Normalizing flows learn complex distributions without example samples
SIMANF: Sample Free Learning of Unnormalized Distributions via Simulated Annealing in Normalizing Flows
Machine Learning
Summary
Learning and sampling from complicated probability shapes that don’t have examples is hard. The authors created SIMANF, a method that slowly changes a simple shape into the complicated target shape while training a model called a normalizing flow at each step. This gradual change helps the model cover all parts of the target shape better and avoid ignoring important details. After this process, the model is fine-tuned using samples it generates itself, even though no real example samples are given during training. The method works well on challenging test problems with many modes and high dimensions.
What this means in practice
- •For statistical modelers: Generate samples from complex target distributions without observing data samples by training models solely on unnormalized density functions.
- •For computational physicists: Simulate lattice field theory distributions with many states by progressively learning their probability shapes without sample data for intermediate steps.
Authors
Vikas Kanaujia
Abstract
Efficiently learning and sampling from high dimensional, multimodal unnormalized distributions without target samples remains a challenging problem. Although normalizing flows can generate samples efficiently, training based on the reverse KL divergence using only the unnormalized target density may suffer from mode collapse. We introduce SIMANF, a sample free framework that integrates simulated annealing with normalizing flows. SIMANF progressively transforms the target distribution from a smooth initial form to the original target distribution and trains the flow sequentially across these stages. By transferring the learned representation between stages, the method promotes mode coverage while progressively capturing finer features of the target distribution. Following annealing, a final refinement stage combines the reverse KL divergence with an importance weighted forward KL objective using samples generated by the flow. SIMANF requires no target samples during training and uses only the unnormalized density. We demonstrate its effectiveness on Many-Well distributions and high dimensional Scalar Phi4 lattice field theory distribution.