提出并行轨迹退火训练法，让能量模型在小数据下也能快速稳定生成高质量样本。
Equilibrium Training of Energy-Based Models with Parallel Trajectory Tempering
- 利用并行轨迹退火保持训练全程采样平衡，避免传统方法的收敛困境。
- 在稀疏科学数据上实现比现有方法更优的生成质量，且对过拟合更鲁棒。
- 无需额外成本即可获得热化时间、均衡样本和精确似然值，适合科研场景。
能量模型（EBM）为科学数据生成提供了可解释框架，但马尔可夫链蒙特卡洛采样效率低常限制其可靠性。本文提出基于并行轨迹退火（PTT）的训练算法，利用优化路径的连续性，在整个学习过程中维持均衡采样。该方法使高多模态、数据稀缺的科学数据集上的训练更加稳定高效。结合水库采样与自适应优化，PTT的计算开销与持久对比散度相当，可作为标准训练方法的实际替代方案。同时，它能直接估计热化时间、获取训练后模型的均衡样本，并以近乎零成本计算精确对数似然。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，也超越了当前最先进深度生成模型，生成更高质量样本，对过拟合和数据有限性更具鲁棒性。结果证明，基于平衡最大似然的EBM训练如今既可行又高效。
原文摘要 · Abstract (English)
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.
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