用少量可学习的控制信号，高效生成复杂分布。
Parameter-Efficient Generative Modeling with Controlled Vector Fields
- 固定向量场+可学习标量控制，构建低参数生成流
- 仅需少量控制通道即可实现高表达力分布迁移
- 适合追求参数效率与模型可解释性的生成建模研究
我们提出一种基于连续时间的生成建模框架，受Chow-Rashevskii定理启发，通过少量固定向量场与可学习的标量控制函数构建表达能力强的流形。不同于学习高维无约束向量场，该方法通过调制固定向量场来生成速度。当固定向量场满足李括号生成条件时，其李代数可覆盖全空间，从而以极小数量的可学习控制通道实现强表达力的分布传输，提供了一种参数高效的几何替代方案。该解耦结构使学习的输出通道数可独立于环境维度设定。我们提出了一个表达性原理，在适当的可控性和适定性假设下，证明此类受控流可将源分布迁移到目标分布。模型使用连续归一化流似然目标进行训练，并在合成数据上展示了概念验证实验。
原文摘要 · Abstract (English)
We introduce a continuous-time generative modeling framework, motivated by the Chow-Rashevskii theorem, that builds expressive flows from a small set of fixed vector fields and learned scalar controls. Instead of learning an unconstrained high-dimensional vector field, our framework constructs the velocity by modulating fixed vector fields with learned scalar control functions. When the fixed fields are bracket-generating, their Lie algebra spans the ambient space, providing a mechanism for expressive transport with only a small number of learned control channels and offering a parameter-efficient geometric alternative to standard vector-field parameterizations. This decoupled formulation yields a structured and interpretable generative model in which the number of learned scalar output channels can be chosen independently of the ambient dimension. We formulate an expressivity principle showing that, under suitable controllability and well-posedness assumptions, such controlled flows can transport a source distribution to a target distribution. We train the resulting model using a continuous-normalizing-flow likelihood objective and present proof-of-concept experiments on synthetic distributions.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。