PERSNET

Preview

The unifying vision of this project is to leverage the interacting fields of Geometrical and Topological Data Analysis and High-Dimensional Statistics to enhance the design, analysis, and monitoring of Deep Neural Network (DNN) architectures.

Gilles Blanchard, Institut de Mathématiques d’Orsay, Université Paris-Saclay

The PERSNET project wants to create new methods and enhancements for DNNs based on topology, geometry, and statistics, in particular in order to monitor deep architectures, regularize or compress them, and take into account their graph connectivity and invariances.

Key words : Geometry, Deep Learning, Transformers, Topological data
analysis, Statistiques, High dimension

Missions

Our researches

Develop fundamental mathematical tools (topological and geometric data analysis, statistics) towards deep learning

Develop and analyze multi-parameter TDA descriptors and methods for the
characterization, analysis and improvement of machine learning and deep learning

Use these tools to improve deep learning architectures for complex data, using geometric and topological descriptors.

Develop a toolbox of new efficient and well-founded mathematical tools to analyse, monitor and improve DNN models

Use these tools to analyze and monitor deep learning architectures themselves (purposes: efficiency, reliability, explainability, anomaly detection).

Extend theoretical understanding of modern deep learning architectures, based on tools from representation of networks in the path space and its geometry, and from high-dimensional statistics. The ambition is to leverage this improved understanding to enhance the learning capabilities of neural network and their efficiency (e.g. by compression).