Melanie Weber

Melanie Weber is an applied mathematician at Harvard whose research uses geometric structure in data to guide machine learning and optimization. She earned degrees in mathematics and physics at Leipzig and a PhD in applied mathematics at Princeton, then held research fellowships at Oxford and the Simons Institute. Her work includes Riemannian optimization, theory on symmetry-aware neural networks, and studies of neural feature geometry. She received a Sloan Research Fellowship in 2024 and an AI2050 Early Career Fellowship in 2025; as of October 2026, she leads Harvard’s Geometric Machine Learning Group.

Now at: Harvard University
Works: 81
Citations: 353
h-index: 10

Publication numbers from OpenAlex, as of 27 October 2026.

Timeline

2016

Mathematics and physics at Leipzig

She earns undergraduate degrees in mathematics and physics at the University of Leipzig in 2016.
2021

An applied mathematics PhD

She earns a PhD in Applied Mathematics at Princeton in 2021 under Charles Fefferman. Her research experience also includes visiting positions at MIT and the Max Planck Institute for Mathematics in the Sciences, and internships in research labs at Facebook, Google and Microsoft.
2021–2022

Oxford and Simons fellowships

From September 2021 to June 2022, she holds a Hooke Research Fellowship at Oxford’s Mathematical Institute. In 2021–2022, she is also a Nicolas Kurti Junior Research Fellow at Brasenose College. During Fall 2021, she is a Research Fellow at the Simons Institute in Berkeley for its Geometric Methods in Optimization and Sampling program.
July 2022

Riemannian Frank-Wolfe methods

In July 2022, she and Suvrit Sra publish the paper Riemannian Optimization via Frank-Wolfe Methods. They propose a Riemannian Frank-Wolfe method for constrained optimization on manifolds and analyze its convergence rates.
2024

Learning under symmetries

In 2024, she coauthors On the Hardness of Learning under Symmetries with Bobak T. Kiani, Thien Le, Hannah Lawrence and Stefanie Jegelka. The paper gives lower bounds for shallow graph neural networks, convolutional networks, invariant polynomials and frame-averaged networks.
2024

A Sloan Research Fellowship

The Alfred P. Sloan Foundation selects her for a Sloan Research Fellowship in Mathematics in 2024.
2025

An AI2050 fellowship

In 2025, Schmidt Sciences names her an AI2050 Early Career Fellow. The fellowship supports her work on geometry-informed models that combine geometric and general-purpose foundation models for resource-efficient AI tools in science.
2025

Neural feature geometry

In 2025, she coauthors Neural Feature Geometry Evolves as Discrete Ricci Flow with Moritz Hehl and Max von Renesse. The paper finds that neural-network transformations resemble a discrete Ricci flow and that nonlinear activations shape feature geometry.
As of October 2026

Harvard’s geometric machine learning group

At Harvard, she is an Assistant Professor of Applied Mathematics and of Computer Science and leads the Geometric Machine Learning Group. Her research uses geometric structure in data to design efficient machine-learning and optimization methods with provable guarantees. In 2026, the paper Neural Feature Geometry Evolves as Discrete Ricci Flow appears at ICML as a spotlight.

Career

NowHarvard UniversityLead, Geometric Machine Learning Group
NowHarvard UniversityAssistant Professor of Applied Mathematics and of Computer Science
2021–2022University of OxfordHooke Research Fellow
2021–2022University of OxfordNicolas Kurti Junior Research Fellow
2021University of California, BerkeleyResearch Fellow
MetaResearch intern
GoogleResearch intern
MicrosoftResearch intern