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cs.LG2025
Deep Neural Networks with General Activations: Super-Convergence in Sobolev Norms
Yahong Yang, Juncai He
This paper establishes a comprehensive approximation result for deep fully-connected neural networks with commonly-used and general activation functions in Sobolev spaces $W^{n,\in…
cs.LG2024
Data-induced multiscale losses and efficient multirate gradient descent schemes
Juncai He, Liangchen Liu, Yen-Hsi Richard Tsai
This paper investigates the impact of multiscale data on machine learning algorithms, particularly in the context of deep learning. A dataset is multiscale if its distribution show…
cs.LG2024
Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss
Yahong Yang, Juncai He
Constructing the architecture of a neural network is a challenging pursuit for the machine learning community, and the dilemma of whether to go deeper or wider remains a persistent…