Publications related to Row and column vectors

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

Unlabeled Principal Component Analysis and Matrix Completion

Yunzhen Yao, Liangzu Peng

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

Microtome Publishing2024

How to Achieve Large-Area Ultra-Fast Operation of MoS 2 Monolayer Flash Memories?

Aleksandra Radenovic, Andras Kis, Mukesh Kumar Tripathi, Asmund Kjellegaard Ottesen, Yanfei Zhao, Guilherme Migliato Marega, Zhenyu Wang, Hyungoo Ji

Memory devices have returned to the spotlight due to increasing interest in using in-memory computing architectures to make data-driven algorithms more energy-efficient. One of the main advantages of this architecture is the efficient performance of vector ...

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

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

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

Alice Cortinovis

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building ...

EPFL2022

Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

Tommaso Vanzan

Iterative substructuring Domain Decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. It is less known that classical overlapping DD methods can also be formulated in substructured for ...

2022

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

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

Locally supported tangential vector, n-vector, and tensor fields

Christopher Brandt

We introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangenti ...

2020

ESSOP: Efficient and Scalable Stochastic Outer Product Architecture for Deep Learning

Irem Boybat Kara, Evangelos Eleftheriou, Abu Sebastian

Deep neural networks (DNNs) have surpassed human-level accuracy in a variety of cognitive tasks but at the cost of significant memory/time requirements in DNN training. This limits their deployment in energy and memory limited applications that require rea ...

IEEE2020

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b, x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m), and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2020

Learning of robust spectral graph dictionaries for distributed processing

Pascal Frossard, Ntorina Thanou

We consider the problem of distributed representation of signals in sensor networks, where sensors exchange quantized information with their neighbors. The signals of interest are assumed to have a sparse representation with spectral graph dictionaries. We ...

SPRINGEROPEN2018

Neural Tanget Kernel: Convergence and Generalization in Neural Networks

Clément Hongler, Franck Raymond Gabriel, Arthur Ulysse Jacot-Guillarmod

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit [12, 9], thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b; x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m) and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2018

Structure preserving model reduction of parametric Hamiltonian systems

Jan Sickmann Hesthaven, Babak Maboudi Afkham

While reduced-order models (ROMs) are popular for approximately solving large systems of differential equations, the stability of reduced models over long-time integration remains an open question. We present a greedy approach for ROM generation of paramet ...

2017

Simultaneous estimation of unwrapped phase and phase derivative from a closed fringe pattern

Pramod Rastogi, Rishikesh Dilip Kulkarni

We propose a new approach for the direct estimation of the unwrapped phase from a single closed fringe pattern. The fringe analysis is performed along a given row/column at a time by approximating the phase with a weighted linear combination of linearly in ...

2016

Closed fringe demodulation using phase decomposition by Fourier basis functions

Pramod Rastogi, Rishikesh Dilip Kulkarni

We report a new technique for the demodulation of a closed fringe pattern by representing the phase as a weighted linear combination of a certain number of linearly independent Fourier basis functions in a given row/column at a time. A state space model is ...

2016

Cross-Intersecting Families of Vectors

János Pach, Gábor Tardos

Given a sequence of positive integers , let denote the family of all sequences of positive integers such that for all . Two families of sequences (or vectors), , are said to be -cross-intersecting if no matter how we select and , there are at least distinc ...

Springer Japan Kk2015

Phase estimation from noisy phase fringe patterns using linearly independent basis functions

Pramod Rastogi, Rishikesh Dilip Kulkarni

A novel technique is proposed for obtaining unwrapped phase estimation from a highly noisy exponential phase field. In this technique, the interference phase is represented as a linear combination of linearly independent and pre-defined basis functions alo ...

Iop Publishing Ltd2015