Zobrazeno 1 - 10
of 26
pro vyhledávání: '"Berkouk, Nicolas"'
Autor:
Meller, Dan, Berkouk, Nicolas
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 yields a new weighted graph connecting what we call spectral neurons, that
Externí odkaz:
http://arxiv.org/abs/2302.08183
Autor:
Berkouk, Nicolas, Nyckees, Luca
Extended and zigzag persistence were introduced more than ten years ago, as generalizations of ordinary persistence. While overcoming certain limitations of ordinary persistence, they both enjoy nice computational properties, which make them an inter
Externí odkaz:
http://arxiv.org/abs/2210.00916
Autor:
Berkouk, Nicolas
The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold $M$ with the Grothendieck group of constructible sheaves on $M$. When $M$ is a finite dimensional real vector space, Kashiwara-Schapira have
Externí odkaz:
http://arxiv.org/abs/2207.06335
Autor:
Berkouk, Nicolas, Petit, Francois
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 pushforward of persistence modules onto $\mathbb{R}$. Projected distanc
Externí odkaz:
http://arxiv.org/abs/2206.08818
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 diagrams are intrinsically (multi-)sets of points in $\mathbb{R}^2$ and
Externí odkaz:
http://arxiv.org/abs/2112.15210
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 persistence modules to sheaves over $\mathbb{R}$, as well as a functor i
Externí odkaz:
http://arxiv.org/abs/1907.09759
Autor:
Berkouk, Nicolas, Petit, Francois
Publikováno v:
Algebr. Geom. Topol. 21 (2021) 247-277
We provide a definition of ephemeral multi-persistent modules and prove that the quotient of persistent modules by the ephemeral ones is equivalent to the category of $\gamma$-sheaves. In the case of one-dimensional persistence, our definition agrees
Externí odkaz:
http://arxiv.org/abs/1902.09933
Autor:
Berkouk, Nicolas
The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous difficulties
Externí odkaz:
http://arxiv.org/abs/1901.09824
Autor:
Berkouk, Nicolas, Ginot, Grégory
Persistent homology has been recently studied with the tools of sheaf theory in the derived setting by Kashiwara and Schapira, after J. Curry has made the first link between persistent homology and sheaves. We prove the isometry theorem in this deriv
Externí odkaz:
http://arxiv.org/abs/1805.09694
Autor:
Berkouk, Nicolas, Ginot, Grégory
Publikováno v:
In Advances in Mathematics 22 January 2022 394
