简化低秩混合模型的流匹配变换
Simplifying Flow Matching Transformations with Low-Rank Mixture Models
AI总结：
提出用概率主成分分析混合模型作为归一化流的潜变量密度，通过KL散度对齐数据分布，简化流变换，加速训练并提升生成质量。
摘要：
归一化流是强大的生成模型，学习复杂数据分布与简单潜变量分布（通常是标准正态密度）之间的可逆映射。然而，由于潜变量密度与数据密度之间的拓扑不匹配，这种潜变量密度的选择可能会给学习的流变换带来不必要的复杂性，导致训练速度变慢和性能次优。在这项工作中，我们提出使用概率主成分分析混合模型（MPPCA）作为归一化流的潜变量密度。我们通过学习一个在KL散度上与数据分布更接近的潜变量分布来简化学习的流变换，从而实现更快的收敛和更好的生成性能。关键的是，MPPCA模型可以使用期望最大化算法快速且廉价地拟合，使其成为在高维生成任务中初始化潜变量分布的实用选择。我们在表格数据和图像数据集上验证了我们的方法，与基线相比，在训练效率和生成质量方面均表现出一致的提升。
英文摘要：
Normalizing flows are powerful generative models that learn an invertible mapping between complex data distributions and simple latent distributions, typically a standard normal density. However, this choice of latent density can impose unnecessary complexity on the learned flow transformation due to the topological mismatch between the latent and data densities, leading to slower training and suboptimal performance. In this work, we propose using mixtures of probabilistic principal component analyzers (MPPCA) as the latent density for normalizing flows. We simplify the learned flow transformation by learning a latent distribution that more closely aligns with the data distribution in terms of KL divergence, thus enabling faster convergence and improved generative performance. Critically, MPPCA models can be fit quickly and cheaply using the expectation-maximization algorithm, making them a practical choice for initializing latent distributions even in high-dimensional generative tasks. We validate our method on both tabular and image datasets, demonstrating consistent gains in training efficiency and generation quality compared to baselines.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
