My articles on deep learning are arranged by topic and connection in this mindmap. The brief describtions may miss some important details. For the full titles, links and co-authors, please see the bibliography below.
A qualitative difference between gradient flows of convex functions in finite- and infinite-dimensional Hilbert spaces
(with Jonathan Siegel) 2023 ArXiv
Achieving acceleration despite very noisy gradients
(with Kanan Gupta and Jonathan Siegel) 2023 ArXiv
Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation
(with Josiah Park) 2022 ArXiv
A priori estimates for classification problems using neural networks
(with Weinan E) 2020 ArXiv
On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime
2020 ArXiv
Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality
2023 ArXiv Journal
Minimum norm interpolation by perceptra: Explicit regularization and implicit bias
(with Jiyoung Park and Ian Pelakh) 2023 ArXiv Conference
Group Equivariant Fourier Neural Operators for Partial Differential Equations
(with Jacob Helwig, Xuan Zhang, Cong Fu, Jerry Kurtin and Shuiwang Ji) 2023 ArXiv Conference
Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysis
2021 Journal ArXiv
Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis
2021 Journal ArXiv
Keeping it together: a phase field version of path-connectedness and its implementation
(with P. Dondl), 2018 Journal ArXiv
Representation Formulas and Pointwise Properties for Barron Functions
(with Weinan E) 2020 Journal ArXiv
Connected Coulomb Columns: Analysis and Numerics
(with P. Dondl, M. Novaga and S. Wolff-Vorbeck), 2018 Journal ArXiv
On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers
(with Weinan E) 2020 Conference ArXiv
Some observations on partial differential equations in Barron and multi-layer spaces
(with Weinan E) 2020 Conference ArXiv
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
(with Weinan E, Chao Ma and Lei Wu) 2020 Journal ArXiv
On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics
(with Weinan E) 2020 Journal ArXiv
The motion of curved dislocations in three dimensions: Simplified linearized elasticity
(with I. Fonseca and J. Ginster), 2020 Journal ArXiv
Can shallow neural networks beat the curse of dimensionality? A mean field training perspective
(with Weinan E), 2020 Journal ArXiv
Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels
(with Weinan E), Res Math Sci, 2020 Journal ArXiv
Confined elasticae and the buckling of cylindrical shells
Adv Calc Var (2020) Journal ArXiv
Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields
(with P. Dondl, M. Novaga and B. Wirth), SIAM Journal on Mathematical Analysis (2019) 51:5 Journal ArXiv
The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Crystal Dislocations
(with P. Dondl and M. Kurzke), Arch Rational Mech Anal (2018) 232 Journal ArXiv
Phase Field Models for Thin Elastic Structures with Topological Constraint
(with P. Dondl and A. Lemenant), Arch Rational Mech Anal (2017) 223 Journal ArXiv
Uniform Regularity and Convergence of Phase Fields for Willmore's Energy
(with P. Dondl), Calc. Var. PDE (2017) 56 Journal ArXiv
On the Boundary Regularity of Phase-Fields for Willmore's Energy
(with P. Dondl), Proc A Royal Soc of Edinburgh (2017) 149:4 Journal ArXiv
Helfrich's Energy and Constrained Minimisation
Comm in Math Sci (2017) 15:8 Journal ArXiv
On the Alexandrov Topology of Sub-Lorentzian Manifolds
(with I. Markina), Geometric Control Theory and Sub-Riemannian Geometry, Springer INdAM Series (2014) Book ArXiv
You can also find my publications on Orcid, Google Scholar and ArXiv or in my CV. Some publications are also available on cvgmt or DeepAI respectively.