12 citations · 17 across the 7 of their papers we have counts for
10 papers
Neural Scaling Laws of Transformer Operator Network
Haoran Yan, Zhongjie Shi, Yuanzhe Xi +2
Transformers have emerged as powerful architectures for learning solution operators of physical systems. Empirically the prediction error has been observed to decrease when the dat…
Learning Theory of Transformers: Local-to-Global Approximation via Softmax Partition of Unity
Zhongjie Shi, Wenjing Liao
This paper investigates the learning theory of Transformer networks for regression tasks on the compact Euclidean domain and -dimensional compact Riemannian manifolds.…
Generic Frameworks for Distributed Functional Optimization and Learning over Time-Varying Networks
Zhan Yu, Zhongjie Shi, Deming Yuan +1
In this paper, we establish a distributed functional optimization (DFO) theory over time-varying networks. The vast majority of existing distributed optimization theories are devel…
High-Probability Convergence Theory for Distributed Composite Optimization with Sub-Weibull Noises
Zhan Yu, Zhongjie Shi, Deming Yuan
With the rapid development of distributed optimization (DO) theory, the distributed stochastic gradient methods (DSGMs) occupy an important position. Although the theory of differe…
Theory of Decentralized Robust Kernel-Based Learning
Zhan Yu, Zhongjie Shi, Ding-Xuan Zhou
We propose a new decentralized robust kernel-based learning algorithm within the framework of reproducing kernel Hilbert spaces (RKHSs) by utilizing a networked system that can be…
Nonlinear functional regression by functional deep neural network with kernel embedding
Zhongjie Shi, Jun Fan, Linhao Song +2
Recently, deep learning has been widely applied in functional data analysis (FDA) with notable empirical success. However, the infinite dimensionality of functional data necessitat…
Learning Theory of Distribution Regression with Neural Networks
Zhongjie Shi, Zhan Yu, Ding-Xuan Zhou
In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classi…
Distributed Gradient Descent for Functional Learning
Zhan Yu, Jun Fan, Zhongjie Shi +1
In recent years, different types of distributed and parallel learning schemes have received increasing attention for their strong advantages in handling large-scale data informatio…
Theory of Deep Convolutional Neural Networks III: Approximating Radial Functions
Tong Mao, Zhongjie Shi, Ding-Xuan Zhou
We consider a family of deep neural networks consisting of two groups of convolutional layers, a downsampling operator, and a fully connected layer. The network structure depends o…
Robust Kernel-based Distribution Regression
Zhan Yu, Daniel W. C. Ho, Ding-Xuan Zhou
Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution regression (DR) which involves two stag…