A Phase-field Approximation of the Perimeter under a Connectedness Constraint. - Patrick W. Dondl; Matteo Novaga; Benedikt Wirth; Stephan Wojtowytsch (SIAM J. Math. Anal., 2019)

Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels. - Weinan E; Stephan Wojtowytsch (CoRR, 2020)

On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime. - Stephan Wojtowytsch (CoRR, 2020)

Representation formulas and pointwise properties for Barron functions. - Weinan E; Stephan Wojtowytsch (CoRR, 2020)

On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics. - Weinan E; Stephan Wojtowytsch (CoRR, 2020)

Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't. - Weinan E; Chao Ma 012; Stephan Wojtowytsch; Lei Wu (CoRR, 2020)

A priori estimates for classification problems using neural networks. - Weinan E; Stephan Wojtowytsch (CoRR, 2020)

Some observations on partial differential equations in Barron and multi-layer spaces. - Weinan E; Stephan Wojtowytsch (CoRR, 2020)

On the emergence of tetrahedral symmetry in the final and penultimate layers of neural network classifiers. - Weinan E; Stephan Wojtowytsch (CoRR, 2020)

Can Shallow Neural Networks Beat the Curse of Dimensionality? A Mean Field Training Perspective. - Stephan Wojtowytsch; Weinan E (IEEE Trans. Artif. Intell., 2020)

Some observations on high-dimensional partial differential equations with Barron data. - Weinan E; Stephan Wojtowytsch (MSML, 2021)

On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers. - Weinan E; Stephan Wojtowytsch (MSML, 2021)

On the Motion of Curved Dislocations in Three Dimensions: Simplified Linearized Elasticity. - Irene Fonseca; Janusz Ginster; Stephan Wojtowytsch (SIAM J. Math. Anal., 2021)

Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation. - Josiah Park; Stephan Wojtowytsch (CoRR, 2022)

Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality. - Stephan Wojtowytsch (CoRR, 2022)

Group Equivariant Fourier Neural Operators for Partial Differential Equations. - Jacob Helwig; Xuan Zhang; Cong Fu 003; Jerry Kurtin; Stephan Wojtowytsch; Shuiwang Ji (ICML, 2023)

Minimum norm interpolation by perceptra: Explicit regularization and implicit bias. - Jiyoung Park 004; Ian Pelakh; Stephan Wojtowytsch (NeurIPS, 2023)

Achieving acceleration despite very noisy gradients. - Kanan Gupta; Jonathan W. Siegel; Stephan Wojtowytsch (CoRR, 2023)

A qualitative difference between gradient flows of convex functions in finite- and infinite-dimensional Hilbert spaces. - Jonathan W. Siegel; Stephan Wojtowytsch (CoRR, 2023)

Stochastic Gradient Descent with Noise of Machine Learning Type Part I: Discrete Time Analysis. - Stephan Wojtowytsch (J. Nonlinear Sci., 2023)

SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations. - Xuan Zhang; Jacob Helwig; Yuchao Lin; Yaochen Xie; Cong Fu 003; Stephan Wojtowytsch; Shuiwang Ji (ICLR, 2024)

Nesterov acceleration despite very noisy gradients. - Kanan Gupta; Jonathan W. Siegel; Stephan Wojtowytsch (NeurIPS, 2024)

Optimal Bump Functions for Shallow ReLU networks: Weight Decay, Depth Separation, Curse of Dimensionality. - Stephan Wojtowytsch (J. Mach. Learn. Res., 2024)

Stochastic Gradient Descent with Noise of Machine Learning Type Part II: Continuous Time Analysis. - Stephan Wojtowytsch (J. Nonlinear Sci., 2024)

Nesterov acceleration in benignly non-convex landscapes. - Kanan Gupta; Stephan Wojtowytsch (ICLR, 2025)

Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs. - Oluwatosin Akande; Patrick W. Dondl; Kanan Gupta; Akwum Onwunta; Stephan Wojtowytsch (CoRR, 2025)

Convex-concave splitting for the Allen-Cahn equation leads to ϵ2-slow movement of interfaces. - Patrick W. Dondl; Akwum Onwunta; Ludwig Striet; Stephan Wojtowytsch (CoRR, 2025)