Escuela de métodos matemáticos en machine learning

Del 3 al 5 de noviembre de 2025 se realizarán dos mini‑cursos introductorios en áreas de mucho desarrollo reciente en la interacción entre matemáticas y machine learning. Estos estarán a cargo de investigadores internacionales destacados que quieren fortalecer sus lazos científicos con el país. Requisitos previos para la escuela: Cursos básicos de cálculo en una y varias variables, probabilidad y estadı́stica y/o álgebra.

Cursos

Curso 1: Mathematics of Diffusion Models

• Orador: Joan Bruna (Courant Institute, New York University)
• Resumen: in this minicourse we will develop the mathematical framework underlying transport-based generative modeling, with special emphasis on score-based diffusion. We will first describe the main challenges of high-dimensional probabilistic modeling, with emphasis both on statistical and computational aspects. We will then focus on transport-based models, encompassing score-based diffusion and stochastic interpolants, and covering the main algorithmic principles and the key mathematical properties. In the last part of the course, we will describe how these tools can go beyond generative modeling, focusing on important applications such as posterior sampling and corrupted data.
• Fechas: 3 sesiones de 1hr 20mins -- 3,4,5 Noviembre

Curso 2: Algebra in machine learning theory

• Oradores: Ben Blum-Smith y Soledad Villar (Department of Applied Mathematics and Statistics, Johns Hopkins University)
• Resumen: There are challenges in machine learning theory for which tools from algebra are useful. Some of these concern symmetry. Learning problems often have built-in symmetry arising from arbitrary choices in how the data is represented. For example, the nodes in a graph are not naturally ordered, but need to be ordered to be represented by its adjacency matrix. For another, point clouds are typically represented by their coordinates with respect to an arbitrary choice of origin. In learning for the physical sciences, additional symmetries in the learning problem can result from the symmetries of physical law. The field of equivariant machine learning studies these learning problems. Tools from algebra---group theory, representation theory, and invariant theory---play a pivotal role. Another circle of challenges comes from the fact that learning problems are often posed most naturally on data of large and varying sizes. For example, applications of graph (or point cloud) learning often involve graphs (or point clouds) that have large, but not all the same, numbers of nodes (or points). Again, tools from algebra---such as representation stability---can help us understand what it means to learn functions on data of varying sizes. Furthermore, there are interesting connections between learning with symmetry and learning on any-sized data. In this minicourse, we will examine these challenges, and the algebraic tools used to explore them.
• Fechas: 3 sesiones de 1hr 20mins -- 3,4,5 Noviembre

Fecha y Lugar

Fechas: Lunes 3, Martes 4 y Miércoles 5 de noviembre de 2025
Horario: 13:00 – 17:00
Lugar: Facultad de Ciencias Económicas (FCEA) en Gonzalo Ramirez.
Salón: TBA

Agenda Provisional

• Lunes 3/11: Curso 1 (parte 1): 13:00 – 14:30 -- Curso 2 (parte 1): 15:00 – 16:30
• Martes 4/11: Curso 1 (parte 2): 13:00 – 14:30 -- Curso 2 (parte 2): 15:00 – 16:30
• Miércoles 5/11: Curso 1 (parte 3): 13:00 – 14:20 -- Curso 2 (parte 3): 14:30 – 16:00

Inscripción

Organizadores

Diego Armentano — (IESTA, FCEA)
Marcelo Fiori — (IMERL, FING)
Mauricio Velasco — (CMAT, FCIEN)