Watch a Harvard CMSA conference talk exploring high-dimensional optimization in statistics and machine learning, focusing on spherical spin glasses. Delve into Mark Sellke's analysis of non-convex optimization problems with random objectives, examining how "stable" optimization algorithms encounter specific thresholds related to geometric landscape properties. Learn about the efficient attainment of algorithmic threshold values through Langevin dynamics and Subag's second-order ascent method. Explore applications to various models including random constraint satisfaction problems at high clause density, tensor PCA, maximum likelihood estimators, and random cubic polynomials. Discover insights into overlap gap properties, algorithm stability, combinatorial optimization, neural network memorization, and complex energy functions across multiple domains including random graphs, multispecies spin glasses, and binary perceptron models.
Algorithmic Thresholds for Spherical Spin Glasses in High-Dimensional Optimization
Harvard CMSA via YouTube
Overview
Syllabus
Introduction
Outline
Motivation
Problem Statement
tensor PCA
maximum likelihood estimator
Random cubic polynomial
Larger degree polynomial
Where does it come from
Random graph example
Random models
Efficient optimization
Brute Force search
Easing models
Random case set
Optimization
Optimization Algorithm
Subog
Moving Radially
Other Questions
General Models
Overlap Gap Property
Example
Stable Algorithms
Overlap Gap
Random KSAT
Algorithm Stability
Overlap Concentration
Additional Results
combinatorial optimization
matching random graphs
multispecies spin glass
Hamiltonian bias
Linear term bias
Complex energy functions
Binary perceptron model
Neural network memorization
Isolated solutions
Dense clusters of solutions
Lunge event dynamics
Mixed models
Conclusion
Taught by
Harvard CMSA
