Publications related to Dot product

Randomized low-rank approximation and its applications

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

EPFL2024

Lithium tantalate photonic integrated circuits for volume manufacturing

Tobias Kippenberg, Mikhail Churaev, Xinru Ji, Zihan Li, Alisa Davydova, Junyin Zhang, Yang Chen, Xi Wang, Kai Huang, Chen Yang

Electro-optical photonic integrated circuits (PICs) based on lithium niobate (LiNbO3) have demonstrated the vast capabilities of materials with a high Pockels coefficient1,2. They enable linear and high-speed modulators operating at complementary metal–oxi ...

2024

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

The unipotent mixing conjecture

Philippe Michel

We show that shifted pairs of discrete or continuous low-lying horocycles equidistribute in the product space of two modular curves. ...

Hebrew Univ Magnes Press2023

High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations

Rafael Vazquez Hernandez, Bernard Kapidani

We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms inv ...

2023

Overflow-free compute memories for edge AI acceleration

David Atienza Alonso, Giovanni Ansaloni, Alexandre Sébastien Julien Levisse, Marco Antonio Rios, Flavio Ponzina

Compute memories are memory arrays augmented with dedicated logic to support arithmetic. They support the efficient execution of data-centric computing patterns, such as those characterizing Artificial Intelligence (AI) algorithms. These architectures can ...

2023

Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Daniel Kressner, Ulf David Persson, Alice Cortinovis

This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic tr ...

SIAM PUBLICATIONS2022

Leveraging topology, geometry, and symmetries for efficient Machine Learning

Michaël Defferrard

When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...

EPFL2022

A Künneth theorem for configuration spaces

Kathryn Hess Bellwald

We construct a spectral sequence converging to the homology of the ordered configuration spaces of a product of parallelizable manifolds. To identify the second page of this spectral sequence, we introduce a version of the Boardman-Vogt tensor product for ...

2022

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 Publishing2021

Yapa: Accelerated Proximal Algorithm For Convex Composite Problems

Mireille El Gheche, Giovanni Chierchia

Proximal splitting methods are standard tools for nonsmooth optimization. While primal-dual methods have become very popular in the last decade for their flexibility, primal methods may still be preferred for two reasons: acceleration schemes are more effe ...

IEEE2021

Cyber-Physical LPG Debutanizer Distillation Columns: Machine-Learning-Based Soft Sensors for Product Quality Monitoring

Jinzhi Lu

Refineries execute a series of interlinked processes, where the product of one unit serves as the input to another process. Potential failures within these processes affect the quality of the end products, operational efficiency, and revenue of the entire ...

2021

Automated Design: A Journey Across Modelling, Optimization, and Education

Cyril Picard

Machine intelligence greatly impacts almost all domains of our societies. It is profoundly changing the field of mechanical engineering with new technical possibilities and processes. The education of future engineers also needs to adapt in terms of techni ...

EPFL2021

Virtual metrology as an approach for product quality estimation in Industry 4.0: a systematic review and integrative conceptual framework

Dimitrios Kyritsis, Gökan May, Foivos Psarommatis Giannakopoulos

Virtual metrology (VM) involves estimating a product's quality directly from production process data without physically measuring it. This enables the product quality of each unit of production to be monitored in real time, while preserving the process eff ...

TAYLOR & FRANCIS LTD2022

Laser-induced liquid micro-jets for drug delivery

Jan Krizek

Jet injection devices have been studied and developed for transdermal drug delivery to avoid the use of needles. Such contact-less devices provide several advantages such as better dose control, lateral and depth localisation, lower collateral damage than ...

EPFL2021

Unconventional time-bandwidth performance of resonant cavities with nonreciprocal coupling

Camille Sophie Brès, Davide Grassani, Ivan Cardea, Kosmas Tsakmakidis

The time-bandwidth limit is a mathematical tenet that affects all reciprocal resonators, stating that the product of the spectral bandwidth that can couple into a resonant system and its characteristic energy decay time is always equal to 1. Here, we devel ...

2021

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: N-body mock challenge for galaxy clustering measurements

Cheng Zhao

We develop a series of N-body data challenges, functional to the final analysis of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16) galaxy sample. The challenges are primarily based on high-fidelity catalogues constructed ...

OXFORD UNIV PRESS2021

Product of experts for robot learning from demonstration

Emmanuel Pignat

Adaptability and ease of programming are key features necessary for a wider spread of robotics in factories and everyday assistance. Learning from demonstration (LfD) is an approach to address this problem. It aims to develop algorithms and interfaces such ...

EPFL2021

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

2021