Academic Research
Academic Research
I conduct Machine Learning research activities on the following topics:
Generative Machine Learning: Diffusion Probabilistic models, Schrödinger Bridges.
Neural Differential Equations: Recurrent and LSTM neural ODEs.
In parallel of the above activities, I maintain academic research activities situated at the intersection of several topics:
Mathematical Physics: Universal KZB equations, quantum algebra, integrable systems.
Numerical Analysis: Exponential Stochastic Runge-Kutta methods
Algebra & Combinatorics: Operad theory, modular tensor categories, Drinfeld associators.
Number theory: Multizeta values, modular forms, differential Galois theory.
Detecting and Defending Against Adversarial Attacks on Automatic Speech Recognition via Diffusion Models (with N. L Kühne, A. H. F. Kitchen, M. S. Jensen, M. S. L. Brøndt, Z.-H. Tan, Ch. Biscio). IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2025.
A Black-Box Watermarking Modulation for Semantic Segmentation Models (with M. Lansary, L. Mattioli, B. Addad, P.-M. Raffi, K. Kapusta) , 38th Conference on Neural Information Processing Systems (Neurips), 2nd Workshop on Regulatable Machine Learning 2024.
ML Model Coverage Assessment by Topological Data Analysis Exploration (withA. Fakhouri, F. Adjed, M. Royer), AI Trustworthiness and Risk Assessment for Challenged Contexts workshop (ATRACC). AAAI Fall Symposium 2024.
A Black-Box Watermarking Modulation for Object Detection Models (with M. Lansary, L. Mattioli, B. Addad, P.-M. Raffi, K. Kapusta), AI Trustworthiness and Risk Assessment for Challenged Contexts workshop (ATRACC). AAAI Fall Symposium 2024.
Leveraging Tropical Algebra to Assess Trustworthy AI (with J. Mattioli, L. Mattioli, K. Quitero, H. Sohier), AI Trustworthiness and Risk Assessment for Challenged Contexts workshop (ATRACC). AAAI Fall Symposium 2024.
AI Systems Trustworthiness Assessment: State of the Art, Workshop on Model-based System Engineering and AI (with A. Awawid, K. Amokrane-Ferka, H. Sohier, J. Mattioli, F. Adjed, S. Khalfaoui), 12th International Conference on Model-Based Software and Systems Engineering (Modelsward), 2024.
Meet DebiAI: A Versatile Open-Source Tool for Streamlined Data Analysis Visualization (with T. Mansion, R. Braud, F. Adjed, A. Amrani, S. Chaouche, F. Bekkar, Y. Randon, L. Cantat), and ML Model Evaluation, International Journal On Advances in Systems and Measurements, 2024.
Real-time weather monitoring and desnowification through image purification (with E. Py, E. Gherbi, N. Fernandez, H. Hajri), AI Ethics (Springer Nature) 4, 75–82, 2024.
A finite-sample generalization bound for stable LPV systems (with D. Racz, M. Petreczky, A. Benczur and D. Daroczy), preprint, 2024
SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models (with N. Fernandez, T. Tran, E. Gherbi, H. Hajri & N. Masmoudi), Proceedings of the 37th Conference on Neural Information Processing Systems (NeurIPS 2023). [60p.]
Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddings (with T. Defourneau, H. Hajri & M. Petreczky), Systems & Control Letters (2023). [10p.]
Noisy Learning for Neural ODEs Acts as a Robustness Locus Widening (with H. Hajri, L. Cantat & M. Petreczky), ICML 2022 (PODS).
Ellipsitomic Associators (with Damien Calaque), Mémoires de la Société Mathématique de France, 2023. [67p.]
On the Universal Ellipsitomic KZB Connection (with Damien Calaque), Selecta Mathematica vol. 26, n. 73 (2020). [50p.]
Surface Drinfeld Torsors I: Higher Genus Associators, Apr. 2020. [52p.]
A Moperadic Approach to Cyclotomic Associators (with Damien Calaque), Apr. 2020. [36p.]
A modular differential equation for ellipsitomic associators
Surface Drinfeld torsors II: orbital theory.
Parenthesized tangles and twists of associators.
Universal origami KZB connections.
Contributions to the theory of KZB associators, PhD thesis, Oct. 2018. [264p.]
(in French) Slides of my defense.
Operadicity of the universal KZ log-connection (rough version). [39p.]
KZB equations in genus zero and one , mini-course at Nagoya University, Japan, Jul. 2018.
Elements of Algebraic Topology (with Sinan Yalin, Daniela Egas-Santander, Marc Stephan), USFQ, Ecuador, Nov. 2016.
Introduction to Quantum Groups, mini-course at USFQ, Ecuador, Nov. 2015.
Introduction to Group Theory, Summer School, Quito, Ecuador, 2012.
(in Spanish) Lesson 1; Exercice Sheet 1
(in Spanish) Lesson 2; Exercice Sheet 2; Solutions 2
(in Spanish) Lesson 3; Exercice Sheet 3; Solutions 3
(in Spanish) Lesson 4; Exercice Sheet 4; Solutions 4