Generative Flow Networks (GFlowNets) are a family of generative models that learn to sample objects from a given probability distribution, potentially known up to a normalizing constant. Instead of working in the object space, GFlowNets proceed by sampling trajectories in an appropriately constructed directed acyclic graph environment, greatly relying on the acyclicity of the graph. In our paper, we revisit the theory that relaxes the acyclicity assumption and present a simpler theoretical framework for non-acyclic GFlowNets in discrete environments. Moreover, we provide various novel theoretical insights related to training with fixed backward policies, the nature of flow functions, and connections between entropy-regularized RL and non-acyclic GFlowNets, which naturally generalize the respective concepts and theoretical results from the acyclic setting. In addition, we experimentally re-examine the concept of loss stability in non-acyclic GFlowNet training, as well as validate our own theoretical findings.

翻译：生成流网络（GFlowNets）是一类生成模型，旨在学习从给定概率分布（可能仅知其未归一化常数）中采样对象。GFlowNets并非直接在对象空间中操作，而是通过在适当构建的有向无环图环境中采样轨迹来实现，这一过程极大地依赖于图的无环性。本文重新审视了放宽无环性假设的理论，提出了一个更简洁的离散环境下非无环GFlowNets的理论框架。此外，我们提供了多项新颖的理论见解，涉及固定后向策略训练、流函数的本质，以及熵正则化强化学习与非无环GFlowNets之间的联系——这些见解自然地推广了无环场景下的相应概念与理论结果。此外，我们通过实验重新检验了非无环GFlowNet训练中损失稳定性的概念，并验证了我们自身的理论发现。