发表机构
Florida State University; Purdue University（佛罗里达州立大学; 普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对归一化流玻尔兹曼生成器因前向KL训练而遗漏模式的问题，提出基于对数比率变差的KLXX损失函数，通过加权变差改进模式覆盖，并证明其渐近无偏，实验验证有效。
AI 中文摘要
归一化流玻尔兹曼生成器保留了可处理的推前密度，但使用前向KL散度训练依赖于目标样本，这些样本可能存在偏差或遗漏模式。因此，流可能遗漏目标质量，而其观测到的重要性权重却给出较高的有效样本量。我们引入了对数比率变差 $\X_\omega$，即在加权测度 $\omega$ 下目标与推前密度对数比率对的平均绝对差，并利用它定义了新的损失函数KLXX。两个对数比率变差被添加到前向KL散度中（由两个X表示）：一个由目标加权以提高准确性，另一个由淬火和回火样本与推前样本的混合加权以搜索候选模式。我们推导了KLXX的Fisher-Rao梯度流，其中两个变差均贡献非正耗散，并给出了KLXX的固定代理误差界。我们在自适应分阶段玻尔兹曼生成器中使用KLXX，并在每个阶段进行重要性重加权。当阶段权重本质有界时，我们界定了其推断方案的采样误差，并证明其在样本量上渐近无偏。在数值测试中，KLXX相比前向KL提高了模式覆盖率。它还改善了生成器针对构建调度所依据的损失的逐阶段诊断。生成器恢复的可观测量接近独立参考值。因此，对数比率变差提供了前向KL损失通常遗漏的信息。
英文摘要
Normalizing flow Boltzmann generators retain a tractable pushforward density, but training with forward KL depends on target samples that may be biased or omit modes. As a result, a flow can miss target mass while its observed importance weights give a high effective sample size. We introduce the log-ratio variation $\X_ω$, the mean absolute pairwise difference of the target-to-pushforward log-density ratio under a weighting measure $ω$, and use it to define KLXX, a new loss function. Two log-ratio variations are added to the forward KL (denoted by the two X's): one weighted by the target to improve accuracy, the other by a mixture of quench and temper samples with pushforward samples to search candidate modes. We derive the Fisher--Rao gradient flow of KLXX, where both variations contribute nonpositive dissipation, and a fixed-surrogate error bound for KLXX. We use KLXX in an adaptive-staging Boltzmann generator, with importance reweighting at every stage. We bound the sampling error of its inference scheme when the stage weights are essentially bounded, and prove it asymptotically unbiased in the sample size. In the numerical tests, KLXX improves mode coverage over forward KL. It also improves the generator's per-stage diagnostics against the loss that built the schedule. The observables the generator recovers are close to independent references. The log-ratio variations thus supply information that the forward KL loss usually omits.
