# Adaptable Logical Control for Large Language Models

arXiv: https://arxiv.org/abs/2406.13892 · HTML: https://mlsanity.com/paper/2406.13892/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 47 references that are in the map.
- First posted on arXiv 19 Jun 2024.

## Builds on (most cited first, 30 of 34)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [CIDEr: Consensus-based Image Description Evaluation](https://mlsanity.com/paper/1411.5726/) (2014)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [SPICE: Semantic Propositional Image Caption Evaluation](https://mlsanity.com/paper/1607.08822/) (2016)
- [A Corpus and Evaluation Framework for Deeper Understanding of Commonsense Stories](https://mlsanity.com/paper/1604.01696/) (2016)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)
- [CoAuthor: Designing a Human-AI Collaborative Writing Dataset for Exploring Language Model Capabilities](https://mlsanity.com/paper/2201.06796/) (2022)
- [Plan-And-Write: Towards Better Automatic Storytelling](https://mlsanity.com/paper/1811.05701/) (2018)
- [Camels in a Changing Climate: Enhancing LM Adaptation with Tulu 2](https://mlsanity.com/paper/2311.10702/) (2023)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [NeuroLogic A*esque Decoding: Constrained Text Generation with Lookahead Heuristics](https://mlsanity.com/paper/2112.08726/) (2021)
- [NeuroLogic Decoding: (Un)supervised Neural Text Generation with Predicate Logic Constraints](https://mlsanity.com/paper/2010.12884/) (2020)
- [Enabling Language Models to Fill in the Blanks](https://mlsanity.com/paper/2005.05339/) (2020)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programs](https://mlsanity.com/paper/2306.03081/) (2023)
- [Evaluating Large Language Models on Controlled Generation Tasks](https://mlsanity.com/paper/2310.14542/) (2023)
- [Creative Writing with an AI-Powered Writing Assistant: Perspectives from Professional Writers](https://mlsanity.com/paper/2211.05030/) (2022)
- [Tractable Control for Autoregressive Language Generation](https://mlsanity.com/paper/2304.07438/) (2023)
- [Controllable Text Generation with Neurally-Decomposed Oracle](https://mlsanity.com/paper/2205.14219/) (2022)
- [Bounding the Capabilities of Large Language Models in Open Text Generation with Prompt Constraints](https://mlsanity.com/paper/2302.09185/) (2023)
- [Zero-shot Sonnet Generation with Discourse-level Planning and Aesthetics Features](https://mlsanity.com/paper/2205.01821/) (2022)
- [A Pseudo-Semantic Loss for Autoregressive Models with Logical Constraints](https://mlsanity.com/paper/2312.03905/) (2023)

## Built on by (most cited first, 30 of 30)

- [Fast Controlled Generation from Language Models with Adaptive Weighted Rejection Sampling](https://mlsanity.com/paper/2504.05410/) (2025)
- [Constrained Sampling for Language Models Should Be Easy: An MCMC Perspective](https://mlsanity.com/paper/2506.05754/) (2025)
- [A Survey on Human-Centric LLMs](https://mlsanity.com/paper/2411.14491/) (2024)
- [Neurosymbolic Diffusion Models](https://mlsanity.com/paper/2505.13138/) (2025)
- [Controllable Generation via Locally Constrained Resampling](https://mlsanity.com/paper/2410.13111/) (2024)
- [Breaking the Factorization Barrier in Diffusion Language Models](https://mlsanity.com/paper/2603.00045/) (2026)
- [Scaling Probabilistic Circuits via Monarch Matrices](https://mlsanity.com/paper/2506.12383/) (2025)
- [Decoupling Task-Solving and Output Formatting in LLM Generation](https://mlsanity.com/paper/2510.03595/) (2025)
- [Fast and Expressive Multi-Byte Prediction with Probabilistic Circuits](https://mlsanity.com/paper/2511.11346/) (2025)
- [TRACE Back from the Future: A Probabilistic Reasoning Approach to Controllable Language Generation](https://mlsanity.com/paper/2504.18535/) (2025)
- [Mitigating Bias in Locally Constrained Decoding via Tractable Proposals](https://mlsanity.com/paper/2606.01926/) (2026)
- [Guaranteed Generation from Large Language Models](https://mlsanity.com/paper/2410.06716/) (2024)
- [Restructuring Tractable Probabilistic Circuits](https://mlsanity.com/paper/2411.12256/) (2024)
- [Neuro-Symbolic Predictive Process Monitoring](https://mlsanity.com/paper/2509.00834/) (2025)
- [Semantic Probabilistic Control of Language Models](https://mlsanity.com/paper/2505.01954/) (2025)
- [Approximately Aligned Decoding](https://mlsanity.com/paper/2410.01103/) (2024)
- [Constrained Adaptive Rejection Sampling](https://mlsanity.com/paper/2510.01902/) (2025)
- [The Limits of Tractable Marginalization](https://mlsanity.com/paper/2506.12020/) (2025)
- [Entropy-Aligned Decoding of LMs for Better Writing and Reasoning](https://mlsanity.com/paper/2601.01714/) (2026)
- [Neurosymbolic LoRA: Why and When to Tune Weights vs. Rewrite Prompts](https://mlsanity.com/paper/2601.12711/) (2026)
- [CoLyricist: Enhancing Lyric Writing with AI through Workflow-Aligned Support](https://mlsanity.com/paper/2602.22606/) (2026)
- [The RAIL Principles for Neurosymbolic AI: Reasoning, Assurances, Interfacing and Learning](https://mlsanity.com/paper/2608.04285/) (2026)
- [Norm-Q: Effective Compression Method for Hidden Markov Models in Neuro-Symbolic Applications](https://mlsanity.com/paper/2509.25439/) (2025)
- [Learning Tractable Distributions Of Language Model Continuations](https://mlsanity.com/paper/2511.16054/) (2025)
- [Prompt Driven Development with Claude Code: Building a Complete TUI Framework for the Ring Programming Language](https://mlsanity.com/paper/2601.17584/) (2026)
- [REASON: Accelerating Probabilistic Logical Reasoning for Scalable Neuro-Symbolic Intelligence](https://mlsanity.com/paper/2601.20784/) (2026)
- [Suffix-Constrained Greedy Search Algorithms for Causal Language Models](https://mlsanity.com/paper/2603.01243/) (2026)
- [Neuro-Symbolic Injection of LTLf Constraints in Autoregressive Reinforcement Learning Policies](https://mlsanity.com/paper/2606.08312/) (2026)
- [Tractable Hierarchical Control of Autoregressive Language Models](https://mlsanity.com/paper/2607.20483/) (2026)
- [ARdena: Scenario-driven control of real-time LLM agents](https://mlsanity.com/paper/2607.22651/) (2026)

## Abstract (arXiv)

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.