Invertible Monotone Operators for Normalizing Flows
This work addresses a bottleneck in normalizing flows for researchers and practitioners in machine learning, offering an incremental improvement over existing ResNet-based models.
The paper tackled the constrained Lipschitz constants in ResNet-based normalizing flows by proposing a monotone formulation using monotone operators and introducing the CPila activation function to improve gradient flow, resulting in Monotone Flows that achieved excellent performance on density estimation benchmarks like MNIST, CIFAR-10, ImageNet32, and ImageNet64.
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.