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.

翻译：我们通过推导首个精确表示，将任意有限参数分类模型（经梯度下降训练）表示为核机器，从而探索神经网络与核方法之间的等价性。我们将精确表示与著名的神经正切核（NTK）进行对比，并讨论了相对于NTK及其他非精确路径核公式的近似误差。我们通过实验证明，该核可以针对实际规模的网络计算至机器精度。利用这一精确核，我们证明了理论贡献能够为神经网络的预测行为提供有用见解，尤其是其泛化机制。