Concept
Saddle point
Related publications (31)
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
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 ...
Berlin2024Augmented Lagrangian Methods for Provable and Scalable Machine Learning
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 ...
EPFL2023A Theory of Finite-Width Neural Networks: Generalization, Scaling Laws, and the Loss Landscape
Deep learning has achieved remarkable success in various challenging tasks such as generating images from natural language or engaging in lengthy conversations with humans.The success in practice stems from the ability to successfully train massive neural ...
EPFL2023Stochastic 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 which holds in a wide range of applications in machine learning and signal processing. This conditio ...
NeurIPS2022Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy
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 HEIDELBERG2022Preconditioners for robust optimal control problems under uncertainty
The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...
2022Learning to Represent and Reconstruct 3D Deformable Objects
Representing and reconstructing 3D deformable shapes are two tightly linked problems that have long been studied within the computer vision field. Deformable shapes are truly ubiquitous in the real world, whether be it specific object classes such as human ...
EPFL2022Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points
The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [3] of this work we established that agents cluster around a network centroid and pr ...
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021A first-order primal-dual method with adaptivity to local smoothness
Volkan Cevher, Maria-Luiza Vladarean
We consider the problem of finding a saddle point for the convex-concave objective , where is a convex function with locally Lipschitz gradient and is convex and possibly non-smooth. We propose an ...
2021