Title: Flow of Spans: Generalizing Language Models to Dynamic Span-Vocabulary via GFlowNets
Primary area: foundation or frontier models, including LLMs
Keywords: generative flow networks, language models

Abstract: Standard autoregressive language models generate text token-by-token from a fixed vocabulary, inducing a *tree-structured state space* when viewing token sampling as an action, which limits flexibility and expressiveness. Recent work introduces dynamic vocabulary by sampling retrieved text spans but overlooks that the same sentence can be composed of spans of varying lengths, lacking explicit modeling of the *directed acyclic graph (DAG) state space*. This leads to restricted exploration of compositional paths and is biased toward the chosen path. Generative Flow Networks (GFlowNets) are powerful for efficient exploring and generalizing over state spaces, particularly those with a DAG structure. However, prior GFlowNets-based language models operate at the token level and remain confined to tree-structured spaces, limiting their potential. In this work, we propose **F**low **o**f **S**pan**S** (**FOSS**), a principled GFlowNets framework for span generation. FoSS constructs a dynamic span vocabulary by segmenting the retrieved text flexibly, ensuring a DAG-structured state space, which allows GFlowNets to explore diverse compositional paths and improve generalization. With specialized reward models, FoSS generates diverse, high-quality text. Empirically, FoSS improves MAUVE scores by up to 12.5\% over Transformer on text generation and achieves 3.5\% gains on knowledge-intensive tasks, consistently outperforming state-of-the-art methods. Scaling experiments further demonstrate FoSS benefits from larger models, more data, and richer retrieval corpora, retaining its advantage over strong baselines.