Presentation
The Tagada team proposes to work on the mathematical and foundational aspects of alignment, with the core objective of designing methods and algorithms with theoretical guaranties and toolboxes for geometric alignment in ML. While Tagada does not aim to compete with the massive computational scale of large industrial labs, this is precisely what motivates our focus on methodological innovation. By developing principled, geometry-aware and data-efficient approaches to alignment, we target problems where insight, structure, and theory matter more than brute-force computation. Our goal is to contribute original, reusable, and scientifically grounded methods that complement, rather than replicate, the resource-intensive strategies of big companies, and that ultimately benefit the broader ML community.
The main challenges that we address are: (i) formulating the notion of geometric alignment as a unified mathematical problem across spaces, models, or structured data; (ii) ensuring the robustness of alignments against perturbations and mismatched distributions; and (iii) designing algorithms that
are both mathematically sound and computationally efficient.
We develop the research program into three methodological axes.
Axis 1: Alignment for Learning on Structured Data
Data are often not only defined by their individual attributes: they also exhibit relationships that reflect global organization, whether through distances in a metric space, links in a graph, or more generally any structure that describes proximity or interactions between elements. Learning methods that leverage such relational information often aim to map (possibly heterogeneous) datasets into a latent space that captures their internal structure (for example, MDS seeks projections that best preserve distances, while contrastive approaches pull similar samples closer and push dissimilar ones apart).
Beyond traditional data alignment, relational alignment frameworks can handle data, either vectorial or structured inputs, but can also generalize to structured systems, such as models, by aligning the internal representations or components of a neural networks. In this context, we aim to study
three main research questions: (i) How can we efficiently quantify alignment between structured data? (ii) How can we develop more robust measures of alignment that work across different domains and types of representations? (iii) How can we increase alignment to improve the performance of learning tasks or allow for deeper model reuse?
One of the methodological building blocks of this axis of research is optimal transport (OT) which provides a way to match entire distributions, not just individual points, while preserving the global and topological structure of the data. We argue that OT will be a key component of a versatile alignment measure, ideal for robust and complex alignments, including those across different domains or between networks.
Axis 2: Geometric Approaches for Machine Learning
Machine and deep learning methodologies have primarily been developed for data lying in Euclidean space. Yet, we often deal with richly structured data that is inherently non-Euclidean and lies on manifolds. A manifold is a continuous space that locally resembles Euclidean space in the neighborhood
of every point. Though locally it is assumed to be a flat space, its global shape may exhibit curvature. A powerful method is to use a Riemannian manifold, with different flavors such as hyperbolic spaces (for hierarchical data), spherical spaces (for data living on a sphere), or semi-definite matrices (when
dealing with covariance matrices, for instance). Geometric Machine Learning approaches, which extend classical Euclidean algorithms to different spaces such as manifolds, have revolutionized the field, including the generalization of classical statistical theory and machine learning. In this axis, we aim to go beyond Euclidean learning, relying on alignment on manifolds.
Axis 3: Properties, Analysis and Algorithmic of Alignments
Geometric alignment in machine learning seeks to integrate the intrinsic structure of data into model design, enhancing interpretability, robustness, and statistical efficiency. By aligning latent spaces with meaningful geometric or semantic relations, such approaches foster transparent and reusable representations grounded in domain knowledge. A first line of research consists in analysing theoretically those potential impacts in machine learning settings. Realizing these benefits at scale also requires computationally efficient and differentiable algorithms. Our research aims to bridge this gap by developing scalable, regularized, and differentiable formulations of geometric alignment methods, enabling their seamless integration into modern learning pipelines.
Applications
While we do not restrict ourselves to a specific application, we will specifically target medical, environmental and natural sciences. Indeed, those domains often come with additional structural information or involve data that is inherently structured and/or heterogeneous.