Concept

Product (mathematics)

Related publications (46)

The first Grushin eigenvalue on cartesian product domains

Joachim Stubbe, Luigi Provenzano, Paolo Luzzini

In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...

WALTER DE GRUYTER GMBH2023

A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis

Annalisa Buffa, Espen Sande, Yannis Dirk Voet

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the li ...

2022

Matrix product states with backflow correlations

Giuseppe Carleo

By taking inspiration from the backflow transformation for correlated systems, we introduce a tensor network Ansatz which extends the well-established matrix product state representation of a quantum many-body wave function. This structure provides enough ...

AMER PHYSICAL SOC2022

Quadratic serendipity element shape functions on general planar polygons

Xiaodong Wei, Juan Cao

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

ELSEVIER SCIENCE SA2022

Neural tensor contractions and the expressive power of deep neural quantum states

Giuseppe Carleo

We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions and that use commonly adopt ...

AMER PHYSICAL SOC2022

Poly-NL: Linear Complexity Non-local Layers With 3rd Order Polynomials

Grigorios Chrysos, Filippos Kokkinos

Spatial self-attention layers, in the form of Non-Local blocks, introduce long-range dependencies in Convolutional Neural Networks by computing pairwise similarities among all possible positions. Such pairwise functions underpin the effectiveness of non-lo ...

IEEE2021

Further results on latent discourse models and word embeddings

Youssef Allouah

We discuss some properties of generative models for word embeddings. Namely, (Arora et al., 2016) proposed a latent discourse model implying the concentration of the partition function of the word vectors. This concentration phenomenon led to an asymptotic ...

MICROTOME PUBL2021

Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention

François Fleuret, Nikolaos Pappas, Angelos Katharopoulos, Apoorv Vyas

Transformers achieve remarkable performance in several tasks but due to their quadratic complexity, with respect to the input’s length, they are prohibitively slow for very long sequences. To address this limitation, we express the self-attention as a line ...

Idiap2020

Learning (from) the Electron Density: Transferability, Conformational and Chemical Diversity

Ksenia Briling, Alberto Fabrizio, Andrea Grisafi

Machine-learning in quantum chemistry is currently booming, with reported applications spanning all molecular properties from simple atomization energies to complex mathematical objects such as the many-body wavefunction. Due to its central role in density ...

2020

Forward-Backward Splitting for Optimal Transport Based Problems

Pascal Frossard, Guillermo Ortiz Jimenez, Mireille El Gheche, Hermina Petric Maretic, Effrosyni Simou

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regula ...

2020

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