Sampling Using Diffusion Processes, From Langevin to Schrödinger
Explore diffusion processes in sampling, from Langevin dynamics to Schrödinger bridges, with insights on geometric methods in optimization and their applications.
Stochastic Analysis and Geometric Functional Inequalities
Explore methods for proving functional inequalities in hypoelliptic diffusions, including geometric and probabilistic approaches, with applications to Langevin dynamics ergodicity.
Speeding up Langevin Dynamics by Mixing
Explore a method to accelerate Langevin dynamics using mixing drift, improving convergence to stationary distribution in polynomial time for systems with multiple local minima.
Constrained Stochastic Processes: From Brownian Motion to Run-and-Tumble Particles
Explore constrained stochastic processes, including Brownian motion, Lévy flights, and run-and-tumble particles. Learn effective dynamics for generating constrained trajectories in various scenarios.
Optimal Transport and High-Dimensional Probability - Langevin Dynamics via Calculus
Explore optimal transport, high-dimensional probability, and Langevin dynamics through advanced calculus techniques in this mathematical deep dive.
Introduction to the Dynamics of Disordered Systems - Equilibrium and Gradient Descent - Part 3
Explore equilibrium dynamics and gradient descent in disordered systems, focusing on theoretical concepts and practical applications in statistical physics and optimization.
Discovering Dynamic Laws from Observations: The Case of Self-Propelled Particles
Explore machine learning techniques for uncovering forces in active matter systems, from cellular to animal scales. Learn to extract local dynamics crucial for understanding collective phenomena.
Estimating Normalizing Constants for Log-Concave Distributions - Algorithms and Lower Bounds
Explore algorithms and lower bounds for estimating normalizing constants in log-concave distributions, covering annealing, Monte Carlo methods, and Langevin dynamics.
Insights on Gradient-Based Algorithms in High-Dimensional Learning
Explore gradient-based algorithms in high-dimensional learning, covering statistical physics solutions for performance analysis in nonconvex settings like spiked mixed matrix-tensor model, perceptron, and phase retrieval.
Diffusion Models
Explore advanced concepts in diffusion models, including theory, applications, and recent developments in probabilistic AI.