论文标题
参数耦合流的通用性在参数差异上
Universality of parametric Coupling Flows over parametric diffeomorphisms
论文作者
论文摘要
基于耦合流的可逆神经网络CFLOWS）具有各种应用，例如图像合成和数据压缩。 CFLOW的近似普遍性对于确保模型表现力至关重要。在本文中，我们证明，如果Cflows可以近似某些单坐标变换，则CFLOW可以近似C^k-norm中的任何差异性。具体而言，我们得出的是，仿射耦合层和可逆线性的组成可以转化这一普遍性。此外，在参数情况下，差异性取决于一些额外的参数，我们证明了我们提出的名为para-clows的参数参数耦合流的相应近似定理。在实践中，我们将Para Crows用作上下文贝叶斯优化任务中的神经替代模型，以在优化性能方面证明其优于其他神经替代模型的优势。
Invertible neural networks based on Coupling Flows CFlows) have various applications such as image synthesis and data compression. The approximation universality for CFlows is of paramount importance to ensure the model expressiveness. In this paper, we prove that CFlows can approximate any diffeomorphism in C^k-norm if its layers can approximate certain single-coordinate transforms. Specifically, we derive that a composition of affine coupling layers and invertible linear transforms achieves this universality. Furthermore, in parametric cases where the diffeomorphism depends on some extra parameters, we prove the corresponding approximation theorems for our proposed parametric coupling flows named Para-CFlows. In practice, we apply Para-CFlows as a neural surrogate model in contextual Bayesian optimization tasks, to demonstrate its superiority over other neural surrogate models in terms of optimization performance.
