Seminario Topological Data Analysis

Día y hora: Martes 4 de junio a las 15:00.

Lugar: Sala 520, departamento de matemáticas, UAM.

Ponente: Rubén Ballester (Universitat de Barcelona).

Título: Topological Data Analysis for Deep Learning.

Resumen: Deep learning uses neural networks to approximate unknown functions and has achieved remarkable results across various disciplines due to the generalization capabilities of such networks. However, many challenges remain in both theory and practice of deep learning. For instance, predicting the generalization performance of neural networks from their parameters stays challenging. On the practical side, optimally incorporating the topology and geometry of data into neural networks is an open research direction. In this talk, we will first review the basics of neural networks, and then we will explore innovative approaches from topological data analysis. On the theoretical side, we will mainly explore a connection between persistent homology and the generalization capabilities of neural networks. On the applied side, we will examine strategies for integrating topological and geometrical properties of the input into neural networks through advanced regularization techniques and topologically enriched inputs.