Our internal Research & Development Laboratory actively contributes to the scientific community with articles and reviews.

Using tools from category theory, we provide a framework where artificial neural networks, and their architectures, can be formally described. We first define the notion of machine in a general categorical context and show how simple machines can be combined into more complex ones. We explore finite-and infinite-depth machines, which generalize neural networks and neural […]

Meaningful low-dimensional representations of dynamical processes are essential to better understand the mechanisms underlying complex systems, from music composition to learning in both biological and artificial intelligence. We suggest describing time-varying systems by considering the evolution of their geometrical and topological properties in time, by using a method based on persistent homology. In the static […]

Persistence has proved to be a valuable tool to analyze real-world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space-valued homology functor, other combinatorial, based on arbitrary set-valued functors. To unify the study of topological and combinatorial persistence in a common categorical framework, we […]