Wojtowytsch, Stephan
- Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
2020/09/22 by E, Weinan, Ma, Chao, Wojtowytsch, Stephan +1 · 8 citations
#26B40 #35Q68 #41A30 #68T07 (primary) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)
- Representation formulas and pointwise properties for Barron functions
2020/06/10 by E, Weinan, Wojtowytsch, Stephan · 5 citations
#26B35 #26B40 #46E15 #68T07 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML)
- Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective
2020/05/21 by Stephan Wojtowytsch, E Weinan, Wojtowytsch, Stephan +1 · 6 citations
Computer Science · Physics and Astronomy · #49Q22 #68T07 #68W25 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications #Stochastic Gradient Optimization Techniques
- Some observations on high-dimensional partial differential equations with Barron data
2020/12/02 by E, Weinan, Wojtowytsch, Stephan · 5 citations
#35C15 #65M80 #68T07 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG)
- Group Equivariant Fourier Neural Operators for Partial Differential Equations
2023/06/09 by Helwig, Jacob, Zhang, Xuan, Fu, Cong +3 · 6 citations
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
- On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime
2020/05/27 by Wojtowytsch, Stephan · 3 citations
#35F20 #35Q68 #49Q22 #68T07 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML)
- On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers
2020/12/10 by E Weinan, E, Weinan, Stephan Wojtowytsch +1 · 2 citations
Computer Science · #Neural Networks and Applications
- Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis
2021/06/04 by Stephan Wojtowytsch, Wojtowytsch, Stephan · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #35K65 #60H30 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Model Reduction and Neural Networks #Neural Networks and Applications #Primary: 90C26 #Secondary: 68T07
- Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality
2022/09/02 by Stephan Wojtowytsch, Wojtowytsch, Stephan · 2 citations
Computer Science · #41A30 #65D40 #68T07 #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and ELM #Neural Networks and Applications #Stochastic Gradient Optimization Techniques
- 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
- Solving the Poisson Equation with Dirichlet data by shallow ReLUα-networks: A regularity and approximation perspective
2024/12/10 by Malhar Vaishampayan, Vaishampayan, Malhar, Stephan Wojtowytsch +1 · 2 citations
Neuroscience · Mathematics · Engineering · #Brain Tumor Detection and Classification #Tensor decomposition and applications #Traffic Prediction and Management Techniques
- Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels
2020/05/21 by E Weinan, Stephan Wojtowytsch, E, Weinan +1 · 3 citations
Computer Science · Engineering · #Neural Networks and Applications #Stochastic Gradient Optimization Techniques #Sparse and Compressive Sensing Techniques
- Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysis
2021/05/04 by Stephan Wojtowytsch, Wojtowytsch, Stephan · 1 citation
Computer Science · Mathematics · #90C15. Secondary: 68T07 #90C30 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Primary: 90C26 #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques
- SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations
2024/03/28 by Xuan Zhang, Zhang, Xuan, Jacob Helwig +11 · 2 citations
Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks
- Nesterov acceleration in benignly non-convex landscapes
2024/10/10 by Kanan Gupta, Stephan Wojtowytsch, Gupta, Kanan +1 · 2 citations
Mathematics · Physics and Astronomy · #Mathematical Biology Tumor Growth #Advanced Thermodynamics and Statistical Mechanics
- 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