ButterflyFlow: Building Invertible Layers with Butterfly Matrices
ButterflyFlow: Building Invertible Layers with Butterfly Matrices
复制标题
DOI：
10.48550/arxiv.2209.13774
复制
发表时间：
2022-09
期刊：
影响因子：
--
通讯作者：
Chenlin Meng;Linqi Zhou;Kristy Choi;Tri Dao;Stefano Ermon
中科院分区：
文献类型：
--
作者：
Chenlin Meng;Linqi Zhou;Kristy Choi;Tri Dao;Stefano Ermon
规范化流使用通过组成可逆层获得的映射来模拟复杂的概率分布。特殊的线性层，如掩码和1x 1卷积，在现有的架构中发挥着关键作用，因为它们增加了表达能力，同时具有易于处理的雅可比矩阵和逆矩阵。我们提出了一个新的家庭的可逆的线性层的基础上的蝴蝶层，这是已知的理论上捕捉复杂的线性结构，包括排列和周期性，但可以被有效地反转。这种表示能力是我们方法的一个关键优势，因为这种结构在许多现实世界的数据集中很常见。基于我们的可逆蝴蝶层，我们构造了一类新的归一化流模型，称为ButterflyFlow。从经验上讲，我们证明了ButterflyFlows不仅在MNIST、CIFAR-10和ImageNet 32 x32等自然图像上实现了强大的密度估计结果，而且在星系图像和MIMIC-III患者队列等结构化数据集上获得了显著更好的对数似然性，同时在内存和计算方面比相关基线更有效。
Normalizing flows model complex probability distributions using maps obtained by composing invertible layers. Special linear layers such as masked and 1x1 convolutions play a key role in existing architectures because they increase expressive power while having tractable Jacobians and inverses. We propose a new family of invertible linear layers based on butterfly layers, which are known to theoretically capture complex linear structures including permutations and periodicity, yet can be inverted efficiently. This representational power is a key advantage of our approach, as such structures are common in many real-world datasets. Based on our invertible butterfly layers, we construct a new class of normalizing flow models called ButterflyFlow. Empirically, we demonstrate that ButterflyFlows not only achieve strong density estimation results on natural images such as MNIST, CIFAR-10, and ImageNet 32x32, but also obtain significantly better log-likelihoods on structured datasets such as galaxy images and MIMIC-III patient cohorts -- all while being more efficient in terms of memory and computation than relevant baselines.