PhD Candidate · FAU Erlangen-Nürnberg

Albert Alcalde

Hello! I work on the mathematics of machine learning, with a focus on the dynamics of deep Transformer models and self-attention mechanisms. I am also interested in data-driven modeling, system identification, and control of dynamical systems.

albert.alcalde@fau.de Google Scholar ORCID GitHub

About me

I am a PhD Candidate at the Chair for Dynamics, Control, Machine Learning and Numerics at FAU Erlangen-Nürnberg, supervised by Prof. Dr. Enrique Zuazua and Prof. Dr. Giovanni Fantuzzi.

Before starting my PhD in 2023, I received a bachelor's degree in Mathematics from Universitat Autònoma de Catalunya in 2022 and a master's degree in Advanced Mathematics and Mathematical Engineering from Universitat Politècnica de Catalunya in 2023.

Publications

  1. 2026

    Reachability and asymptotics of Gaussian Transformer dynamics

    Albert Alcalde, Zhengping Ji, Enrique Zuazua.

    Preprint arXiv
  2. 2026

    Quantifying concentration phenomena of mean-field Transformers in the low-temperature regime

    Albert Alcalde, Leon Bungert, Konstantin Riedl, Tim Roith.

    Preprint arXiv
  3. 2026

    Attention's forward pass and Frank-Wolfe

    Albert Alcalde, Borjan Geshkovski, Domènec Ruiz-Balet. Forty-third International Conference on Machine Learning (ICML).

    Conference paper OpenReview
  4. 2026

    Exact sequence interpolation with Transformers

    Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua. Mathematical Foundations of Machine Learning.

    Journal paper DOI
  5. 2026

    Time-delayed Transformers for data-driven modeling of low-dimensional dynamics

    Albert Alcalde, Markus Widhalm, Emre Yılmaz. Machine Learning: Science and Technology.

    Journal paper DOI
  6. 2026

    Data-driven discovery of polynomial ODEs with provably bounded solutions

    Albert Alcalde, Giovanni Fantuzzi.

    Preprint arXiv
  7. 2025

    Clustering in pure-attention hardmax Transformers and its role in sentiment analysis

    Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua. SIAM Journal on Mathematics of Data Science.

    Journal paper DOI

News

  1. Presented a talk at the XI Partial Differential Equations, Optimization, Numerics, and Machine Learning, in Benasque (Spain).

  2. Presented a talk at the Workshop on the Mathematics of Transformers, in Oxford (UK).

  3. Presented a talk at Seminari Informal de Matemàtiques de Barcelona (SIMBa), in Barcelona (Spain).

  4. Presented a talk at Applied Mathematics Winter School 2026, in Garmisch-Partenkirchen (Germany).

  5. Presented a talk at Oberseminar "Mathematik des Maschinellen Lernens und Angewandte Analysis", in Würzburg (Germany).

  6. Presented a talk at the Mathematics of Scientific Machine Learning and Digital Twins workshop, in Erice (Italy).

  7. Presented a talk at European Conference on Computational Optimization (ECCO25), in Klagenfurt (Austria).

  8. Attended the DESY Mathematics of Transformers Workshop, in Hamburg (Germany).

  9. Presented a talk at CIRM Workshop on Mathematical and Computational Foundations of Digital Twins, in Marseille (France).

  10. Delivered lectures on numerical examples at the EECI-IGSC 2025: Control and Machine Learning Summer School, in Dubrovnik (Croatia).

  11. Presented a talk at SIAM Conference on Applications of Dynamical Systems, in Denver (US).

  12. Attended the Machine Learning and PDEs Workshop, in Erlangen (Germany).

  13. Attended the Oberwolfach Seminar: Control and Machine Learning, in Oberwolfach (Germany).

  14. Presented a poster at SIAM Conference on Mathematics of Data Science, in Atlanta (US).

  15. Presented a poster at CIN-PDE 2024, in Shanghai (China).