Topology and Geometry for Trustworthy Machine Learning

The talk presents a new approach to trustworthy machine learning based on multi-scale topology and the interaction geometry of transformers, aimed at making models more reliable and interpretable.
Topology:

• Representation Topology Divergence (RTD) compares different embeddings of the same dataset.
• RTD-AE is an autoencoder that preserves the global structure and cluster geometry in latent space.
• Scalar Function Topology Divergence (SFTD) compares sublevel-set topology of scalar fields on shared domains (pixels, voxels, graph nodes), localizing discrepancies for supervision and diagnosis; it improves 3D reconstruction in microscopy and flags topological errors in segmentation.
• RTD-Lite scales comparisons to large graphs while retaining essential multi-scale connectivity signals.

Interaction geometry:
Signals from attention graphs and query–key alignment (QK-alignment) indicate when a model effectively "knows" the answer but fails to select it, improving interpretability and performance in multiple-choice QA. Topological features of attention correlate with artificial-text detection and linguistic acceptability. A topology-driven intrinsic dimension score serves as a model-agnostic signal for text provenance, with successful transfer to speech tasks. The result is a practical, interpretable, and efficient approach that provides diagnostic and training signals transferable across domains.