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Concept

Maximum and minimum

Related publications (29)

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Nicolas Boumal

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

Siam Publications2024

The effect of smooth parametrizations on nonconvex optimization landscapes

Nicolas Boumal

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

Springer Heidelberg2024

Avoidance of Concave Obstacles Through Rotation of Nonlinear Dynamics

Aude Billard, Lukas Huber

Controlling complex tasks in robotic systems, such as circular motion for cleaning or following curvy lines, can be dealt with using nonlinear vector fields. This article introduces a novel approach called the rotational obstacle avoidance method (ROAM) fo ...

Ieee-Inst Electrical Electronics Engineers Inc2024

Beyond Local Optimality of Buffer and Splitter Insertion for AQFP Circuits

Giovanni De Micheli, Heinz Riener, Siang-Yun Lee

Adiabatic quantum-flux parametron (AQFP) is an energy-efficient superconducting technology. Buffer and splitter (B/S) cells must be inserted to an AQFP circuit to meet the technology-imposed constraints on path balancing and fanout branching. These cells a ...

ACM2022

Level-set-based Shape Optimization on Soft Magnetic Composites with Isotropy Constraint

Yves Perriard, Adrien Jean-Michel Thabuis, Xiaotao Ren

Soft Magnetic Composites (SMCs) demonstrate excellent potentials for electromagnetic applications. The isotropy is one critical feature in designing the composite. This work presents a shape optimization algorithm for SMCs subject to isotropy and volume co ...

Institute of Electrical and Electronics Engineers2022

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function

Patrick Thiran, Negar Kiyavash, Saber Salehkaleybar

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with

1\le\alpha\le2

which holds in a wide range of applications in machine learning and signal processing. This conditio ...

NeurIPS2022

Lagrangian analysis of bio-inspired vortex ring formation

Karen Ann J Mulleners, Mrudhula Baskaran

Pulsatile jet propulsion is a highly energy-efficient swimming mode used by various species of aquatic animals that continues to inspire engineers of underwater vehicles. Here, we present a bio-inspired jet propulsor that combines the flexible hull of a je ...

2022

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

Linear Speedup In Saddle-Point Escape For Decentralized Non-Convex Optimization

Ali H. Sayed, Stefan Vlaski

Under appropriate cooperation protocols and parameter choices, fully decentralized solutions for stochastic optimization have been shown to match the performance of centralized solutions and result in linear speedup (in the number of agents) relative to no ...

IEEE2020

Second-order guarantees in centralized, federated and decentralized nonconvex optimization

Ali H. Sayed, Stefan Vlaski

Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in general, in the s ...

INT PRESS BOSTON, INC2020

Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval

Lenka Zdeborová, Florent Gérard Krzakala

Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem. Here we fo ...

Curran Associates, Inc.2020

Concentration phenomena for a fractional Choquard equation with magnetic field

Tomohiko Sano

We consider the following nonlinear fractional Choquard equation epsilon(2s) (-Delta)(A/epsilon)(s) u + V(x)u = epsilon(mu-N) (1/vertical bar x vertical bar(mu) * F vertical bar mu vertical bar(2))) f(vertical bar u vertical bar(2))u in R-N, where epsilon ...

2019

Adaptive damage retention mechanism enables healthier yeast population

Riccardo Dainese

During cytokinesis in budding yeast (Saccharomyces cerevisiae) damaged proteins are distributed asymmetrically between the daughter and the mother cell. Retention of damaged proteins is a crucial mechanism ensuring a healthy daughter cell with full replica ...

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD2019

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Ali H. Sayed, Stefan Vlaski

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In this work we establish that agents cluster around a network centroid in the mean-fourth sen ...

IEEE2019

Test and lower bound modeling of keyed shear connections in RC shear walls

Aurelio Muttoni, Jesper Harrild Sorensen

This paper presents an investigation into the ultimate behavior of a recently developed design for keyed shear connections. The influence of the key depth on the failure mode and ductility of the connection has been studied by push-off tests. The tests sho ...

Engineering Structures2018

Fréchet means in Wasserstein space : theory and algorithms

Yoav Zemel

This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces,

\mathcal W_2 ( \mathbb R^d )

. This question arises naturally from the problem of separating amplitude and phase variation i ...

EPFL2017

Criteria for the existence of a potential well

Charles Stuart

We consider a critical point u(0) of a functional f is an element of C-1 (H, R), where H is a real Hilbert space, and formulate criteria ensuring that u(0) lies in a potential well of f without supposing that f' is Frechet differentiable at u(0). The deriv ...

Pergamon-Elsevier Science Ltd2017

Inference for Generalized Linear Models via Alternating Directions and Bethe Free Energy Minimization

Ulugbek Kamilov

Generalized linear models, where a random vector x is observed through a noisy, possibly nonlinear, function of a linear transform z = A x, arise in a range of applications in nonlinear filtering and regression. Approximate message passing (AMP) methods, b ...

IEEE2017

Global Identification of Kinetic Parameters via the Extent-based Incremental Approach

Dominique Bonvin, Julien Léo Billeter, Diogo Filipe Mateus Rodrigues

The identification of reaction kinetics represents the main challenge in building models for reaction systems. The identification task can be performed via either simultaneous model identification (SMI) or incremental model identification (IMI), the latter ...

2017

Spatial Sound Localization via Multipath Euclidean Distance Matrix Recovery

Philip Neil Garner, Hervé Bourlard, Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

A novel localization approach is proposed in order to find the position of an individual source using recordings of a single microphone in a reverberant enclosure. The multipath propagation is modeled by multiple virtual microphones as images of the actual ...

Ieee-Inst Electrical Electronics Engineers Inc2015

Related publications (29)

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Nicolas Boumal

Siam Publications2024

The effect of smooth parametrizations on nonconvex optimization landscapes

Nicolas Boumal

Springer Heidelberg2024

Avoidance of Concave Obstacles Through Rotation of Nonlinear Dynamics

Aude Billard, Lukas Huber

Ieee-Inst Electrical Electronics Engineers Inc2024

Beyond Local Optimality of Buffer and Splitter Insertion for AQFP Circuits

Giovanni De Micheli, Heinz Riener, Siang-Yun Lee

ACM2022

Level-set-based Shape Optimization on Soft Magnetic Composites with Isotropy Constraint

Yves Perriard, Adrien Jean-Michel Thabuis, Xiaotao Ren

Institute of Electrical and Electronics Engineers2022

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function

Patrick Thiran, Negar Kiyavash, Saber Salehkaleybar

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with

1\le\alpha\le2

which holds in a wide range of applications in machine learning and signal processing. This conditio ...

NeurIPS2022

Lagrangian analysis of bio-inspired vortex ring formation

Karen Ann J Mulleners, Mrudhula Baskaran

2022

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

\mathcal W_2 ( \mathbb R^d )

. This question arises naturally from the problem of separating amplitude and phase variation i ...

EPFL2017