论文标题
可逆的单调操作员用于归一流的流动
Invertible Monotone Operators for Normalizing Flows
论文作者
论文摘要
通过学习可逆变换，将简单分布转移到复杂分布中，将模型概率分布归一化。由于基于RESNET的标准化流的结构比基于耦合的模型的构造更灵活，因此近年来已经广泛研究了基于RESNET的标准化流。尽管具有建筑灵活性，但众所周知，当前基于重新连接的模型受到Lipschitz常数约束的影响。在本文中，我们提出单调公式，以使用单调算子克服Lipschitz常数问题，并提供深入的理论分析。此外，我们构建了一个称为conventated Pila（CPILA）的激活函数，以改善梯度流。最终的模型单调流动在多密度估计基准（MNIST，CIFAR-10，Imagenet32，Imagenet64）上表现出卓越的性能。代码可从https://github.com/mlvlab/monotoneflows获得。
Normalizing flows model probability distributions by learning invertible transformations that transfer a simple distribution into complex distributions. Since the architecture of ResNet-based normalizing flows is more flexible than that of coupling-based models, ResNet-based normalizing flows have been widely studied in recent years. Despite their architectural flexibility, it is well-known that the current ResNet-based models suffer from constrained Lipschitz constants. In this paper, we propose the monotone formulation to overcome the issue of the Lipschitz constants using monotone operators and provide an in-depth theoretical analysis. Furthermore, we construct an activation function called Concatenated Pila (CPila) to improve gradient flow. The resulting model, Monotone Flows, exhibits an excellent performance on multiple density estimation benchmarks (MNIST, CIFAR-10, ImageNet32, ImageNet64). Code is available at https://github.com/mlvlab/MonotoneFlows.
