AI 中文总结
SIMANF将模拟退火与归一化流结合，无需目标样本即可学习高维多模态非归一化分布，通过渐进变换和阶段间表示传递克服模式坍缩，并在多井及Phi4格点场论分布上验证了有效性。
AI 中文摘要
在没有目标样本的情况下，高效学习并采样高维、多模态的非归一化分布仍然是一个具有挑战性的问题。尽管归一化流能够高效生成样本，但仅使用非归一化目标密度基于反向KL散度进行训练可能会遭受模式坍缩。我们提出了SIMANF，一个将模拟退火与归一化流相结合的无样本框架。SIMANF逐步将目标分布从平滑的初始形式转换到原始目标分布，并跨这些阶段顺序训练流。通过在阶段间传递学习到的表示，该方法促进模式覆盖，同时逐步捕捉目标分布的更精细特征。在退火之后，一个最终的细化阶段结合了反向KL散度与使用流生成的样本的基于重要性加权的前向KL目标。SIMANF在训练期间不需要目标样本，仅使用非归一化密度。我们在多井分布和高维标量Phi4格点场论分布上展示了其有效性。
英文摘要
Efficiently learning and sampling from high dimensional, multimodal unnormalized distributions without target samples remains a challenging problem. Although normalizing flows can generate samples efficiently, training based on the reverse KL divergence using only the unnormalized target density may suffer from mode collapse. We introduce SIMANF, a sample free framework that integrates simulated annealing with normalizing flows. SIMANF progressively transforms the target distribution from a smooth initial form to the original target distribution and trains the flow sequentially across these stages. By transferring the learned representation between stages, the method promotes mode coverage while progressively capturing finer features of the target distribution. Following annealing, a final refinement stage combines the reverse KL divergence with an importance weighted forward KL objective using samples generated by the flow. SIMANF requires no target samples during training and uses only the unnormalized density. We demonstrate its effectiveness on Many-Well distributions and high dimensional Scalar Phi4 lattice field theory distribution.
