CoDeFeL. Control for Deep and Federated Learning

Principal Investigator

Enrique Zuazua

Enrique Zuazua

Project info

  • Grant agreement Nº: 101096251-CoDeFeL
  • ERC Advanced Grant 2022. Control for Deep and Federated Learning (CoDeFeL)
  • Principal Investigator (PI): Prof. Enrique Zuazua
  • Host Institution: Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU, Germany) and DeustoCCM (Deusto University, Spain)
  • Duration: 5 years (2024 – 2029)

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Machine Learning (ML) is transforming Applied Mathematics, creating powerful new methodologies while raising fundamental questions about why learning algorithms work, how their dynamics can be understood and controlled, and how their complexity, robustness and computational cost can be quantified.

The ERC Advanced Grant CoDeFeL – Control for Deep and Federated Learning addresses these questions by bringing together Control Theory, dynamical systems, optimization and PDEs with modern ML. The central idea is to view learning algorithms not simply as black-box optimization procedures, but as dynamical systems that can be analysed, designed and controlled mathematically.

Four interconnected research directions shape the CoDeFeL research agenda:

  • Deep Learning architectures, studying neural networks, especially ResNets, as dynamical systems, using controllability, sparsity and turnpike theory to understand learning dynamics and design simpler, more efficient architectures.
  • Complexity, robustness and interpretability, investigating how data structure, network architecture and training dynamics are connected, developing mathematical tools to analyse complexity, sensitivity, robustness and explainability
  • Federated Learning, developing mathematically grounded methods for distributed and privacy-preserving learning, with particular attention to convergence, information leakage, robustness and heterogeneous data.
  • Data-aware modelling, combining data-driven learning with ODE/PDE models and control, developing hybrid modelling methodologies for complex real-world applications, including digital health.

In the long term, CoDeFeL aims to provide the mathematical foundations for making modern learning systems more trustworthy, predictable, efficient, robust, interpretable and privacy-aware, while at the same time expanding Control Theory towards new challenges arising in Artificial Intelligence.


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The CoDeFeL project (ERC-2022-ADG) has received funding from the European Union’s Horizon ERC Grants programme under grant agreement No. 101096251. The views and opinions expressed are solely those of the author(s) and do not necessarily reflect those of the European Research Council Executive Agency (ERCEA). Neither the European Union nor the granting authority can be held responsible for them.