CRANE: Reasoning with constrained LLM generation

Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but prior works have empirically observed that strict enforcement of formal constraints often diminishes the reasoning capabilities of LLMs. In this work, we first provide a theoretical explanation for why constraining LLM outputs to very restrictive grammars that only allow syntactically valid final answers reduces the reasoning capabilities of the model. Second, we demonstrate that by augmenting the output grammar with carefully designed additional rules, it is always possible to preserve the reasoning capabilities of the LLM while ensuring syntactic and semantic correctness in its outputs. Building on these theoretical insights, we propose a reasoning-augmented constrained decoding algorithm, CRANE, which effectively balances the correctness of constrained generation with the flexibility of unconstrained generation. Experiments on multiple open-source LLMs and benchmarks show that CRANE significantly outperforms both state-of-the-artconstrained decoding strategies and standard unconstrained decoding, showing up to 10% points accuracy improvement over baselines on challenging symbolic reasoning benchmarks GSM-symbolic and FOLIO.

We study the relationship between reasoning and constrained LLM generation. While strict grammar constraints can hinder reasoning, we theoretically demonstrate that augmenting the output grammar with additional rules can preserve reasoning capabilities. Building on this insight, we introduce CRANE, a decoding algorithm that balances constraint enforcement with reasoning flexibility. CRANE achieves up to 10% percentage points higher accuracy than prior methods on symbolic reasoning tasks such as GSM-symbolic and FOLIO.