# Constrained Paraphrase Consistency for LLM Hallucination Detection

arXiv: https://arxiv.org/abs/2606.08158 · HTML: https://mlsanity.com/paper/2606.08158/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 19 references that are in the map.
- First posted on arXiv 6 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Evaluating the Factual Consistency of Abstractive Text Summarization](https://mlsanity.com/paper/1910.12840/) (2019)
- [SummaC: Re-Visiting NLI-based Models for Inconsistency Detection in Summarization](https://mlsanity.com/paper/2111.09525/) (2021)
- [Hallucination of Multimodal Large Language Models: A Survey](https://mlsanity.com/paper/2404.18930/) (2024)
- [AlignScore: Evaluating Factual Consistency with a Unified Alignment Function](https://mlsanity.com/paper/2305.16739/) (2023)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [MiniCheck: Efficient Fact-Checking of LLMs on Grounding Documents](https://mlsanity.com/paper/2404.10774/) (2024)
- [Neural Machine Translation: A Review and Survey](https://mlsanity.com/paper/1912.02047/) (2019)
- [Hallucination Detection in Large Language Models with Metamorphic Relations](https://mlsanity.com/paper/2502.15844/) (2025)
- [Abstractive Text Summarization: State of the Art, Challenges, and Improvements](https://mlsanity.com/paper/2409.02413/) (2024)
- [FactCG: Enhancing Fact Checkers with Graph-Based Multi-Hop Data](https://mlsanity.com/paper/2501.17144/) (2025)
- [Paraphrase and Aggregate with Large Language Models for Minimizing Intent Classification Errors](https://mlsanity.com/paper/2406.17163/) (2024)
- [Self-learn to Explain Siamese Networks Robustly](https://mlsanity.com/paper/2109.07371/) (2021)
- [Towards Effective Paraphrasing for Information Disguise](https://mlsanity.com/paper/2311.05018/) (2023)
- [Jeffreys divergence-based regularization of neural network output distribution applied to speaker recognition](https://mlsanity.com/paper/2312.16885/) (2023)

## Abstract (arXiv)

Large language models (LLMs) can generate factually inconsistent claims, motivating accurate and scalable hallucination detectors. Prior work largely enlarges training sets via synthesis or new annotations, introducing increasing cost and potential bias while underusing the consistency implied by semantically equivalent paraphrases. We propose Consistency-Constrained Hallucination Detector (CCHD), which formulates training as a constrained optimization problem. The standard cross-entropy on original document-claim pairs is complemented by (i) paraphrase-consistency constraints bounding divergence across paraphrased views, and (ii) label-preservation constraints tying paraphrases to ground truth. We solve the problem by gradient descent-ascent over model parameters and per-view Lagrange multipliers, adding only a few scalar dual variables and no inference-time overhead. With DeBERTa and Flan-T5 backbones, CCHD consistently outperforms strong baselines (FactCG, MiniCheck, and AlignScore) on standard factuality benchmarks, demonstrating its superiority on hallucination detection.