8 citations · 8 across the 4 of their papers we have counts for
6 papers
Coupled tensor models for probability mass function estimation: Part II, Uniqueness of the model
Philippe Flores, Konstantin Usevich, David Brie
In this paper, uniqueness properties of a coupled tensor model are studied. This new coupled tensor model is used in a new method called Partial Coupled Tensor Factorization of 3D…
Coupled tensor models for probability mass function estimation: Part I, Principles and algorithms
Philippe Flores, Konstantin Usevich, David Brie
In this article, a Probability Mass Function (PMF) estimation method which tames the curse of dimensionality is proposed. This method, called Partial Coupled Tensor Factorization o…
Low-Rank Tensor Decompositions for the Theory of Neural Networks
Ricardo Borsoi, Konstantin Usevich, Marianne Clausel
The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions…
Identifiability of Deep Polynomial Neural Networks
Konstantin Usevich, Ricardo Borsoi, Clara Dérand +1
Polynomial Neural Networks (PNNs) possess a rich algebraic and geometric structure. However, their identifiability -- a key property for ensuring interpretability -- remains poorly…
Personalized Coupled Tensor Decomposition for Multimodal Data Fusion: Uniqueness and Algorithms
Ricardo Augusto Borsoi, Konstantin Usevich, David Brie +1
Coupled tensor decompositions (CTDs) perform data fusion by linking factors from different datasets. Although many CTDs have been already proposed, current works do not address imp…
The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures
Marianne Clausel, Joscha Diehl, Raphael Mignot +3
We establish the well-definedness of the barycenter (in the sense of Buser and Karcher) for every integrable measure on the free nilpotent Lie group of step (over $\mathbb{R}^d…