This work focuses on an application of Topological Data Analysis (TDA), to improve the reliability of Artificial Intelligence (AI) solutions used in critical systems.

Machine Learning models are increasingly used in industry, to perform various tasks ranging from monitoring manufacturing processes, to being integrated into products sold by a company. While AI can be useful in a lot of cases, it may become risky when used in critical systems, where failure modes imply serious consequences.

Critical systems, due to their complexity and sensitivity, impose high requirements in terms of reliability, safety, and robustness, which are often difficult to meet with classical approaches. In this context, TDA appears as a relevant tool, to extract properties linked to the global structure of the data and contribute to error detection and explainability of AI models.

For this presentation, we focus on the use of the Mapper algorithm, with the aim of identifying sources of errors in a Machine Learning model performing a task, arising from the data or from the model’s architecture. The main case study is an image classification task by a Convolutional Neural Network, applied to digits recognition, in a similar framework as [1].

In that case, Mapper can help retrieve information on the distribution of data points within the latent spaces of the model and highlight clusters that correspond to errors of prediction. Those clusters are expected to be linked with the topological attributes of Mapper, and to provide information on sources of errors.

This internship was completed within the cortAIx Labs entity of Thales.

References:

[1] Leo Carlsson, Mikael Vejdemo-Johansson, Gunnar Carlsson, and Pör Jönsson. Fibers of failure: Classifying errors in predictive processes.Algorithms, 13(6), 2020.

[2] Eduardo Paluzo-Hidalgo, Latent Space Topology Evolution in Multilayer Perceptrons, arXiv, 2025.

[3] Gardinazzi, Viswanathan, Panerai, Ansuini, Cazzaniga, Biagetti.Persistent Topological Features in Large Language Models, arXiv, 2025.

[4] Théo Lacombe, Yuichi Ike, Mathieu Carrière, Frédéric Chazal, Marc Glisse, Yuhei Umeda, Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs, 2021 International Joint Conference on Artificial Intelligence, 2021.