Patrícia Muñoz Ewald

I am a 5th year PhD candidate in Mathematics at UT Austin working with Thomas Chen. Nowadays, I mostly spend my time thinking about neural networks. You can find my work here.

I was previously at the University of São Paulo, where I got a bachelor's degree in physics, and later a master's degree in mathematics, studying gauge theory.

Here is my cv (last updated: July 2025).

News

• I have accepted a postdoctoral position at UCLA.
• I will be giving a talk at Boston College on September 17.
• I was accepted to the Rising Stars in Data Science workshop, to take place November 11-12 at Stanford.
• Our paper Interpretable global minima of deep ReLU neural networks on sequentially separable data has appeared online at JMLR. I will present a poster at NeurIPS 2025.
• I will be giving a talk at the SIAM TX-LA Sectional Meeting, on September 27.
• I will be attending the Harvard CMSA workshop on The Geometry of Machine Learning, September 15-18.

Contact info: You can generally find me in my office PMA 11.138 or email me at ewald at utexas.edu.

My current areas of interest are mathematical foundations of deep learning, and mathematical physics.

Papers

1. Gradient flow in parameter space is equivalent to linear interpolation in output space (with T. Chen). J. Geom. Phys., 222, Article No. 105765 (2026). Journal. arXiv.
2. Interpretable global minima of deep ReLU neural networks on sequentially separable data (with T. Chen). J. Mach. Learn. Res., 26 (173): 1-31 (2025). Journal, arXiv.
3. On non-approximability of zero loss global L^2 minimizers by gradient descent in deep learning (with T. Chen). Theor. Appl. Mech., 52 (1), 67-73 (2025). Journal, arXiv.

Preprints

4. Explicit neural network classifiers for non-separable data. Submitted, arXiv.
5. Architecture independent generalization bounds for overparametrized deep ReLU networks (with T. Chen, C.-K. Chien, A.G. Moore). Submitted, arXiv.
6. Geometric structure of deep learning networks and construction of global L^2 minimizers (with T. Chen). Submitted, arXiv.
7. Geometric structure of shallow neural networks and constructive L^2 cost minimization (with T. Chen). Submitted, arXiv.

Other

• Compactness in gauge theory (2021). My master's thesis on the Uhlenbeck gauge fixing and compactness theorems for connections on principal bundles, pdf.

Here are a few things I find cool, useful, or informative.

• Michael Atiyah came to USP in 2010 and gave an interview (text in Portuguese).

Latex

I enjoy cool software and programming, and for that reason I like to use some fancy tools with Latex. Here are some:

• I write on vim using vimtex and UltiSnips, inspired by this article.
• I've been using git and github to keep track of work on my manuscripts.
• Packages I find useful for long drafts: todonotes and showkeys.