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This paper establishes an exact correspondence between neural network training and Hamilton-Jacobi initial-value problems, unifying deep learning architectures through a deformation parameter.
This paper identifies neural network training as a search through Hamilton-Jacobi initial-value problems, showing that residual networks, transformers, and RNNs discretize the same class of viscous Hamilton-Jacobi equations. It derives quantitative consequences including minimax optimal generalization rates, adversarial robustness bounds, and a closed-form influence function.