Designing losses for data-free training of normalizing flows on Boltzmann distributions
This work addresses the challenge of data scarcity in computational physics by enabling data-free training, which is incremental as it builds on existing normalizing flow methods but introduces a novel loss to overcome specific limitations.
The paper tackled the problem of training normalizing flows for Boltzmann distributions without requiring expensive simulation data, by proposing a new loss function that prevents mode collapse. The result demonstrated successful optimization of imperfect pre-trained models on 3D molecular configurations without training data, achieving this for the first time in such tasks.
Generating a Boltzmann distribution in high dimension has recently been achieved with Normalizing Flows, which enable fast and exact computation of the generated density, and thus unbiased estimation of expectations. However, current implementations rely on accurate training data, which typically comes from computationally expensive simulations. There is therefore a clear incentive to train models with incomplete or no data by relying solely on the target density, which can be obtained from a physical energy model (up to a constant factor). For that purpose, we analyze the properties of standard losses based on Kullback-Leibler divergences. We showcase their limitations, in particular a strong propensity for mode collapse during optimization on high-dimensional distributions. We then propose strategies to alleviate these issues, most importantly a new loss function well-grounded in theory and with suitable optimization properties. Using as a benchmark the generation of 3D molecular configurations, we show on several tasks that, for the first time, imperfect pre-trained models can be further optimized in the absence of training data.