42 citations · 42 across the 2 of their papers we have counts for
11 papers
Theory of the Frequency Principle for General Deep Neural Networks
Tao Luo, Zheng Ma, Zhi-Qin John Xu +1
Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Princip…
An overview of condensation phenomenon in deep learning
Zhi-Qin John Xu, Yaoyu Zhang, Zhangchen Zhou
In this paper, we provide an overview of a common phenomenon, condensation, observed during the nonlinear training of neural networks: During the nonlinear training of neural netwo…
Understanding the Language Model to Solve the Symbolic Multi-Step Reasoning Problem from the Perspective of Buffer Mechanism
Zhiwei Wang, Yunji Wang, Zhongwang Zhang +7
Large language models have consistently struggled with complex reasoning tasks, such as mathematical problem-solving. Investigating the internal reasoning mechanisms of these model…
Solving multiscale dynamical systems by deep learning
Junjie Yao, Yuxiao Yi, Liangkai Hang +5
Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of s…
Embedding Principle in Depth for the Loss Landscape Analysis of Deep Neural Networks
Zhiwei Bai, Tao Luo, Zhi-Qin John Xu +1
Understanding the relation between deep and shallow neural networks is extremely important for the theoretical study of deep learning. In this work, we discover an embedding princi…
Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization
Leyang Zhang, Yaoyu Zhang, Tao Luo
Under mild assumptions, we investigate the geometry of the loss landscape for two-layer neural networks in the vicinity of global minima. Utilizing novel techniques, we demonstrate…