We explore the equivalence between neural networks and kernel methods by
deriving the first exact representation of any finite-size parametric
classification model trained with gradient descent as a kernel machine. We
compare our exact representation to the well-known Neural Tangent Kernel (NTK)
and discuss approximation error relative to the NTK and other non-exact path
kernel formulations. We experimentally demonstrate that the kernel can be
computed for realistic networks up to machine precision. We use this exact
kernel to show that our theoretical contribution can provide useful insights
into the predictions made by neural networks, particularly the way in which
they generalize.

我们通过从梯度下降训练的任何有限大小参数化分类模型中推导出的首个完全表示，探索了神经网络和核方法之间的等价性，并将我们的精确表示与著名的神经切向核 (NTK) 进行比较，并讨论相对于 NTK 和其他非精确路径核公式的近似误差。我们通过实验证明，该核能够以机器精度计算实现，并利用该精确核展示我们的理论贡献能够为神经网络所作的预测提供有用的洞察，特别是它们的泛化方式。