F act CG : Enhancing Fact Checkers with Graph-Based Multi-Hop Data (2025)

Abstract: Prior research on training grounded factuality classification models to detect hallucinations in large language models (LLMs) has relied on public natural language inference (NLI) data and synthetic data. However, conventional NLI datasets are not well-suited for document-level reasoning, which is critical for detecting LLM hallucinations. Recent approaches to document-level synthetic data generation involve iteratively removing sentences from documents and annotating factuality using LLM-based prompts. While effective, this method is computationally expensive for long documents and limited by the LLM’s capabilities. In this work, we analyze the differences between existing synthetic training data used in state-of-the-art models and real LLM output claims. Based on our findings, we propose a novel approach for synthetic data generation, CG2C, that leverages multi-hop reasoning on context graphs extracted from documents. Our fact checker model, FactCG, demonstrates improved performance with more connected reasoning, using the same backbone models. Experiments show it even outperforms GPT-4-o on the LLM-Aggrefact benchmark with much smaller model size.

## introduction large language models (llms) have shown remarkable progress in generating fluent and coherent text across domains. they are capable of generating text conditioned on documents, leading to various applications, such as summarization @xcite , retrieval augmented generation @xcite , etc. however, one of the major challenges faced by these models is the tendency to generate hallucinated statements that are factually incorrect or not grounded in the provided document @xcite a spanish newspaper: a source close to messi revealed that, due to the club's financial issues, he is very likely to leave the club he has served for many years. 2020; @xcite . detecting these hallucinations is critical for providing trustworthy and responsible llm services. to identify hallucinations in llm outputs (claims), recent efforts focuses on llm-based approaches and training grounded factuality classification models. llm-based approaches @xcite @xcite leveraging prompts are easy to use and benefit from the strong generalization capabilities of llms. however, they are not cost-effective for real application use as they often require asking llm to generate claims multiple times @xcite , sending each entity of interest iteratively to identify faithfulness @xcite , or leveraging chain-of-thought to generate long sequence of reasoning chain per claim judgement @xcite . therefore, they are mainly used as annotation tools to guide the training of smaller grounded factuality classifiers or treated as strong baselines for benchmark comparison purposes. to make online hallucinations detectors, various studies focuses on training grounded factuality classification models. their training process usually leverages natural language inference (nli) datasets @xcite , adapting other reasoning tasks to the nli framework @xcite or synthetic data generation techniques @xcite . our approach lies under this category with a focus on adapting and generating more complex data. in this work, we investigate the patterns of existing training data and compare it to real llmgenerated claims. we notice there is a nonnegligible difference in the complexity of claims and the reasoning process required for claim verification on grounding documents. we propose context graph to claim (cg2c), a synthetic data generation approach that is able to generate complex multi-hop claims in a more fine-grained and cost-effective way than past studies without any human annotation effort. it also does not leverage llm-based approaches to generate training data labels, hence it is not bounded by llm-based approaches' performances. we verify its effectiveness on top of state-of-the-art models by teaching them to do complex multi-hop reasoning. experiments show that our model, factcg, achieves stateof-the-art performance on the llm-aggrefact @xcite grounded factuality benchmark compared to trained models under a billion parameters. its performance is not bounded by gpt that is used to construct cg2c. moreover, factcg does more connected reasoning than leveraging dataset artifacts. our contributions are three-fold: fact-checking methods. there are two main approaches to detect hallucinations without altering llm architectures. one relies on llms evaluating their own outputs, like selfcheckgpt @xcite , or leveraging chain-of-thought strategies, as seen in g-eval @xcite , cove @xcite , and conli @xcite . the other focuses on training cost-efficient factuality classifiers. summac @xcite adapts nli models for document-level factual checks, while qafacteval @xcite uses question answering (qa) metrics. factcc @xcite ) predicts summary consistency, and alignscore @xcite trains on large-scale unified nli data. minicheck @xcite generates training data using llms to label and outperforms previous work on humanannotated real llm hallucination benchmark llm-aggrefact @xcite . our work continue the study on improving fact-checking models by enhancing llm-generated data complexity and controllability. fact-checking data. several studies focus on creating datasets for hallucination detection, either for training or benchmarking. aggrefact @xcite evaluates factual consistency in summarization (cnn/dm, xsum), while to-fueval @xcite targets dialogue summarization. wice @xcite is a textual entailment dataset based on wikipedia claims. reveal @xcite benchmarks chainof-thought reasoning in open-domain qa, and claimverify @xcite evaluates correctness and groundedness in generative search engines' responses. factcheck @xcite constructs a document-level factuality benchmark, while expertqa @xcite focuses on long-form qa with verified attributions. lfqa @xcite assesses llm-generated sentences for factual support by the documents that are either retrieved by humans, models, or randomly selected. ragtruth @xcite analyzes wordlevel hallucinations in various domains and tasks within the standard retrieval-augmented generation frameworks for llm applications. halueval @xcite is an llm evaluation benchmark with synthetically generated hallucination data. multi-hop reasoning. multi-hop reasoning refers to inference over multiple steps. various studies focused on generating qa datasets where multihop reasoning on documents is required to get the answer, such as hotpotqa @xcite , 2wikimultihopqa @xcite , musique @xcite . however, various studies show that models often exploit dataset artifacts to produce correct answers without connecting information across multiple supporting facts even when multi-fact reasoning is required @xcite @xcite , namely disconnected reasoning (dire) @xcite . ## problem formulation given a document doc and a claim c, we consider c to be grounded in doc if a generic reader would affirm the statement "according to doc, c is true". conversely, c is ungrounded with respect to doc if it conflicts with or cannot be verified against doc. our objective is to model a function to detect ungrounded hallucinations in llm-generated claims against documents at the sentence-level. we define grounded as 1 and ungrounded as 0. m is a classifier that first maps each ⟨doc, c⟩ pair into a confidence score of judging c is grounded in doc, formally defined as m(doc, c) ∈ [0, 1]. we then use a threshold to convert confidence score into a binary prediction as most recent grounded factuality detection industrial applications now support dynamic threshold tuning @xcite , we consider the threshold to be dynamically adjustable to its optimal level for per-scenario detection and follow the past work @xcite @xcite . ## analysis on multi-hops in claims in this section, we conduct a proof of concept experiment on the multi-hop in llm-generated claims. we try to answer the following two research questions (rq): rq1: to what extent do llm-generated claims, based on grounding documents, require multi-hop reasoning for fact verification? rq2: to what extent do current state-of-the-art synthetic claims, based on grounding documents, require multi-hop reasoning for fact verification? ## improving model with context graph to multi-hop claim (cg2c) in this section, we study whether we can improve the state-of-the-art grounded factuality models with synthetically generated data via context graph to multi-hop claims (cg2c). specifically, the study follows two steps, each addressing a research question: rq3: can we improve grounded factuality models by generating synthetic data leveraging large-scale public multi-hop datasets? rq4: can we improve grounded factuality models by generating synthetic multi-hop data leveraging documents only? in this section, we study rq3. we leverage publicly available multi-hop question answering (mhqa) datasets to synthetically construct grounded factuality data for model training, namely cg2c-mhqa. specifically, we use hotpotqa @xcite and musique @xcite , where each data sample contains a source document doc, a question q, an answer ans and supporting sentences doc support , which is a subset of doc that provides evidence for the answer. we leverage llms to convert ⟨ans, q⟩ to a single declarative statement. we define the converted statement as claim c. hotpotqa. we leverage the train-hard split in hotpotqa to ensure each data sample requires complex multi-hop reasoning across multiple paragraphs. we treat the ⟨doc, c⟩ pair as a positive sample. we then randomly select positive samples to corrupt them into negative samples by following the steps below. firstly, since doc support is provided, we extract g s from doc support and then leverage the ⟨g s , c⟩ pair to get a context sub-graph g c , using the same strategy described in section 4.1. secondly, from the g c , we randomly select a triple and leverage llms to remove the relation between entities in the triple from doc to form doc neg . finally, the ⟨doc neg , c⟩ pair forms a negative sample. inspired by @xcite , we further reduce the dataset size by leveraging roberta-large trained on the multinli dataset, @xcite to select difficult samples. as the nli model predicts each sample from {entailment, contradiction, neutral}, we define a mapping function f (•) for the model output y as: we remove data that roberta mnli foot_0 predicts correctly. musique. we leverage 3-hop and 4-hop data from the musique dataset to diversify from hotpotqa where most of the data is 2-hop. the ⟨doc, c⟩ pairs with c converted from unanswerable ⟨q, ans⟩ pairs are treated as negative samples and answerable pairs are treated as positive samples. similar to hotpotqa, we remove data that roberta mnli predicts incorrectly. merge. we merge synthetically constructed data from hotpotqa and musique into cg2c-mhqa. ## experiments in this section, we compare factcg models with other approaches on grounded factuality datasets. ## evaluation on connected reasoning as qa models suffer from disconnected reasoning, they leverage exploited dataset artifacts to produce correct answers instead of connecting information across multi-hops. we conduct a similar connected reasoning (core) analysis on the multi-hop reasoning chain of trained grounded factuality models similar to @xcite . we would like to answer the research question: rq5: does factcg has more connected reasoning than models not trained on cg2c datasets?