155 citations · 987 across the 104 of their papers we have counts for
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Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View
Tong Mao, Jinchao Xu
Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom. However, practical computation operates under finite precisi…
On the Dimension-Free Approximation of Deep Neural Networks for Symmetric Korobov Functions
Yulong Lu, Tong Mao, Jinchao Xu +1
Deep neural networks have been widely used as universal approximators for functions with inherent physical structures, including permutation symmetry. In this paper, we construct s…
Self-composing neural operators for high-frequency and multiscale PDE surrogates
Juncai He, Xinliang Liu, Jinchao Xu
Addressing the computational challenges of high-frequency and multiscale partial differential equations (PDEs), this work introduces a self-composing neural operator (SC-NO) framew…
Expressivity and Approximation Properties of Deep Neural Networks with ReLU Activation
Juncai He, Tong Mao, Jinchao Xu
In this paper, we investigate the expressivity and approximation properties of deep neural networks employing the ReLU activation function for . Although deep ReLU ne…
MgNO: Efficient Parameterization of Linear Operators via Multigrid
Juncai He, Xinliang Liu, Jinchao Xu
In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural o…
DualFL: A Duality-based Federated Learning Algorithm with Communication Acceleration in the General Convex Regime
Jongho Park, Jinchao Xu
We propose a new training algorithm, named DualFL (Dualized Federated Learning), for solving distributed optimization problems in federated learning. DualFL achieves communication…