Tagada aims to develop a mathematical and algorithmic theory of geometric alignment in artificial intelligence. We define alignment as the problem of establishing explicit correspondences between mathematical objects such as structured or multimodal data, probability distributions, latent spaces, manifolds, and neural network models. Such a problem arises frequently in modern machine learning as collection of open data, variety of acquisition protocols or zoos of pre-trained neural networks flourish and impose to establish correspondences so as to maximise performance, fairness or trustworthiness of the associated algorithmic procedures. Our ambition is to provide rigorous methods grounded in geometry, statistics, and optimization that enhance the robustness, transferability, and interpretability of machine learning models. At the end of the spectrum, the psycho-social notion of alignment with human values could be targeted as an important perspective, but the team’s primary focus is on the mathematical foundations of alignment. One key ingredient of Tagada is connecting our methodological, theoretical, and algorithmic results with real world applications. We hence target problems arising from the medical or natural sciences, and more generally in the thematic of AI for Science.
Research directions
The goal of Tagada is to develop a mathematical and algorithmic theory of alignment in AI systems.
We aim to formalize and provide tools for alignment at different levels:
- Structured, multimodal, and/or heterogeneous data.
- Representation spaces (latent spaces, manifolds, graphs, or tree spaces)
- Models (transfer, distillation, interoperability)
The ambition is to combine tools from optimal transport, differential geometry, probabilistic models, graph theory, and robust statistics with an algorithmic perspective to propose rigorous methods that enhance the learning performance, robustness, transferability, interpretability, and ethics of AI models. The mathematical foundations can connect to the broader question of AI alignment.
We develop the research program into three methodological axes.
- Alignment for Learning on Structured Data
- Geometric Approaches for Machine Learning
- Properties, Analysis and Algorithmic of Alignments
