How degenerate is the parametrization of neural networks with the ReLU activation function? - Dennis Elbrächter; Julius Berner; Philipp Grohs (NeurIPS, 2019)

Towards a regularity theory for ReLU networks - chain rule and global error estimates. - Julius Berner; Dennis Elbrächter; Philipp Grohs; Arnulf Jentzen (CoRR, 2019)

Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning. - Julius Berner; Markus Dablander; Philipp Grohs (NeurIPS, 2020)

Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations. - Julius Berner; Philipp Grohs; Arnulf Jentzen (SIAM J. Math. Data Sci., 2020)

The Modern Mathematics of Deep Learning. - Julius Berner; Philipp Grohs; Gitta Kutyniok; Philipp Petersen (CoRR, 2021)

Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning. - Lorenz Richter; Julius Berner (ICML, 2022)

Training ReLU networks to high uniform accuracy is intractable. - Julius Berner; Philipp Grohs; Felix Voigtländer (CoRR, 2022)

Learning ReLU networks to high uniform accuracy is intractable. - Julius Berner; Philipp Grohs; Felix Voigtländer (ICLR, 2023)

Mathematical Capabilities of ChatGPT. - Simon Frieder; Luca Pinchetti; Alexis Chevalier; Ryan-Rhys Griffiths; Tommaso Salvatori; Thomas Lukasiewicz; Philipp Petersen; Julius Berner (NeurIPS, 2023)

Large Language Models for Mathematicians. - Simon Frieder; Julius Berner; Philipp Petersen; Thomas Lukasiewicz (CoRR, 2023)

The IMO Small Challenge: Not-Too-Hard Olympiad Math Datasets for LLMs. - Simon Frieder; Mirek Olsák; Julius Berner; Thomas Lukasiewicz (Tiny Papers @ ICLR, 2024)

Improved sampling via learned diffusions. - Lorenz Richter; Julius Berner (ICLR, 2024)

DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training. - Zhongkai Hao; Chang Su; Songming Liu; Julius Berner; Chengyang Ying; Hang Su 006; Anima Anandkumar; Jian Song; Jun Zhu 001 (ICML, 2024)

Neural Operators with Localized Integral and Differential Kernels. - Miguel Liu-Schiaffini; Julius Berner; Boris Bonev; Thorsten Kurth; Kamyar Azizzadenesheli; Anima Anandkumar (ICML, 2024)

Solving Poisson Equations using Neural Walk-on-Spheres. - Hong Chul Nam; Julius Berner; Anima Anandkumar (ICML, 2024)

Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs. - Md. Ashiqur Rahman; Robert Joseph George; Mogab Elleithy; Daniel V. Leibovici; Zongyi Li; Boris Bonev; Colin White; Julius Berner; Raymond A. Yeh; Jean Kossaifi; Kamyar Azizzadenesheli; Animashree Anandkumar (NeurIPS, 2024)

Reduced-Order Neural Operators: Learning Lagrangian Dynamics on Highly Sparse Graphs. - Hrishikesh Viswanath; Yue Chang; Julius Berner; Peter Yichen Chen; Aniket Bera (CoRR, 2024)

Dynamical Measure Transport and Neural PDE Solvers for Sampling. - Jingtong Sun; Julius Berner; Lorenz Richter; Marius Zeinhofer; Johannes Müller; Kamyar Azizzadenesheli; Anima Anandkumar (CoRR, 2024)

Beyond Closure Models: Learning Chaotic-Systems via Physics-Informed Neural Operators. - Chuwei Wang; Julius Berner; Zongyi Li; Di Zhou; Jiayun Wang; Jane Bae; Anima Anandkumar (CoRR, 2024)

Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems. - Freya Shah; Taylor L. Patti; Julius Berner; Bahareh Tolooshams; Jean Kossaifi; Anima Anandkumar (CoRR, 2024)

A Library for Learning Neural Operators. - Jean Kossaifi; Nikola B. Kovachki; Zongyi Li; David Pitt; Miguel Liu-Schiaffini; Robert Joseph George; Boris Bonev; Kamyar Azizzadenesheli; Julius Berner; Anima Anandkumar (CoRR, 2024)

Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning. - Simon Frieder; Jonas Bayer; Katherine M. Collins; Julius Berner; Jacob Loader; András Juhász; Fabian Ruehle; Sean Welleck; Gabriel Poesia; Ryan-Rhys Griffiths; Adrian Weller; Anirudh Goyal; et al. (CoRR, 2024)

An optimal control perspective on diffusion-based generative modeling. - Julius Berner; Lorenz Richter; Karen Ullrich (Trans. Mach. Learn. Res., 2024)

Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing. - Bingliang Zhang; Wenda Chu; Julius Berner; Chenlin Meng; Anima Anandkumar; Yang Song 011 (CVPR, 2025)

Underdamped Diffusion Bridges with Applications to Sampling. - Denis Blessing; Julius Berner; Lorenz Richter; Gerhard Neumann (ICLR, 2025)

Sequential Controlled Langevin Diffusions. - Junhua Chen; Lorenz Richter; Julius Berner; Denis Blessing; Gerhard Neumann; Anima Anandkumar (ICLR, 2025)

Robust Representation Consistency Model via Contrastive Denoising. - Jiachen Lei; Julius Berner; Jiongxiao Wang; Zhongzhu Chen; Chaowei Xiao; Zhongjie Ba; Kui Ren 001; Jun Zhu 001; Anima Anandkumar (ICLR, 2025)

From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster training. - Julius Berner; Lorenz Richter; Marcin Sendera; Jarrid Rector-Brooks; Nikolay Malkin (CoRR, 2025)

Robust Representation Consistency Model via Contrastive Denoising. - Jiachen Lei; Julius Berner; Jiongxiao Wang; Zhongzhu Chen; Zhongjia Ba; Kui Ren 001; Jun Zhu 001; Anima Anandkumar (CoRR, 2025)

Enabling Automatic Differentiation with Mollified Graph Neural Operators. - Ryan Y. Lin; Julius Berner; Valentin Duruisseaux; David Pitt; Daniel V. Leibovici; Jean Kossaifi; Kamyar Azizzadenesheli; Anima Anandkumar (CoRR, 2025)

Guided Diffusion Sampling on Function Spaces with Applications to PDEs. - Jiachen Yao; Abbas Mammadov; Julius Berner; Gavin Kerrigan; Jong Chul Ye; Kamyar Azizzadenesheli; Anima Anandkumar (CoRR, 2025)

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning. - Julius Berner; Miguel Liu-Schiaffini; Jean Kossaifi; Valentin Duruisseaux; Boris Bonev; Kamyar Azizzadenesheli; Anima Anandkumar (CoRR, 2025)