25 citations · 43 across the 9 of their papers we have counts for
9 papers
Singular Value Representation: A New Graph Perspective On Neural Networks
Dan Meller, Nicolas Berkouk
We introduce the Singular Value Representation (SVR), a new method to represent the internal state of neural networks using SVD factorization of the weights. This construction yiel…
One Diamond to Rule Them All: Old and new topics about zigzag, levelsets and extended persistence
Nicolas Berkouk, Luca Nyckees
Extended and zigzag persistence were introduced more than ten years ago, as generalizations of ordinary persistence. While overcoming certain limitations of ordinary persistence, t…
Persistence and the Sheaf-Function Correspondence
Nicolas Berkouk
The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold with the Grothendieck group of constructible sheaves on . When…
Projected distances for multi-parameter persistence modules
Nicolas Berkouk, Francois Petit
Relying on sheaf theory, we introduce the notions of projected barcodes and projected distances for multi-parameter persistence modules. Projected barcodes are defined as derived p…
Persformer: A Transformer Architecture for Topological Machine Learning
Raphael Reinauer, Matteo Caorsi, Nicolas Berkouk
One of the main challenges of Topological Data Analysis (TDA) is to extract features from persistent diagrams directly usable by machine learning algorithms. Indeed, persistence di…
Level-sets persistence and sheaf theory
Nicolas Berkouk, Grégory Ginot, Steve Oudot
In this paper we provide an explicit connection between level-sets persistence and derived sheaf theory over the real line. In particular we construct a functor from 2-parameter pe…