Research map / Learning theory and algorithms / Kernels and regression theory
Minimax optimality of convolutional neural networks for infinite dimensional input-output problems and separation from kernel methods
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Theoretical analysis showing dilated convolutional neural networks achieve minimax optimal rates for infinite-dimensional input-output function estimation, and separate them from kernel methods.
Problem
Function estimation theory for deep learning with infinite-dimensional inputs and outputs (e.g., text-to-image), where prior work on dilated CNNs covered only infinite-dimensional inputs with one-dimensional outputs.
Approach
Extends minimax estimation analysis of dilated CNNs to infinite-dimensional input and output settings and shows a separation from kernel methods in this regime.
Key results
- Establishes minimax optimality of dilated convolutional neural networks for infinite-dimensional input-output problems (per title; abstract truncated).
- Shows separation between dilated CNNs and kernel methods in the infinite-dimensional input-output setting (per title).
Experimental setup
Baselines: kernel methods
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