Despite the success of Large Language Models (LLMs) on various tasks following human instructions, controlling model generation to follow strict constraints at inference time poses a persistent challenge. In this paper, we introduce Ctrl-G, a neuro-symbolic framework that enables tractable and adaptable control of LLM generation to follow logical constraints reliably. Ctrl-G combines any production-ready LLM with a Hidden Markov Model (HMM), guiding LLM outputs to adhere to logical constraints represented as deterministic finite automata. We show that Ctrl-G, when a TULU2-7B model is coupled with a 2B-parameter HMM, outperforms GPT4 in text editing: on the task of generating text insertions/continuations following logical constraints, our approach achieves over 30% higher satisfaction rate in human evaluation. When applied to medium-size language models (e.g., GPT2-large), Ctrl-G also beats its counterparts on standard benchmarks by large margins. Additionally, as a proof-of-concept study, we use Ctrl-G to assist LLM reasoning on the GSM benchmark, foreshadowing the application of Ctrl-G, as well as other constrained generation approaches, beyond traditional language generation tasks.

Large Language Models (LLMs) still produce gender-stereotyped language even in occupation-neutral contexts that reflect deep societal biases (Rudinger et al., 2018). To address this, prior work has proposed prompting, constrained decoding (Dathathri et al., 2020; Zhou et al., 2024), post-processing, and fine-tuning-based alignment (Rafailov et al., 2023; Ravfogel et al., 2022). However, the comparative efficacy and learning dynamics remain little understood. We report a comparative analysis of six control techniques for bias mitigation: prompt-only, generate-and-filter, DFA-based Ctrl-G decoding, Supervised Fine-Tuning (SFT), Direct Preference Optimization (DPO), and Iterative Nullspace Projection (INLP). We evaluate each method on a compositional constraint task. This task requires generating sentences that contain at least one agentic and one communal descriptor for each of the twenty Winogender-derived occupations. We quantify trade-offs between control strength and naturalness with evaluations of constraint compliance, lexical diversity, and fluency. Our results reveal key contrasts among the methods: SFT achieves 99.87 +- 0.15% compliance and high lexical diversity, while DPO, despite similar training stability, fails at 4.53 +- 0.82%. Ctrl-G guarantees perfect compliance, but at the cost of severely reduced fluency and diversity. Preference-based learning fundamentally differs: it cannot satisfy compositional constraints, as binary preference signals encode ranking, not logical conjunctions. Only explicit positive supervision enables mitigation of compositional biases; preference-based alignment fails to generalize logical structures, underscoring the limitations of preference learning and the necessity of explicit supervision for fair and fluent controlled generation.

Despite the success of Large Language Models (LLMs) on various tasks following human instructions, controlling model generation to follow strict constraints at inference time poses a persistent challenge. In this paper, we introduce Ctrl-G, a neuro-symbolic framework that enables tractable and adaptable control of LLM generation to follow logical constraints reliably. Ctrl-G combines any production-ready LLM with a Hidden Markov Model (HMM), guiding LLM outputs to adhere to logical constraints represented as deterministic finite automata. We show that Ctrl-G, when a TULU2-7B model is coupled with a 2B-parameter HMM, outperforms GPT4 in text editing: on the task of generating text insertions/continuations following logical constraints, our approach achieves over 30% higher satisfaction rate in human evaluation. When applied to medium-size language models (e.g., GPT2-large), Ctrl-G also beats its counterparts on standard benchmarks by large margins.

Despite the success of Large Language Models (LLMs) on various tasks following human instructions, controlling model generation at inference time poses a persistent challenge. In this paper, we introduce Ctrl-G, an adaptable framework that facilitates tractable and flexible control of LLM generation to reliably follow logical constraints. Ctrl-G combines any production-ready LLM with a Hidden Markov Model, enabling LLM outputs to adhere to logical constraints represented as deterministic finite automata. We show that Ctrl-G, when applied to a TULU2-7B model, outperforms GPT3.5 and GPT4 on the task of interactive text editing: specifically, for the task of generating text insertions/continuations following logical constraints, Ctrl-G achieves over 30% higher satisfaction rate in human evaluation compared to GPT4. When applied to medium-size language models (e.g., GPT2-large), Ctrl-G also beats its counterparts for constrained generation by large margins on standard benchmarks. Additionally, as a proof-of-concept study, we experiment Ctrl-G on the Grade School Math benchmark to assist LLM reasoning, foreshadowing the application of Ctrl-G, as well as other constrained generation approaches, beyond traditional language generation tasks.