1 citations · 1 across the 5 of their papers we have counts for
7 papers
A mixed residual method for biharmonic equations in spectral Barron spaces
Mengjia Bai, Kuo Gai, Shuai Lu
We propose a mixed residual method (MIM) for numerically solving the biharmonic equation with nonhomogeneous clamped boundary conditions. By establishing the well-posedness of the…
Deep Residual Networks Learn the Geodesic Curve in the Wasserstein Space
Kuo Gai, Shihua Zhang
Recent studies revealed the mathematical connection between deep neural networks (DNNs) and dynamic systems. However, the specific dynamics that DNNs, especially deep residual netw…
Beyond Neural Collapse: Task-Intrinsic Geometry Governs Neural Representations in Modular Arithmetic
Hu Tan, Kuo Gai, Shihua Zhang
While neural collapse (NC) predicts that a -class-balanced classifier should organize terminal representations as a -dimensional simplex equiangular tight frame (ETF), mo…
Deciphering Two Training Clocks in Grokking via Deep Linear Network Theory with Conditional ReLU Reduction
Hu Tan, Kuo Gai, Shihua Zhang
Grokking suggests that fitting the training data and learning a simple underlying rule may occur on different time scales. We formalize this phenomenon by separating the fast decay…
Deciphering Shortcut Learning from an Evolutionary Game Theory Perspective
Xiayang Li, Kuo Gai, Shihua Zhang
Shortcut learning causes deep learning models to rely on non-essential features within the data. However, its formation in deep neural network training still lacks theoretical unde…
OTAD: An Optimal Transport-Induced Robust Model for Agnostic Adversarial Attack
Kuo Gai, Sicong Wang, Shihua Zhang
Deep neural networks (DNNs) are vulnerable to small adversarial perturbations of the inputs, posing a significant challenge to their reliability and robustness. Empirical methods s…