limit for
the CK is described by iterating the Marcenko-Pastur map across the hidden
layers. The limit for the NTK is equivalent to that of a linear combination of
the CK matrices across layers, and may be described by recursive fixed-point
equations that extend this Marcenko-Pastur map. We demonstrate the agreement of
these asymptotic predictions with the observed spectra for both synthetic and
CIFAR-10 training data, and we perform a small simulation to investigate the
evolutions of these spectra over training.

研究神经网络中的共轭内核和神经切向内核的特征值分布，证明在随机初始化权重、具有近似成对正交性的输入样本和网络宽度与样本大小成线性增长的渐近情况下，CK 和 NTK 的特征值分布会收敛到确定性极限，并描述了 CK 和 NTK 的极限情况，其中 CK 的极限情况是通过在隐藏层之间迭代 Marcenko-Pastur 映射描述的。