# Publications

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.

## Preprints

Achieving acceleration despite very noisy gradients

(with Kanan Gupta and Jonathan Siegel) 2023 ArXivOptimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality

2022 ArXiv

Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation

(with Josiah Park) 2022 ArXiv

Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis

2021 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

## Published and accepted articles

Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysis

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.