A Theory of Non-Acyclic Generative Flow Networks
This work addresses a foundational problem in generative modeling for researchers, enabling broader application of GFlowNets by removing acyclicity constraints, though it is incremental as it builds on existing GFlowNet theory.
The paper tackles the limitation of acyclicity in GFlowNets by extending their theory to measurable spaces without cycle restrictions, defining a new family of losses to prevent cycles, and validating these principles through experiments on graphs and continuous tasks.
GFlowNets is a novel flow-based method for learning a stochastic policy to generate objects via a sequence of actions and with probability proportional to a given positive reward. We contribute to relaxing hypotheses limiting the application range of GFlowNets, in particular: acyclicity (or lack thereof). To this end, we extend the theory of GFlowNets on measurable spaces which includes continuous state spaces without cycle restrictions, and provide a generalization of cycles in this generalized context. We show that losses used so far push flows to get stuck into cycles and we define a family of losses solving this issue. Experiments on graphs and continuous tasks validate those principles.