关于保体积与基于耦合的归一化流的普适性
On the Universality of Volume-Preserving and Coupling-Based Normalizing Flows
AI总结：
本文提出理论框架证明条件良好的基于耦合的归一化流具分布普适性，而保体积流非普适且需修复表达能力，弥合了实证与理论差距。
摘要：
我们提出了一个新颖的理论框架，用于理解归一化流的表达能力。尽管归一化流在科学应用中很普遍，但由于其受限的架构，对其全面理解仍然难以实现。现有定理由于需要使用任意病态的神经网络而显得不足，限制了实际适用性。我们为条件良好的基于耦合的归一化流（如RealNVP）提出了一个分布普适性定理。此外，我们证明了保体积归一化流不是普适的，揭示了它们实际学习的分布，并展示了如何修复其表达能力。我们的结果支持了普遍观点，即仿射及相关耦合具有表达力，且通常优于保体积流，从而弥合了实证结果与理论理解之间的差距。
英文摘要：
We present a novel theoretical framework for understanding the expressive power of normalizing flows. Despite their prevalence in scientific applications, a comprehensive understanding of flows remains elusive due to their restricted architectures. Existing theorems fall short as they require the use of arbitrarily ill-conditioned neural networks, limiting practical applicability. We propose a distributional universality theorem for well-conditioned coupling-based normalizing flows such as RealNVP. In addition, we show that volume-preserving normalizing flows are not universal, what distribution they learn instead, and how to fix their expressivity. Our results support the general wisdom that affine and related couplings are expressive and in general outperform volume-preserving flows, bridging a gap between empirical results and theoretical understanding.
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。
