No importance ranking can be simultaneously faithful, stable, and complete under symmetry — at any level of a model, from input features to internal circuits — and we prove it in Lean 4. If you have ...

We establish a new theory which unifies various aspects of topological approaches for data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise ...

Metric geometry is a considerable extension of Riemannian geometry that, in recent decades, has proven very useful. A newer direction described in this article can moreover be viewed as an extension ...

Earlier this month the Mathematics Institute at Uppsala University hosted a conference called Categorification in Algebra and Topology, clearly a theme close to our collective heart. As yet there are ...

This blog entry is an excuse for continuing our discussion of cartesian closed categories (CCCs) and the λ-calculus in a slightly more organized way. Let’s focus on more or less “traditional” aspects ...