Stephan Wojtowytsch

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All published works

Action	Title	Year	Authors
+ PDF Chat	Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs	2024	Oluwatosin Akande Patrick Dondl Kanan Gupta Akwum Onwunta Stephan Wojtowytsch
+ PDF Chat	Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective	2024	Malhar Vaishampayan Stephan Wojtowytsch
+ PDF Chat	Nesterov acceleration in benignly non-convex landscapes	2024	Kanan Gupta Stephan Wojtowytsch
+ PDF Chat	A note on spatially inhomogeneous Cahn-Hilliard energies	2024	Stephan Wojtowytsch
+ PDF Chat	SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations	2024	Xuan Zhang Jacob Helwig Yuchao Lin Yaochen Xie Cong Fu Stephan Wojtowytsch Shuiwang Ji
+	A Qualitative Difference Between Gradient Flows of Convex Functions in Finite- and Infinite-Dimensional Hilbert Spaces	2024	Jonathan W. Siegel Stephan Wojtowytsch
+	Stochastic Gradient Descent with Noise of Machine Learning Type Part II: Continuous Time Analysis	2023	Stephan Wojtowytsch
+ PDF Chat	Stochastic Gradient Descent with Noise of Machine Learning Type Part I: Discrete Time Analysis	2023	Stephan Wojtowytsch
+	Achieving acceleration despite very noisy gradients	2023	Kanan Gupta Jonathan H. Siegel Stephan Wojtowytsch
+	Group Equivariant Fourier Neural Operators for Partial Differential Equations	2023	Jacob Helwig Xuan Zhang Cong Fu Jerry Kurtin Stephan Wojtowytsch Shuiwang Ji
+	A qualitative difference between gradient flows of convex functions in finite- and infinite-dimensional Hilbert spaces	2023	Jonathan W. Siegel Stephan Wojtowytsch
+	Minimum norm interpolation by perceptra: Explicit regularization and implicit bias	2023	Jiyoung Park Ian Pelakh Stephan Wojtowytsch
+	Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation	2022	Josiah Park Stephan Wojtowytsch
+	Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality	2022	Stephan Wojtowytsch
+ PDF Chat	Connected Coulomb columns: analysis and numerics	2021	Patrick Dondl Matteo Novaga Stephan Wojtowytsch Steve Wolff-Vorbeck
+ PDF Chat	Kolmogorov width decay and poor approximators in machine learning: shallow neural networks, random feature models and neural tangent kernels	2021	E Weinan Stephan Wojtowytsch
+ PDF Chat	Keeping it together: A phase-field version of path-connectedness and its implementation	2021	Patrick Dondl Stephan Wojtowytsch
+ PDF Chat	On the Motion of Curved Dislocations in Three Dimensions: Simplified Linearized Elasticity	2021	Irene Fonseca Janusz Ginster Stephan Wojtowytsch
+	Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysis	2021	Stephan Wojtowytsch
+	Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis	2021	Stephan Wojtowytsch
+	On the emergence of tetrahedral symmetry in the final and penultimate layers of neural network classifiers.	2020	E Weinan Stephan Wojtowytsch
+	Some observations on partial differential equations in Barron and multi-layer spaces.	2020	E Weinan Stephan Wojtowytsch
+ PDF Chat	Can Shallow Neural Networks Beat the Curse of Dimensionality? A Mean Field Training Perspective	2020	Stephan Wojtowytsch E Weinan
+	On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime	2020	Stephan Wojtowytsch
+	On the motion of curved dislocations in three dimensions: Simplified linearized elasticity	2020	Irene Fonseca Janusz Ginster Stephan Wojtowytsch
+ PDF Chat	Confined elasticae and the buckling of cylindrical shells	2020	Stephan Wojtowytsch
+	Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels	2020	E Weinan Stephan Wojtowytsch
+	Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective	2020	Stephan Wojtowytsch E Weinan
+	Representation formulas and pointwise properties for Barron functions	2020	E Weinan Stephan Wojtowytsch
+	On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics	2020	E Weinan Stephan Wojtowytsch
+	Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't	2020	E Weinan Chao Ma Stephan Wojtowytsch Lei Wu
+	A priori estimates for classification problems using neural networks	2020	E Weinan Stephan Wojtowytsch
+ PDF Chat	Towards a Mathematical Understanding of Neural Network-Based Machine Learning: What We Know and What We Don't	2020	Weinan E Weinan E Chao Ma Chao Lei Wu Stephan Wojtowytsch
+	Some observations on high-dimensional partial differential equations with Barron data	2020	E Weinan Stephan Wojtowytsch
+	On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime	2020	Stephan Wojtowytsch
+	On the motion of curved dislocations in three dimensions: Simplified linearized elasticity	2020	Irene Fonseca Janusz Ginster Stephan Wojtowytsch
+	On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers	2020	E Weinan Stephan Wojtowytsch
+ PDF Chat	On the boundary regularity of phase-fields for Willmore's energy	2018	Patrick Dondl Stephan Wojtowytsch
+	Confined elasticae and the buckling of cylindrical shells	2018	Stephan Wojtowytsch
+ PDF Chat	The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Plastic Slip	2018	Patrick Dondl Matthias Kurzke Stephan Wojtowytsch
+	Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields	2018	Patrick Dondl Matteo Novaga Benedikt Wirth Stephan Wojtowytsch
+	Confined elasticae and the buckling of cylindrical shells	2018	Stephan Wojtowytsch
+	Keeping it together: a phase field version of path-connectedness and its implementation	2018	Patrick Dondl Stephan Wojtowytsch
+	On the Boundary Regularity of Phase-Fields for Willmore's Energy	2017	Patrick Dondl Stephan Wojtowytsch
+ PDF Chat	Uniform regularity and convergence of phase-fields for Willmore’s energy	2017	Patrick Dondl Stephan Wojtowytsch
+	Phase-field models for thin elastic structures : Willmore's energy and topological constraints	2017	Stephan Wojtowytsch
+ PDF Chat	Helfrich’s energy and constrained minimisation	2017	Stephan Wojtowytsch
+	On the Boundary Regularity of Phase-Fields for Willmore's Energy	2017	Patrick Dondl Stephan Wojtowytsch
+ PDF Chat	Phase Field Models for Thin Elastic Structures with Topological Constraint	2016	Patrick Dondl Antoine Lemenant Stephan Wojtowytsch
+	Helfrich's Energy and Constrained Minimisation	2016	Stephan Wojtowytsch
+	Helfrich's Energy and Constrained Minimisation	2016	Stephan Wojtowytsch
+	Uniform Regularity and Convergence of Phase-Fields for Willmore's Energy	2015	Patrick Dondl Stephan Wojtowytsch
+	Uniform Regularity and Convergence of Phase-Fields for Willmore's Energy	2015	Patrick Dondl Stephan Wojtowytsch
+ PDF Chat	On the Alexandrov Topology of sub-Lorentzian Manifolds	2014	Irina Markina Stephan Wojtowytsch
+	On the Alexandrov Topology of sub-Lorentzian Manifolds	2013	Irina Markina Stephan Wojtowytsch

Common Coauthors

Coauthor	Papers Together
Patrick Dondl	13
E Weinan	12
Kanan Gupta	3
Irene Fonseca	3
Janusz Ginster	3
Shuiwang Ji	2
Jonathan W. Siegel	2
Cong Fu	2
Matteo Novaga	2
Irina Markina	2
Jacob Helwig	2
Chao Ma	1
Yuchao Lin	1
Lei Wu	1
Yaochen Xie	1
Chao Ma Chao	1
Weinan E Weinan E	1
Jonathan H. Siegel	1
Malhar Vaishampayan	1
Xuan Zhang	1
Ian Pelakh	1
Oluwatosin Akande	1
Steve Wolff-Vorbeck	1
Lei Wu	1
Matthias Kurzke	1
Akwum Onwunta	1
Benedikt Wirth	1
Josiah Park	1
Antoine Lemenant	1
Jerry Kurtin	1
Xuan Zhang	1
Jiyoung Park	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Phase Field Models for Thin Elastic Structures with Topological Constraint	2016	Patrick Dondl Antoine Lemenant Stephan Wojtowytsch	10
+	Barron Spaces and the Compositional Function Spaces for Neural Network Models.	2019	E Weinan Chao Ma Lei Wu	9
+ PDF Chat	A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics	2020	E Weinan Chao Ma Lei Wu	8
+ PDF Chat	<i>A priori</i> estimates of the population risk for two-layer neural networks	2019	E Weinan Chao Ma Lei Wu	8
+ PDF Chat	Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss	2020	Lénaïc Chizat Francis Bach	8
+ PDF Chat	Machine learning from a continuous viewpoint, I	2020	E Weinan Chao Ma Lei Wu	7
+	Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks	2019	Kaitong Hu Zhenjie Ren David Šiška Łukasz Szpruch	5
+ PDF Chat	On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport	2018	Lénaïc Chizat Francis Bach	5
+ PDF Chat	A mean field view of the landscape of two-layer neural networks	2018	Mei Song Andrea Montanari Phan-Minh Nguyen	5
+	Representation formulas and pointwise properties for Barron functions	2020	E Weinan Stephan Wojtowytsch	5
+ PDF Chat	Mean Field Analysis of Neural Networks: A Law of Large Numbers	2020	Justin Sirignano Konstantinos Spiliopoulos	5
+	Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels	2020	E Weinan Stephan Wojtowytsch	5
+	A rigorous framework for the mean field limit of multilayer neural networks	2023	Phan-Minh Nguyen Huy Tuan Pham	5
+	Functional Analysis, Sobolev Spaces and Partial Differential Equations	2010	Haı̈m Brezis	5
+	Measure Theory and Fine Properties of Functions	2018	Lawrence C. Evans Ronald F. Garzepy	5
+	On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics	2020	E Weinan Stephan Wojtowytsch	5
+	Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective	2020	Stephan Wojtowytsch E Weinan	5
+	Neural Tangent Kernel: Convergence and Generalization in Neural Networks	2018	Arthur Paul Jacot Franck Gabriel Clément Hongler	5
+	Gradient Descent Provably Optimizes Over-parameterized Neural Networks	2018	Simon S. Du Xiyu Zhai Barnabás Póczos Aarti Singh	4
+	Neural networks as Interacting Particle Systems: Asymptotic convexity of the Loss Landscape and Universal Scaling of the Approximation Error	2018	Grant M. Rotskoff Eric Vanden‐Eijnden	4
+	Gradient Descent Provably Optimizes Over-parameterized Neural Networks	2018	Simon S. Du Xiyu Zhai Barnabás Póczos Aarti Singh	4
+	Dynamics of Stochastic Gradient Algorithms	2015	Qianxiao Li Cheng Tai E Weinan	4
+ PDF Chat	Approximation of Length Minimization Problems Among Compact Connected Sets	2015	Matthieu Bonnivard Antoine Lemenant Filippo Santambrogio	4
+	On Exact Computation with an Infinitely Wide Neural Net	2019	Sanjeev Arora Simon S. Du Wei Hu Zhiyuan Li Ruslan Salakhutdinov Ruosong Wang	4
+ PDF Chat	Uniform approximation of functions with random bases	2008	Ali Rahimi Benjamin Recht	4
+ PDF Chat	On the rate of convergence in Wasserstein distance of the empirical measure	2014	Nicolas Fournier Arnaud Guillin	4
+	Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections.	2019	E Weinan Chao Ma Qingcan Wang Lei Wu	4
+	On a Modified Conjecture of De Giorgi	2006	Matthias Röger Reiner Schätzle	4
+ PDF Chat	Elliptic Partial Differential Equations of Second Order	2001	David Gilbarg Neil S. Trudinger	4
+ PDF Chat	Kolmogorov width decay and poor approximators in machine learning: shallow neural networks, random feature models and neural tangent kernels	2021	E Weinan Stephan Wojtowytsch	4
+	A singular perturbation problem with integral curvature bound	2007	Yuko Nagase Yoshihiro Tonegawa	3
+ PDF Chat	The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Plastic Slip	2018	Patrick Dondl Matthias Kurzke Stephan Wojtowytsch	3
+ PDF Chat	On the diffusion approximation of nonconvex stochastic gradient descent	2019	Wenqing Hu Chris Junchi Li Lei Li Jian‐Guo Liu	3
+	The loss landscape of overparameterized neural networks	2018	Yaim Cooper	3
+	Risk Bounds for High-dimensional Ridge Function Combinations Including Neural Networks	2016	Jason M. Klusowski Andrew R. Barron	3
+	Optimal Transport for Applied Mathematicians : Calculus of Variations, PDEs, and Modeling	2015	Filippo Santambrogio	3
+	Gradient Flows: In Metric Spaces and in the Space of Probability Measures	2005	Luigi Ambrosio Nicola Gigli Giuseppe Savaré	3
+	On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime	2020	Stephan Wojtowytsch	3
+	Uniform convergence of a singular perturbation problem	1995	Luis Caffarelli Antonio Cordóba	3
+	New surfaces of constant mean curvature	1993	Karsten Große-Brauckmann	3
+	The Variational Formulation of the Fokker--Planck Equation	1998	Richard W. Jordan David Kinderlehrer Félix Otto	3
+ PDF Chat	Phase-field approximations of the Willmore functional and flow	2014	Élie Bretin Simon Masnou Èdouard Oudet	3
+ PDF Chat	Confined Elastic Curves	2011	Patrick Dondl Luca Mugnai Matthias Röger	3
+	Trainability and Accuracy of Neural Networks: An Interacting Particle System Approach	2018	Grant M. Rotskoff Eric Vanden‐Eijnden	3
+	A gradient bound and a liouville theorem for nonlinear poisson equations	1985	Luciano Modica	3
+	Approximation of functions	2017	George G. Lorentz	3
+	A mean-field limit for certain deep neural networks	2019	Dyego Carlos Souza Anacleto de Araújo Roberto I. Oliveira Daniel Yukimura	3
+	Mean Field Limit of the Learning Dynamics of Multilayer Neural Networks	2019	Phan-Minh Nguyen	3
+	A Priori Estimates of the Population Risk for Residual Networks	2019	E Weinan Chao Ma Qingcan Wang	3
+ PDF Chat	Uniform regularity and convergence of phase-fields for Willmore’s energy	2017	Patrick Dondl Stephan Wojtowytsch	3