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Weave of Formal Thought: Sound-and-complete constrained decoding with learned latent syntax for code LLMs

The paper introduces Weave of Formal Thought (WoFT), a framework combining a formally sound-and-complete constrained decoder for code generation with a latent-variable fine-tuning method that teaches LLMs to interleave grammar non-terminals during generation. The constrained decoder extends generalized LR (GLR) parsing with speculative lexing to handle context-sensitive lexing and maximal-munch tokenization, addressing gaps in prior constrained-decoding work. A reweighted wake-sleep (RWS) fine-tuning objective on StarCoder2-3B achieves a 14.3% relative reduction in per-token cross-entropy over a text-only SFT baseline on Python, suggesting that explicit structural scaffolding recovers information lost in flat autoregressive training.