# Semantic Probabilistic Control of Language Models

arXiv: https://arxiv.org/abs/2505.01954 · HTML: https://mlsanity.com/paper/2505.01954/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 77 references that are in the map.
- First posted on arXiv 4 May 2025.

## Builds on (most cited first, 30 of 60)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [Universal Adversarial Triggers for Attacking and Analyzing NLP](https://mlsanity.com/paper/1908.07125/) (2019)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [Smarter, Better, Faster, Longer: A Modern Bidirectional Encoder for Fast, Memory Efficient, and Long Context Finetuning and Inference](https://mlsanity.com/paper/2412.13663/) (2024)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [Self-Diagnosis and Self-Debiasing: A Proposal for Reducing Corpus-Based Bias in NLP](https://mlsanity.com/paper/2103.00453/) (2021)
- [Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons](https://mlsanity.com/paper/2301.11270/) (2023)
- [Lexically Constrained Decoding for Sequence Generation Using Grid Beam Search](https://mlsanity.com/paper/1704.07138/) (2017)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [Grammar-Constrained Decoding for Structured NLP Tasks without Finetuning](https://mlsanity.com/paper/2305.13971/) (2023)
- [Preference Fine-Tuning of LLMs Should Leverage Suboptimal, On-Policy Data](https://mlsanity.com/paper/2404.14367/) (2024)
- [Fast Lexically Constrained Decoding with Dynamic Beam Allocation for Neural Machine Translation](https://mlsanity.com/paper/1804.06609/) (2018)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [Synchromesh: Reliable code generation from pre-trained language models](https://mlsanity.com/paper/2201.11227/) (2022)
- [NeuroLogic A*esque Decoding: Constrained Text Generation with Lookahead Heuristics](https://mlsanity.com/paper/2112.08726/) (2021)
- [Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs](https://mlsanity.com/paper/2407.01082/) (2024)
- [NeuroLogic Decoding: (Un)supervised Neural Text Generation with Predicate Logic Constraints](https://mlsanity.com/paper/2010.12884/) (2020)
- [RL with KL penalties is better viewed as Bayesian inference](https://mlsanity.com/paper/2205.11275/) (2022)
- [Learning to Write with Cooperative Discriminators](https://mlsanity.com/paper/1805.06087/) (2018)
- [FollowBench: A Multi-level Fine-grained Constraints Following Benchmark for Large Language Models](https://mlsanity.com/paper/2310.20410/) (2023)
- [Fast Best-of-N Decoding via Speculative Rejection](https://mlsanity.com/paper/2410.20290/) (2024)
- [Prompting Is Programming: A Query Language for Large Language Models](https://mlsanity.com/paper/2212.06094/) (2022)

## Built on by (most cited first, 4 of 4)

- [Neurosymbolic Diffusion Models](https://mlsanity.com/paper/2505.13138/) (2025)
- [RefineStat: Efficient Exploration for Probabilistic Program Synthesis](https://mlsanity.com/paper/2509.01082/) (2025)
- [Entropy-Aligned Decoding of LMs for Better Writing and Reasoning](https://mlsanity.com/paper/2601.01714/) (2026)
- [Learning Tractable Distributions Of Language Model Continuations](https://mlsanity.com/paper/2511.16054/) (2025)

## Abstract (arXiv)

Semantic control entails steering LM generations towards satisfying subtle non-lexical constraints, e.g., toxicity, sentiment, or politeness, attributes that can be captured by a sequence-level verifier. It can thus be viewed as sampling from the LM distribution conditioned on the target attribute, a computationally intractable problem due to the non-decomposable nature of the verifier. Existing approaches to LM control either only deal with syntactic constraints which cannot capture the aforementioned attributes, or rely on sampling to explore the conditional LM distribution, an ineffective estimator for low-probability events. In this work, we leverage a verifier's gradient information to efficiently reason over all generations that satisfy the target attribute, enabling precise steering of LM generations by reweighing the next-token distribution. Starting from an initial sample, we create a local LM distribution favoring semantically similar sentences. This approximation enables the tractable computation of an expected sentence embedding. We use this expected embedding, informed by the verifier's evaluation at the initial sample, to estimate the probability of satisfying the constraint, which directly informs the update to the next-token distribution. We evaluated the effectiveness of our approach in controlling the toxicity, sentiment, and topic-adherence of LMs yielding generations satisfying the constraint with high probability (>95%) without degrading their quality.