Charles Arnal

I am a postdoctoral researcher at Meta, working on reasoning in Large Language Models.
Before that, I completed a first postdoc in Topological Data Analysis at the Laboratoire de Mathématiques d'Orsay, Paris-Saclay, and a PhD under the supervision of Ilia Itenberg, at the IMJ-PRG, Sorbonne Université.
My research interests include Machine Learning in general and Large Language Models in particular, as well as Topological Data Analysis, Real Algebraic Geometry, and any topic at the intersection of Geometry and Statistics.

Publications

Real algebraic geometry

Patchworking real algebraic hypersurfaces with asymptotically large Betti numbers, in the Journal of Topology, 2022.
Lefschetz section theorems for tropical hypersurfaces, with Arthur Renaudineau and Kristin Shaw, in the Annales Henri Lebesgue, 2021.
Complex conjugation and simplicial algebraic hypersurfaces, arXiv preprint arXiv:2105.12100, 2021.

Topological data analysis and computational geometry

Critical points of the distance function to a generic submanifold, with Vincent Divol and David Cohen-Steiner, arXiv preprint arXiv:2312.13147, 2024.
Wasserstein convergence of Čech persistence diagrams for samplings of submanifolds, with Vincent Divol and David Cohen-Steiner, in NeurIPS, 2024.
The distance function to a finite set is a topological Morse function, arxiv preprint arxiv:2407.15578, 2024.

Machine learning and statistics

Unveiling Simplicities of Attention: Adaptive Long-Context Head Identification, with Konstantin Donhauser, Mohammad Pezeshki, Vivien Cabannes, David Lopez-Paz and Kartik Ahuja, arXiv preprint arXiv:2502.09647, 2025.
The KRAB-Zinc Finger protein ZKSCAN3 represses enhancers via embedded retrotransposons, with Daniel Moore, Eugenia Wong, Stefan Walter Schoenfelder, Mikhail Spivakov, Simon Andrews and Maria A Christophorou, bioRxiv preprint, 2025.
Learning with Hidden Factorial Structures, with Clement Berenfeld, Simon Rosenberg and Vivien Cabannes, arXiv preprint arXiv:2411.01375, 2025.
Compositional Risk Minimization, with Divyat Mahajan, Mohammad Pezeshki, Ioannis Mitliagkas, Kartik Ahuja and Pascal Vincent, arXiv preprint arXiv:2410.06303, 2024.
Prompt Selection Matters: Enhancing Text Annotations for Social Sciences with Large Language Models, with Louis Abraham and Antoine Marie, arXiv preprint arxiv:2407.10645, 2024.
Iteration Head: A Mechanistic Study of Chain-of-Thought, with Vivien Cabannes, Wassim Bouaziz, Alice Yang, Francois Charton and Julia Kempe, in NeurIPS, 2024.
Mode Estimation with Partial Feedback, with Vivien Cabannes and Vianney Perchet, in COLT, 2024.
Touring sampling with pushforward maps, with Vivien Cabannes, in ICASSP, 2024 (Best Industry Paper award).
MAGDiff: Covariate Data Set Shift Detection via Activation Graphs of Deep Neural Networks, with Felix Hensel, Mathieu Carrière, Théo Lacombe, Hiroaki Kurihara, Yuichi Ike and Frédéric Chazal, in the Transactions on Machine Learning Research, 2024.
Convolution of a symmetric log-concave distribution and a symmetric bimodal distribution can have any number of modes, in the Statistics & Probability Letters, 2021.

PhD thesis

Patchworking, tropical homology, and Betti numbers of real algebraic hypersurfaces