这篇论文提出了PTT方法，让能量模型训练又快又稳，在RBM上成绩比现有方法好，还能顺便算热化时间，值得看看。
该论文提出并行轨迹回火（Parallel Trajectory Tempering, PTT）训练算法，用于改进能量模型（Energy-Based Models, EBMs）的马尔可夫链蒙特卡洛（MCMC）混合问题。PTT利用优化路径的连续性，在整个学习过程中维持平衡采样，从而在高度多模态且数据稀少的科学数据集上实现稳定快速训练。与持久对比散度（Persistent Contrastive Divergence）相比，PTT的计算成本相当，并能直接估计热化时间、平衡样本和对数似然。在受限玻尔兹曼机（Restricted Boltzmann Machines）实验中，PTT持续超越现有EBM训练方法；在离散表格数据上，它同样优于当前最先进的深度生成模型，生成更高质量的样本且对过拟合和有限数据更具鲁棒性。
Equilibrium Training of Energy-Based Models with Parallel Trajectory Tempering
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.