Critical Point

Critical points, representing extrema or saddle points in mathematical functions, are central to optimization problems across diverse scientific fields. Current research focuses on understanding the behavior of critical points in complex systems, including neural networks (e.g., convolutional recurrent networks, weakly convex regularized networks) and physical models (e.g., site percolation). This research aims to improve the efficiency and convergence of optimization algorithms, enhance the accuracy of data analysis techniques (like gait-based re-identification), and provide deeper insights into the dynamics of complex systems near phase transitions. The findings have implications for various applications, from improving machine learning model training to advancing scientific understanding of phenomena exhibiting critical behavior.

Papers

August 26, 2024

Symmetry & Critical Points
Yossi Arjevani
Cyclic Symmetry Symmetry Breaking Nonconvex Function Invariant Function Critical Point

May 22, 2024

On the dynamics of convolutional recurrent neural networks near their critical point
Aditi Chandra, Marcelo O. Magnasco
Real World Convolution Kernel Convolutional Recurrent Neural Network Smooth Activation Function Critical Point Compressive Memory

February 1, 2024

Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation
Zakhar Shumaylov, Jeremy Budd, Subhadip Mukherjee, Carola-Bibiane Schönlieb
Inverse Problem Early Stage Convergence Regularization Model Primal Dual Convex Regularization Variational Regularization Convex Neural Network Critical Point Convergent Regularization

December 29, 2023

A Large-Scale Re-identification Analysis in Sporting Scenarios: the Betrayal of Reaching a Critical Point
David Freire-Obregón, Javier Lorenzo-Navarro, Oliverio J. Santana, Daniel Hernández-Sosa, Modesto Castrillón-Santana
Gait Recognition Gait Representation Decouple Re Identification Player Re Identification Critical Point Betrayal Detection

November 20, 2023

Particle density and critical point for studying site percolation by finite size scaling
Dian Xu, Shanshan Wang, Feng Gao, Wei Li, Jianmin Shen
Unsupervised Learning Phase Transition Particle Density Critical Point Percolation Threshold Finite Size

July 18, 2023

Promoting Exploration in Memory-Augmented Adam using Critical Momenta
Pranshu Malviya, Gonçalo Mordido, Aristide Baratin, Reza Babanezhad Harikandeh, Jerry Huang, Simon Lacoste-Julien, Razvan Pascanu, Sarath Chandar
Gradient Based Flat Minimum Superior Optimizer Memory Augmentation Exploration Performance Memory Augmented Critical Point

June 13, 2023

Symmetry & Critical Points for Symmetric Tensor Decomposition Problems
Yossi Arjevani, Gal Vinograd
Hessian Matrix Nonconvex Optimization Cyclic Symmetry Local Optimization Critical Point

April 12, 2023

Function Space and Critical Points of Linear Convolutional Networks
Kathlén Kohn, Guido Montúfar, Vahid Shahverdi, Matthew Trager
Convolutional Neural Network Deep Linear Dense Network Function Space Linear Network Sparse Factorization Critical Point

March 6, 2023

Critical Points and Convergence Analysis of Generative Deep Linear Networks Trained with Bures-Wasserstein Loss
Pierre Bréchet, Katerina Papagiannouli, Jing An, Guido Montúfar
Gradient Descent Matrix Factorization Gradient Flow Convergence Analysis Low Rank Matrix Deep Generative Critical Point

July 13, 2022

Visualizing Confidence Intervals for Critical Point Probabilities in 2D Scalar Field Ensembles
Dominik Vietinghoff, Michael Böttinger, Gerik Scheuermann, Christian Heine
Data Uncertainty Topological Analysis Uncertainty Visualization Critical Point Simulation Ensemble

Critical Point

Papers

Symmetry & Critical Points

On the dynamics of convolutional recurrent neural networks near their critical point

Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation

A Large-Scale Re-identification Analysis in Sporting Scenarios: the Betrayal of Reaching a Critical Point

Particle density and critical point for studying site percolation by finite size scaling

Promoting Exploration in Memory-Augmented Adam using Critical Momenta

Symmetry & Critical Points for Symmetric Tensor Decomposition Problems

Function Space and Critical Points of Linear Convolutional Networks

Critical Points and Convergence Analysis of Generative Deep Linear Networks Trained with Bures-Wasserstein Loss

Visualizing Confidence Intervals for Critical Point Probabilities in 2D Scalar Field Ensembles