Improving Normalizing Flow Models with MCMC-Based Correction on the Ackley Function
College
College of Sciences
Department
Computer Science
Graduate Level
Doctoral
Graduate Program/Concentration
AI/ML
Presentation Type
Poster Presentation
Abstract
Normalizing Flows (NFs) are widely used for density estimation and generative modeling due to their ability to learn complex distributions through invertible transformations. However, their accuracy is often limited by imperfect training, insufficient expressivity, and mode collapse, particularly when modeling multimodal or rugged landscapes such as the Ackley function. In this work, we propose a Markov Chain Monte Carlo (MCMC)-based correction framework to refine the learned distribution of a trained Normalizing Flow. By first training an NF model on samples from the Ackley function, we apply MCMC as a post-processing step to correct discrepancies and improve the fidelity of the generated samples. Our approach ensures better approximation of the target distribution by mitigating biases introduced during training and enhancing sample diversity. We evaluate the effectiveness of this method through quantitative comparisons of likelihood estimation, convergence properties, and error reduction. The results demonstrate that incorporating MCMC correction significantly improves the accuracy and robustness of Normalizing Flow models, making them more reliable for applications in complex, high-dimensional optimization and density estimation tasks.
Keywords
Generative AI, Ackley Function, Normalizing Flow, MCMC
Improving Normalizing Flow Models with MCMC-Based Correction on the Ackley Function
Normalizing Flows (NFs) are widely used for density estimation and generative modeling due to their ability to learn complex distributions through invertible transformations. However, their accuracy is often limited by imperfect training, insufficient expressivity, and mode collapse, particularly when modeling multimodal or rugged landscapes such as the Ackley function. In this work, we propose a Markov Chain Monte Carlo (MCMC)-based correction framework to refine the learned distribution of a trained Normalizing Flow. By first training an NF model on samples from the Ackley function, we apply MCMC as a post-processing step to correct discrepancies and improve the fidelity of the generated samples. Our approach ensures better approximation of the target distribution by mitigating biases introduced during training and enhancing sample diversity. We evaluate the effectiveness of this method through quantitative comparisons of likelihood estimation, convergence properties, and error reduction. The results demonstrate that incorporating MCMC correction significantly improves the accuracy and robustness of Normalizing Flow models, making them more reliable for applications in complex, high-dimensional optimization and density estimation tasks.