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Despite the success of autoregressive large language models in textgeneration, it remains a major challenge to generate text that satisfiescomplex constraints: sampling from the conditional distribution${\Pr}(\text{text} | \alpha)$ is intractable for even the simplest lexicalconstraints $\alpha$. To overcome this challenge, we propose to use tractableprobabilistic models (TPMs) to impose lexical constraints in autoregressivetext generation models, which we refer to as GeLaTo (Generating Language withTractable Constraints). To demonstrate the effectiveness of this framework, weuse distilled hidden Markov models, where we can efficiently compute${\Pr}(\text{text} | \alpha)$, to guide autoregressive generation from GPT2.GeLaTo achieves state-of-the-art performance on challenging benchmarks forconstrained text generation (e.g., CommonGen), beating various strong baselinesby a large margin. Our work not only opens up new avenues for controlling largelanguage models but also motivates the development of more expressive TPMs.

Tractable Control for Autoregressive Language Generation