Siegel, Jonathan W.

1. On the Activation Function Dependence of the Spectral Bias of Neural Networks
   2022/08/09 by Qingguo Hong, Hong, Qingguo, Jonathan W. Siegel +5 · 9 citations
   Computer Science · #Neural Networks and Applications #Machine Learning and ELM #Stochastic Gradient Optimization Techniques
2. Characterization of the Variation Spaces Corresponding to Shallow Neural Networks
   2021/06/28 by Siegel, Jonathan W., Xu, Jinchao · 7 citations
   #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
3. High-Order Approximation Rates for Shallow Neural Networks with Cosine and ReLU^k Activation Functions
   2020/12/14 by Siegel, Jonathan W., Xu, Jinchao · 6 citations
   #41A25 #FOS: Mathematics #Numerical Analysis (math.NA)
4. Accelerated First-Order Methods: Differential Equations and Lyapunov Functions
   2019/03/13 by Siegel, Jonathan W. · 3 citations
   #65K10 #90C06 #90C25 #FOS: Mathematics #Optimization and Control (math.OC)
5. Greedy Training Algorithms for Neural Networks and Applications to PDEs
   2021/07/09 by Jonathan W. Siegel, Siegel, Jonathan W., Qingguo Hong +7 · 3 citations
   Engineering · Physics and Astronomy · #65H20 #65N22 #65N30 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
6. Equivariant Frames and the Impossibility of Continuous Canonicalization
   2024/02/25 by Nadav Dym, Dym, Nadav, Hannah Lawrence +3 · 5 citations
   Engineering · #Advanced Numerical Analysis Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG)
7. Convergence and error control of consistent PINNs for elliptic PDEs
   2024/06/13 by Andrea Bonito, Bonito, Andrea, Ronald DeVore +5 · 4 citations
   Mathematics · Physics and Astronomy · Engineering · #Numerical methods for differential equations #Model Reduction and Neural Networks #Advanced Numerical Methods in Computational Mathematics
8. Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks
   2023/07/28 by Siegel, Jonathan W. · 2 citations
   #41A25 #41A46 #52A21 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)
9. A qualitative difference between gradient flows of convex functions in finite- and infinite-dimensional Hilbert spaces
   2023/10/26 by Jonathan W. Siegel, Siegel, Jonathan W., Stephan Wojtowytsch +1 · 2 citations
   Mathematics · Medicine · Computer Science · #Nonlinear Partial Differential Equations #Bone and Joint Diseases #Optimization and Variational Analysis
10. Nesterov acceleration despite very noisy gradients
    2023/02/10 by Kanan Gupta, Gupta, Kanan, Stephan Wojtowytsch +2 · 1 citation
    Computer Science · Engineering · #Stochastic Gradient Optimization Techniques #Sparse and Compressive Sensing Techniques #Domain Adaptation and Few-Shot Learning
11. Optimal Convergence Rates for the Orthogonal Greedy Algorithm
    2021/06/28 by Siegel, Jonathan W., Xu, Jinchao · 1 citation
    #41A25 #41A46 #46N30 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Statistics Theory (math.ST)
12. Optimal Recovery Meets Minimax Estimation
    2025/02/24 by DeVore, Ronald, Nowak, Robert D., Parhi, Rahul +2 · 1 citation
    #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Statistics Theory (math.ST)