Publications associées à Extremum

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

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 ...

Piscataway2024

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 ...

2022

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, Arthur Jacot

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

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

The effect of smooth parametrizations on nonconvex optimization landscapes

Avoidance of Concave Obstacles Through Rotation of Nonlinear Dynamics

Beyond Local Optimality of Buffer and Splitter Insertion for AQFP Circuits

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

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

Lagrangian analysis of bio-inspired vortex ring formation

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

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

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

The effect of smooth parametrizations on nonconvex optimization landscapes

Avoidance of Concave Obstacles Through Rotation of Nonlinear Dynamics

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

Lagrangian analysis of bio-inspired vortex ring formation

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

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

Beyond Local Optimality of Buffer and Splitter Insertion for AQFP Circuits

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

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

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