AutoNF: Automated Architecture Optimization of Normalizing Flows with Unconstrained Continuous Relaxation Admitting Optimal Discrete Solution

Abstract

Normalizing flows (NF) build upon invertible neural networks and have wide applications in probabilistic modeling. Currently, building a powerful yet computationally efficient flow model relies on empirical fine-tuning over a large design space. While introducing neural architecture search (NAS) to NF is desirable, the invertibility constraint of NF brings new challenges to existing NAS methods whose application is limited to unstructured neural networks. Developing efficient NAS methods specifically for NF remains an open problem. We present AutoNF, the first automated NF architectural optimization framework. First, we present a new mixture distribution formulation that allows efficient differentiable architecture search of flow models without violating the invertibility constraint. Second, under the new formulation, we convert the original NP-hard combinatorial NF architectural optimization problem to an unconstrained continuous relaxation admitting the discrete optimal architectural solution, circumventing the loss of optimality due to binarization in architectural optimization. We evaluate AutoNF with various density estimation datasets and show its superior performance-cost trade-offs over a set of existing hand-crafted baselines.