Jeffreys Flow: Robust Boltzmann Generators for Rare Event Sampling via Parallel Tempering Distillation
arXiv:2604.05303v1 Announce Type: new Abstract: Sampling physical systems with rough energy landscapes is hindered by rare events and metastable trapping. While Boltzmann generators already offer a solution, their reliance on the reverse Kullback--Leibler divergence frequently induces catastrophic mode collapse, missing specific modes in multi-modal distributions. Here, we introduce the Jeffreys Flow, a robust generative framework that mitigates this failure by distilling empirical sampling data from Parallel Tempering trajectories using the symmetric Jeffreys divergence. This formulation effectively balances local target-seeking precision with global modes coverage. We show that minimizing Jeffreys divergence suppresses mode collapse and structurally corrects inherent inaccuracies via distillation of the empirical reference data. We demonstrate the framework's scalability and accuracy on highly non-convex multidimensional benchmarks, including the systematic correction of stochastic
arXiv:2604.05303v1 Announce Type: new Abstract: Sampling physical systems with rough energy landscapes is hindered by rare events and metastable trapping. While Boltzmann generators already offer a solution, their reliance on the reverse Kullback--Leibler divergence frequently induces catastrophic mode collapse, missing specific modes in multi-modal distributions. Here, we introduce the Jeffreys Flow, a robust generative framework that mitigates this failure by distilling empirical sampling data from Parallel Tempering trajectories using the symmetric Jeffreys divergence. This formulation effectively balances local target-seeking precision with global modes coverage. We show that minimizing Jeffreys divergence suppresses mode collapse and structurally corrects inherent inaccuracies via distillation of the empirical reference data. We demonstrate the framework's scalability and accuracy on highly non-convex multidimensional benchmarks, including the systematic correction of stochastic gradient biases in Replica Exchange Stochastic Gradient Langevin Dynamics and the massive acceleration of exact importance sampling in Path Integral Monte Carlo for quantum thermal states.
Executive Summary
The article introduces the Jeffreys Flow, a novel generative framework designed to address the critical challenge of sampling physical systems with rough energy landscapes, where rare events and metastable trapping pose significant obstacles. Building upon Boltzmann generators, the authors propose a paradigm shift by leveraging the symmetric Jeffreys divergence for distillation of empirical sampling data from Parallel Tempering trajectories. This approach effectively mitigates the mode collapse issue inherent to the reverse Kullback-Leibler divergence, ensuring both local precision and global mode coverage. The framework demonstrates remarkable scalability and accuracy across highly non-convex, multidimensional benchmarks, while also enabling systematic correction of stochastic gradient biases and acceleration of exact importance sampling in advanced quantum thermal state simulations.
Key Points
- ▸ The Jeffreys Flow framework addresses mode collapse in Boltzmann generators by replacing the reverse Kullback-Leibler divergence with the symmetric Jeffreys divergence, thereby improving global mode coverage while maintaining local precision.
- ▸ The framework distills empirical sampling data from Parallel Tempering trajectories, structurally correcting inaccuracies and biases inherent in stochastic gradient methods (e.g., SGRLD) and enhancing exact importance sampling in Path Integral Monte Carlo for quantum systems.
- ▸ The proposed method demonstrates exceptional scalability and accuracy on complex, non-convex, multidimensional benchmarks, including corrections for stochastic gradient biases and acceleration of exact importance sampling in quantum thermal state simulations.
Merits
Innovative Theoretical Framework
The introduction of the Jeffreys divergence in place of the reverse Kullback-Leibler divergence represents a significant theoretical advancement, addressing a well-documented failure mode (mode collapse) in generative modeling for physical systems.
Broad Applicability Across Domains
The framework's demonstrated efficacy in correcting biases in stochastic gradient methods and accelerating importance sampling in quantum simulations underscores its versatility and potential impact across computational physics, chemistry, and machine learning.
Scalability and Robustness
The method's performance on highly non-convex, multidimensional benchmarks highlights its scalability and robustness, making it a promising tool for tackling complex energy landscapes in real-world applications.
Demerits
Computational Overhead
The reliance on Parallel Tempering trajectories and distillation of empirical sampling data may introduce additional computational overhead, particularly in high-dimensional systems, potentially limiting accessibility for resource-constrained researchers.
Dependence on Parallel Tempering
The framework's effectiveness is contingent on the quality and diversity of the Parallel Tempering trajectories used for distillation, which may pose challenges in systems where such trajectories are difficult to generate or are inherently limited.
Theoretical Complexity
The use of Jeffreys divergence, while theoretically elegant, may introduce computational and conceptual complexities that could hinder widespread adoption by practitioners without advanced expertise in information geometry or statistical mechanics.
Expert Commentary
The Jeffreys Flow represents a significant leap forward in the quest to overcome the limitations of traditional Boltzmann generators, which have long struggled with mode collapse in multimodal distributions. By introducing the symmetric Jeffreys divergence, the authors elegantly address a fundamental tension between local precision and global mode coverage—a trade-off that has plagued generative models in statistical physics and machine learning alike. The framework's ability to distill empirical data from Parallel Tempering trajectories not only corrects inherent inaccuracies but also provides a scalable solution for complex systems. The demonstrated corrections to stochastic gradient biases and acceleration of exact importance sampling in quantum simulations are particularly noteworthy, as they bridge critical gaps in computational physics and machine learning. However, the reliance on Parallel Tempering and the theoretical complexity of Jeffreys divergence may pose challenges for widespread adoption. Future work should focus on reducing computational overhead and simplifying implementation to ensure broader accessibility. This work sets a new benchmark for generative modeling in physical systems and underscores the transformative potential of information geometry in scientific computing.
Recommendations
- ✓ Develop user-friendly software implementations and toolkits to lower the barrier to entry for practitioners in computational physics and machine learning, thereby facilitating broader adoption of the Jeffreys Flow framework.
- ✓ Explore hybrid approaches that combine the Jeffreys Flow with other advanced sampling techniques (e.g., variational inference, neural ODEs) to further enhance robustness and scalability in high-dimensional systems.
- ✓ Conduct further empirical studies to validate the framework across a wider range of physical systems and benchmarks, including real-world datasets, to solidify its generalizability and practical utility.
- ✓ Investigate the theoretical foundations of the Jeffreys Flow to better understand its convergence properties, stability, and relationship to other divergence measures, thereby providing deeper insights into its advantages and limitations.
Sources
Original: arXiv - cs.LG