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Concept

Inflection point

Related publications (24)

Photothermal spectroscopy on-chip sensor for the measurement of a PMMA film using a silicon nitride micro-ring resonator and an external cavity quantum cascade laser

Simone Iadanza

Laser-based mid-infrared (mid-IR) photothermal spectroscopy (PTS) represents a selective, fast, and sensitive analytical technique. Recent developments in laser design permits the coverage of wider spectral regions in combination with higher power, enablin ...

Walter De Gruyter Gmbh2024

Dynamical system approach to navigation around obstacles

Aude Billard, Aradhana Nayak

In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...

2024

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Mehmet Fatih Sahin

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

EPFL2023

Data-Driven Control and Optimization under Noisy and Uncertain Conditions

Baiwei Guo

Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...

EPFL2023

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

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

Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization

Volkan Cevher, Ali Kavis, Kimon Antonakopoulos, Leello Tadesse Dadi, Efstratios Panteleimon Skoulakis

We propose an adaptive variance-reduction method, called AdaSpider, for minimization of L-smooth, non-convex functions with a finite-sum structure. In essence, AdaSpider combines an AdaGrad-inspired [Duchi et al., 2011, McMahan & Streeter, 2010], but a fai ...

2022

From SU(2)5 to SU(2)3 Wess-Zumino-Witten transitions in a frustrated spin-52 chain

Frédéric Mila, Natalia Chepiga

We investigate the properties of a frustrated spin-5/2 chain with next-nearest-neighbor two- and three-site interactions, with two questions in mind: the nature of the transition into the dimerized phase induced by the three-site interaction, and the possi ...

2022

Development of a new method to determine the axial void velocity profile in BWRs from measurements of the in-core neutron noise

Mathieu Hursin

Determination of the local void fraction in BWRs from in-core neutron noise measurements requires the knowledge of the axial velocity of the void. The purpose of this paper is to revisit the problem of determining the axial void velocity profile from the t ...

PERGAMON-ELSEVIER SCIENCE LTD2021

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

Global bifurcation at isolated singular points of the Hadamard derivative

Charles Stuart

Consider F is an element of C(RxX,Y) such that F(lambda, 0) = 0 for all lambda is an element of R, where X and Y are Banach spaces. Bifurcation from the line Rx{0} of trivial solutions is investigated in cases where F(lambda, center dot ) need not be Frech ...

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

A Catalyst Framework for Minimax Optimization

Negar Kiyavash

We introduce a generic two-loop scheme for smooth minimax optimization with strongly-convex-concave objectives. Our approach applies the accelerated proximal point framework (or Catalyst) to the associated dual problem and takes full advantage of existing ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2020

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Volkan Cevher, Ahmet Alacaoglu, Fabian Ricardo Latorre Gomez, Armin Eftekhari, Mehmet Fatih Sahin

We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is closely related to t ...

2019

Detachment evolution on the TCV tokamak

Basil Duval, Holger Reimerdes, Marco Wischmeier, Benoît Labit, Christian Gabriel Theiler, Umar Sheikh, Cedric Kar-Wai Tsui, Wouter Vijvers, Kevin Henricus Annemarie Verhaegh

Divertor detachment in the TCV tokamak has been investigated through experiments and modelling. Density ramp experiments were carried out in ohmic heated L-mode pulses with the ion del B drift directed away from the primary X-point, similar to previous stu ...

Elsevier2017

Bifurcation at isolated singular points for a degenerate elliptic eigenvalue problem

Charles Stuart

We consider bifurcation from the line of trivial solutions for a nonlinear eigenvalue problem on a bounded open subset, Omega, of R-N with N >= 3, containing 0. The leading term is a degenerate elliptic operator of the form L(u) = del . A del u where A is ...

Pergamon-Elsevier Science Ltd2015

Low rank differential equations for Hamiltonian matrix nearness problems

Daniel Kressner

For a Hamiltonian matrix with purely imaginary eigenvalues, we aim to determine the nearest Hamiltonian matrix such that some or all eigenvalues leave the imaginary axis. Conversely, for a Hamiltonian matrix with all eigenvalues lying off the imaginary axi ...

Springer2015

The flux-coordinate independent approach applied to X-point geometries

A Flux-Coordinate Independent (FCI) approach for anisotropic systems, not based on magnetic flux coordinates, has been introduced in Hariri and Ottaviani [Comput. Phys. Commun. 184, 2419 (2013)]. In this paper, we show that the approach can tackle magnetic ...

Amer Inst Physics2014

Bifurcation at isolated singular points of the Hadamard derivative

Charles Stuart

For Banach spaces X and Y, we consider bifurcation from the line of trivial solutions for the equation F(lambda, u) = 0, where F : R x X -> Y with F(lambda, 0) = 0 for all lambda is an element of R. The focus is on the situation where F(lambda, center dot) ...

Royal Society of Edinburgh Scotland Foundation, Cambridge2014

Higgs-Dilaton cosmology: Universality versus criticality

Mikhail Chapochnikov, Javier Rubio

The Higgs-Dilaton model is able to produce an early inflationary expansion followed by a dark energy dominated era responsible for the late time acceleration of the Universe. At tree level, the model predicts a small tensor-to-scalar ratio (0.0021

American Physical Society2014

Related publications (24)

Photothermal spectroscopy on-chip sensor for the measurement of a PMMA film using a silicon nitride micro-ring resonator and an external cavity quantum cascade laser

Simone Iadanza

Walter De Gruyter Gmbh2024

Dynamical system approach to navigation around obstacles

Aude Billard, Aradhana Nayak

2024

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Mehmet Fatih Sahin

EPFL2023

Data-Driven Control and Optimization under Noisy and Uncertain Conditions

Baiwei Guo

EPFL2023

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

SPRINGER HEIDELBERG2022

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

Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization

Volkan Cevher, Ali Kavis, Kimon Antonakopoulos, Leello Tadesse Dadi, Efstratios Panteleimon Skoulakis

2022

From SU(2)5 to SU(2)3 Wess-Zumino-Witten transitions in a frustrated spin-52 chain

Frédéric Mila, Natalia Chepiga

2022

Development of a new method to determine the axial void velocity profile in BWRs from measurements of the in-core neutron noise

Mathieu Hursin

PERGAMON-ELSEVIER SCIENCE LTD2021

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