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 ...

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 ...

We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison [Fuglede B, Kadison R (1952) Ann Math 55:520–530], and a generalization for appropriate groups of ...

Then K K is the category of substructures of a countable structure M M which is universal and homogeneous. Examples include the Rado graph as the Fraïssé limit of the category of finite graphs and ...

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 ...