Variational Inference for Cyclic Learning

Cyclic learning, which involves training with pairs of inverse tasks and utilizes cycle-consistency in the design of loss functions, has emerged as a powerful paradigm for weakly-supervised learning. However, its potential remains under-explored due to the current methods’ narrow focus on domain-specific implementations. In this work, we develop generalized solutions for both pairwise cycle-consistent tasks and self-cycle-consistent tasks. By formulating cross-domain mappings as conditional probability functions, we reformulate the cycle-consistency objective as an evidence lower bound optimization problem via variational inference. Based on this formulation, we further propose two training strategies for arbitrary cyclic learning tasks: single-step optimization and alternating optimization. Our framework demonstrates broad applicability across diverse tasks. In unpaired image translation, it not only provides a theoretical justification for CycleGAN but also leads to CycleGN—a competitive GAN-free alternative. For unsupervised tracking, CycleTrack and CycleTrack-EM achieve state-of-the-art performance on multiple benchmarks. This work establishes the theoretical foundations of cyclic learning and offers a general paradigm for future research.