发表机构
Université Paris-Saclay; CNRS; INRIA; Escuela Técnica Superior de Ingenieros Industriales; Universidad Politécnica de Madrid; Universidad Complutense de Madrid（巴黎萨克雷大学; 法国国家科学研究中心; 法国国家信息与自动化研究所; 工业工程师高等技术学院; 马德里理工大学; 马德里康普顿斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出基于并行轨迹回火（PTT）的 EBM 训练算法，结合水库采样与自适应优化，可稳定快速训练，性能优于现有方法，使 EBM 的均衡最大似然训练更实用高效。
AI 中文摘要
能量基模型（EBMs）为科学数据的生成式建模提供了可解释框架，但马尔可夫链蒙特卡罗混合性差常限制其可靠性。我们提出一种基于并行轨迹回火（PTT）的训练算法，该算法利用优化路径的连续性，在整个学习过程中维持均衡采样，从而能在多模态程度高且数据稀缺的科学数据集上实现稳定快速的训练。结合 reservoir sampling（水库采样）和自适应优化，PTT 的计算成本与持续对比散度相当，可作为标准训练方法的实用替代方案。它还能以几乎无额外成本的方式直接估计热化时间、训练模型的均衡样本以及准确的对数似然。在受限玻尔兹曼机上的实验表明，PTT 始终优于现有 EBM 训练方法；在离散表格数据上，其性能也超过了最先进的深度生成模型，生成样本质量更高，且对过拟合和数据有限的鲁棒性更强。我们的研究使 EBM 的均衡最大似然训练变得实用且计算高效。
英文摘要
Energy-Based Models (EBMs) provide an interpretable framework for generative modeling of scientific data, but poor Markov Chain Monte Carlo mixing often limits their reliability. We introduce a training algorithm based on Parallel Trajectory Tempering (PTT), which exploits the continuity of the optimization path to maintain equilibrium sampling throughout learning. This enables stable and fast training on highly multimodal and data-scarce scientific datasets. Combined with reservoir sampling and adaptive optimization, PTT has a computational cost comparable to Persistent Contrastive Divergence, making it a practical replacement for standard training methods. It also provides direct estimates of thermalization times, equilibrium samples from trained models, and accurate log-likelihoods at essentially no additional cost. Experiments on Restricted Boltzmann Machines show that PTT consistently outperforms existing EBM training approaches. On discrete tabular data, it also surpasses state-of-the-art deep generative models, yielding higher-quality samples and greater robustness to overfitting and limited data. Our results make equilibrium maximum-likelihood training of EBMs practical and computationally efficient.
Comments11 pages, 7 figures
