Explainable Hallucination through Natural Language Inference Mapping
Authors: Wei-Fan Chen, Zhixue Zhao, Akbar Karimi, Lucie Flek
Accepted at: acl25

Explainable Hallucination through Natural Language Inference Mapping

Wei-Fan Chen1,3   Zhixue Zhao2   Akbar Karimi1,3   Lucie Flek1,3
1Bonn-Aachen International Center for Information Technology, University of Bonn, Germany
2Computer Science School, University of Sheffield, United Kingdom
3Lamarr Institute for Machine Learning and Artificial Intelligence, Germany
chen@bit.uni-bonn.de

Abstract

Large language models (LLMs) often generate hallucinated content, making it crucial to identify and quantify inconsistencies in their outputs. We introduce HaluMap, a post-hoc framework that detects hallucinations by mapping entailment and contradiction relations between source inputs and generated outputs using a natural language inference (NLI) model. To improve reliability, we propose a calibration step leveraging intra-text relations to refine predictions. HaluMap outperforms state-of-the-art NLI-based methods by five percentage points compared to other training-free approaches, while providing clear, interpretable explanations. As a training-free and model-agnostic approach, HaluMap offers a practical solution for verifying LLM outputs across diverse NLP tasks. The resources of this paper are available at https://github.com/caisa-lab/ac125-halumap.

1 Introduction

Despite their advanced capabilities in generating fluent and human-like texts, Large Language Models (LLMs) are still limited by their hallucination problem (Augenstein et al., 2024; Huang et al., 2025), where LLMs generate text containing fabricated information, factuality hallucinations, or inconsistent with the input, faithfulness hallucinations (Maynez et al., 2020). Hallucination in LLMs occurs in many NLP applications, particularly evident in summarization, where models may generate summaries that are partially or entirely unsupported by the source document (Maynez et al., 2020). Accurately identifying and quantifying these hallucinated segments within the summary is crucial not only to improve the reliability of LLM outputs but also to enable targeted revisions for enhanced accuracy and trustworthiness in practical deployments.

In particular, we are interested in the faithfulness hallucination, where the generated output misses logical consistency compared to the input (Huang et al., 2025). To find such (in)consistency, many existing methods use NLI to approach the faithfulness hallucination (Falke et al., 2019; Goyal and Durrett, 2020; Laban et al., 2022), where they mainly use the entailment or contradiction probabilities from an NLI model to capture the consistency or the inconsistency between a document and its summary. While such NLI approaches successfully capture the overall hallucination in general, it is still unclear which parts of the summary are hallucinated as shown in Figure 1(a).

To close the gap, we propose HaluMap, a framework designed to build heatmap-like relations between the source input and the generated output for faithful hallucination detection. As shown in Figure 1(b), HaluMap highlights the hallucinated sections of the summary, thereby enhancing the explainability of the hallucination detection tasks. HaluMap operates by first decomposing the source and the output into segments. It then employs an NLI model to examine the entailment and contradiction relations between any two segments. The two relations enable the identification of sections in the texts that do not align, indicating potential hallucinations. To enhance the precision of entailment

![Vanilla NLI visualization and Calibrated HaluMap visualization showing hallucination detection](page_1012_370_388_246.png)

Figure 1: (a) Vanilla NLI visualization doesn’t reveal where the hallucination is. (b) Calibrated HaluMap shows that the 6th sentence in the summary is hallucinated in context of the given document. Higher values indicate hallucinations.
and contradiction relations as mentioned, we introduce SelfHaluMap, which computes the HaluMap within the same text, i.e. within the source document. This self-referential analysis serves as a calibration mechanism, effectively filtering out background noise and ensuring that highlighted discrepancies accurately reflect genuine inconsistencies.

Our approach achieves a five-percentage-point improvement over state-of-the-art NLI-based, training-free methods in detecting hallucinations across various tasks, including summarization, dialogue generation, and question answering. Moreover, HaluMap, as a training-free method, outperforms several supervised training methods while providing interpretable results through the entailment and contradiction scores for segments.

2 Related Work

Several works have used NLI as a tool to detect hallucinations (Goyal and Durrett, 2020; Laban et al., 2022; Chrysostomou et al., 2024). For instance, Laban et al. (2022) divide both the document and summary into sentences and using an NLI matrix, they find that using both entailment and contraction probabilities for each pair leads to boosts in performance. In addition, they introduce a benchmark for inconsistency detection in summarization and carry out the NLI score calculation on the sentence level. Similarly, Goyal and Durrett (2020) break down the hypotheses into dependency arcs and measure the entailment of each resulting relation with the source document.

Migrating from pre-trained encoder models to large language models, Yang et al. (2024) utilize ChatGPT variants as the scoring tool. Dhuliawala et al. (2023) propose the chain of verification technique which makes the LLM correct a hallucinated answer by asking simpler additional questions that are easier for the model to answer. Min et al. (2023) break down generated biographies by LLMs into atomic facts and propose a score for evaluating the factuality of an LLM generation based on the number of correct atomic facts that the language model has generated. Similarly, Mündler et al. (2023) use an LLM with the Chain-of-Thought (CoT) prompting (Wei et al., 2022) to detect self-contradictory sentences. In addition, prompting ChatGPT (OpenAI, 2022), Luo et al. (2023) show that it can detect hallucinations in summaries in a zero-shot setting and CoT prompting further improves its performance. Farquhar et al. (2024) cluster factoids in the LLM responses using semantic entropy and bidirectional entailment, identifying the clusters with lower semantic entropy as likely confabulations. While previous work has explored various ways to detect inconsistencies, an explainable component in these modes is lacking. Our approach consists of an explainable map that highlights the detected inconsistencies.

Besides detecting hallucination, previous work aimed to reduce the hallucination in the generated output. Approaches include modifying the LLM distribution of output to improve the context consistency (Shi et al., 2024) or leveraging knowledge bases to identify hallucination and further guide the generation process (Choi et al., 2023). For example, Chen et al. (2024) use references to generate more faithful outputs in an autoencoder-based model, where they also map the NLI relations to hallucination.

3 Method

Our method consists of two stages: 1) building an NLI map of the two inputs, e.g. a document and its summary; and 2) calibrating the NLI map. Using the NLI map, we can then compute the overall hallucination strength as well as visualize the hallucinated parts of the text (see Figure 2).

3.1 Building NLI Matrix

Given a document \( d = [d_1, d_2, ..., d_M] \) and an associated text \( t = [t_1, t_2, ..., t_N] \) (e.g. a summary of \( d \)), let \( M \) and \( N \) be the numbers of textual segments in \( d \) and \( t \), respectively. We apply an NLI model\(^1\) predicting the relationship (i.e. entailment, neutral, or contradiction) between each pair of segments (\( d_m, t_n \)), where \( m \) and \( n \) are the index of \( d \) and \( t \). A text segment can be a paragraph, sentence, or clause, depending on the task and the application.

![Overview of the proposed HaluMap and calibrated HaluMap.](page_1012_186_377_246.png)

Figure 2: Overview of the proposed HaluMap and calibrated HaluMap.

\(^1\)microsoft/deberta-large-mnli
The three scores, ent_{m,n}, neu_{m,n}, and con_{m,n} sum to one. After computing these scores for all segment pairs, we construct a three-dimensional NLI matrix \( \mathbb{N} \in \mathbb{R}^{M \times N \times 3} \), where the last dimension corresponds to the three scores.

3.2 Calibrating NLI Matrix

While the initial NLI matrix can be used directly to identify which segment pair of the document and the text are not aligning with each other (i.e. which segment within t is hallucinated), we found that using the matrix directly does not effectively indicate hallucinated segments. As illustrated in Figure 1(a), it is not visible which segments are likely to be hallucinated.

Therefore, we propose calibrating the NLI matrix using a *self-NLI matrix*. The intuition behind this is that, within one document, there are unlikely contradicted parts, and any two text segments in one document should have an NLI relation of entailment or neutral. With this in mind, we build a self-NLI matrix within one document. We construct a self-NLI matrix \( \mathbb{N}_{self} \in \mathbb{R}^{M \times M \times 3} \) via computing any two text segments of . Figure 4 in Appendix A.2 shows the contradiction matrix of a document, where the red spots demonstrate the contradiction. Such a phenomenon could be the result of an unreliable NLI model, or some inherent feature of the text. To reduce the impact of such an issue, we first compute an average vector of \( \mathbb{N}_{self} \) along one of its second axes. The averaged vector \( \bar{\mathbb{N}}_{self} \in R^{M,3} \) presents an inherent contradiction value of each text segment. Then, we compute the calibrated NLI matrix \( \tilde{\mathbb{N}} \) where each element of it for one NLI score s is: \( \tilde{\mathbb{N}}_{m,n,s} = \mathbb{N}_{m,n,s} - \bar{\mathbb{N}}_{self,m,s} \), meaning that each element of \( \tilde{\mathbb{N}} \) is subtracted by its background noise. After the subtraction, the calibrated NLI matrix keeps its shape as [M, N, 3]. As shown in Figure 1(b), the calibrated NLI matrix can now be used in the later process.

3.3 Overall Hallucination Strength

To estimate the overall hallucination, Laban et al. (2022) proposed to rely on the entailment values of the NLI matrix . In practice, they first find out the maximum entailment values among all sentences of d in \( t_n \) , and then apply a mean operator on the resulting vector. Following the notation used in Laban et al. (2022), the final entailment strength is *mean(max(\( \mathbb{N}_e \), axis = 0), axis = 1)*, where \( \mathbb{N}_e \) is the entailment NLI matrix. Conceptually, this equation can be seen as the average pooling of the maximum pooling of \( \mathbb{N}_e \). Laban et al. (2022) only tested on the entailment values \( \mathbb{N}_e \). We suggest the final contradiction strength to be *max(max(\( \mathbb{N}_c \), axis = 0), axis = 1)*, where \( \mathbb{N}_c \) is the contradiction NLI matrix.

The intuition for choosing the two operations for the entailment value is as follows. From t’s perspective, as long as one part of d can entail \( t_n \), \( t_n \) can be seen as entail (or consistent). Therefore, the first operation should be maximum to find out the most likely entailed part and its entailment value. Given that all segments are considered to be equally important, the second operation should be mean.

For the contradiction values, a segment \( t_n \) is hallucinated (contradicted with d), as long as any segments in d contradict \( t_n \). Therefore, the first operation is taking the maximum. Second, we consider t to be hallucinated even if just part of it is hallucinated. Hence, the second operation should be maximum as well\footnote{Other combinations of operations can be found in A.1.}.

4 Experiments and Results

4.1 Baselines

We compare our method with state-of-the-art related approaches that utilize NLI. We briefly described their approach in Section 2: MNLI-doc uses RoBERTa (Liu et al., 2019) fine-tuned on MNLI (Williams et al., 2018). DAE (Goyal and Durrett, 2020) uses ELECTRA (Clark et al., 2020) to obtain NLI scores (Laban et al., 2022) while SIFiD (Yang et al., 2024) uses LLMs (ChatGPT 3.5/4 Turbo). Given the size of our utilized DeBERTa model (He et al., 2020), and for a fair comparison, we compare our results with their results from ChatGPT 3.5 Turbo. SummaC (Laban et al., 2022) is a benchmark for inconsistency detection, using BERT-base and BERT-large models (Devlin et al., 2019). In addition to these models, we compare our results with ChatGPT in zero-shot and zero-shot with CoT prompting.

4.2 Datasets

To fully test HaluMap, we consider SummaC (Laban et al., 2022), HaluEval (Li et al., 2023), and LLM-AggrFact datasets (Tang et al., 2024), the experiment settings are as follows.

SummaC consistent label means not hallucination and the inconsistent label means hallucination.
<table>
  <tr>
    <th>Model Name</th>
    <th>CGS</th>
    <th>XSF</th>
    <th>Poly</th>
    <th>FactCC</th>
    <th>Frank</th>
    <th>Avg.</th>
  </tr>
  <tr>
    <td>MNLI-doc</td>
    <td>57.6</td>
    <td>57.5</td>
    <td>61.0</td>
    <td>61.3</td>
    <td>63.6</td>
    <td>61.3</td>
  </tr>
  <tr>
    <td>DAE</td>
    <td>63.4</td>
    <td>50.8</td>
    <td>62.8</td>
    <td>75.9</td>
    <td>61.7</td>
    <td>64.2</td>
  </tr>
  <tr>
    <td>SIFiD-Ent</td>
    <td>65.5</td>
    <td>63.9</td>
    <td>37.5</td>
    <td>81.0</td>
    <td>81.6</td>
    <td>68.1</td>
  </tr>
  <tr>
    <td>SIFiD-Ent<sub>CoT</sub></td>
    <td>65.7</td>
    <td>60.3</td>
    <td>52.7</td>
    <td>82.3</td>
    <td>81.6</td>
    <td>70.3</td>
  </tr>
  <tr>
    <td>SummaC<sub>ZS</sub></td>
    <td>70.4</td>
    <td>58.4</td>
    <td>62.0</td>
    <td>83.8</td>
    <td>79.0</td>
    <td>70.7</td>
  </tr>
  <tr>
    <td>ChatGPT<sub>ZS</sub></td>
    <td>63.3</td>
    <td>64.7</td>
    <td>56.9</td>
    <td>74.7</td>
    <td>80.9</td>
    <td>69.5</td>
  </tr>
  <tr>
    <td>ChatGPT<sub>ZS-CoT</sub></td>
    <td>74.3</td>
    <td>63.1</td>
    <td>61.4</td>
    <td>79.5</td>
    <td><b>82.6</b></td>
    <td>74.0</td>
  </tr>
  <tr>
    <td>HaluMap<sub>e</sub></td>
    <td><b>74.9</b></td>
    <td><b>66.8</b></td>
    <td>61.8</td>
    <td>86.3</td>
    <td>80.7</td>
    <td>74.4</td>
  </tr>
  <tr>
    <td>HaluMap<sub>e</sub> (Cal.)</td>
    <td>76.5</td>
    <td>66.3</td>
    <td><b>66.2</b></td>
    <td><b>89.5</b></td>
    <td>80.6</td>
    <td><b>75.8</b></td>
  </tr>
</table>

Table 1: Balanced accuracies of the baselines, SummaC, and our approach (HaluMap) with the entailment values.

<table>
  <tr>
    <th>Benchmark</th>
    <th>Dataset</th>
    <th>Size</th>
    <th>% Hallu.</th>
  </tr>
  <tr>
    <td rowspan="4">SummaC</td>
    <td>CGS</td>
    <td>400</td>
    <td>50.2</td>
  </tr>
  <tr>
    <td>XSF</td>
    <td>1250</td>
    <td>89.8</td>
  </tr>
  <tr>
    <td>Poly</td>
    <td>634</td>
    <td>93.4</td>
  </tr>
  <tr>
    <td>FactCC</td>
    <td>503</td>
    <td>15.0</td>
  </tr>
  <tr>
    <td>FRANK</td>
    <td>1575</td>
    <td>66.8</td>
  </tr>
  <tr>
    <td rowspan="3">HaluEval</td>
    <td>Summarization</td>
    <td>20,000</td>
    <td>50.0</td>
  </tr>
  <tr>
    <td>Dialogue w/ history</td>
    <td>20,000</td>
    <td>50.0</td>
  </tr>
  <tr>
    <td>QA w/ Knowledge</td>
    <td>20,000</td>
    <td>50.0</td>
  </tr>
  <tr>
    <td rowspan="8">LLM-AggreFact</td>
    <td>AggreFact-CNN</td>
    <td>558</td>
    <td>10.2</td>
  </tr>
  <tr>
    <td>AggreFact-XSum</td>
    <td>558</td>
    <td>48.9</td>
  </tr>
  <tr>
    <td>TofuEval-Media</td>
    <td>726</td>
    <td>23.7</td>
  </tr>
  <tr>
    <td>TofuEval-MeetB</td>
    <td>772</td>
    <td>19.4</td>
  </tr>
  <tr>
    <td>Wice</td>
    <td>358</td>
    <td>68.9</td>
  </tr>
  <tr>
    <td>Reveal</td>
    <td>1710</td>
    <td>76.7</td>
  </tr>
  <tr>
    <td>ClaimVerify</td>
    <td>1088</td>
    <td>27.5</td>
  </tr>
  <tr>
    <td>FactCheck</td>
    <td>1566</td>
    <td>75.0</td>
  </tr>
  <tr>
    <td>ExpertQA</td>
    <td>3702</td>
    <td>19.7</td>
  </tr>
  <tr>
    <td>LFQA</td>
    <td>1911</td>
    <td>41.3</td>
  </tr>
</table>

Table 2: Number of instances and percentage of hallucination in SummaC, HaluEval, and the test set of LLM-AggreFact. Note that Summeval from SummaC was discard in the experiments.

<table>
  <tr>
    <th>Model Name</th>
    <th>Sum.</th>
    <th>Dialogue</th>
    <th>QA</th>
    <th>Avg.</th>
  </tr>
  <tr>
    <td>ChatGPT (gpt-3.5-turbo)</td>
    <td>58.5</td>
    <td><b>72.4</b></td>
    <td>62.6</td>
    <td>64.5</td>
  </tr>
  <tr>
    <td>Llama3-8b</td>
    <td>56.9</td>
    <td>62.8</td>
    <td>49.8</td>
    <td>56.5</td>
  </tr>
  <tr>
    <td>SummaC<sub>ZS</sub></td>
    <td>62.1</td>
    <td>56.0</td>
    <td>65.5</td>
    <td>61.2</td>
  </tr>
  <tr>
    <td>HaluMap<sub>e</sub></td>
    <td>72.7</td>
    <td>64.7</td>
    <td>69.3</td>
    <td>68.9</td>
  </tr>
  <tr>
    <td>HaluMap<sub>e</sub> (Cal.)</td>
    <td><b>73.3</b></td>
    <td>65.2</td>
    <td><b>69.7</b></td>
    <td><b>69.4</b></td>
  </tr>
</table>

Table 3: Accuracies of the baselines, Llama3-8b, SummaC by running their codes ourselves, and our approach (HaluMap) on the three HaluEval subsets (summarization, dialogue generation and QA).

In our experiments, we follow the setting in SummaC. The statistics for this dataset can be found in Table 2. The utilized datasets from SummaC are as follows: CGS contains articles from the CNN/DM dataset (Nallapati et al., 2016) and model-generated summaries (Falke et al., 2019). XSF (Maynez et al., 2020) is a collection of human-annotated abstractive summaries from XSum (Narayan et al., 2018). Both extrinsic and intrinsic hallucination are considered. Poly includes summaries from the CNN/DM dataset with eight different errors (Huang et al., 2020). We consider accuracy errors to be the inconsistent label. FactCC (Kryściński et al., 2020) also comprises summaries from the CNN/DM dataset. It comes with a test split where the consistent and inconsistent labels are annotated by the authors. FRANK (Pagnoni et al., 2021) contains summaries from both CNN/DM and XSum articles. Summaries are considered to be consistent if a majority of the annotations of the summary contain no error. We consider accuracy errors to be the inconsistent label.

HaluEval contains three specific tasks, namely summarization, question answering, and dialogue generation (Li et al., 2023). The authors used ChatGPT to label the hallucination answers. There are 10,000 instances per task to form 20,000 article-summary pairs pairs (10,000 with valid summaries and 10,000 containing hallucinations.

LLM-AggreFact is one of the largest collections of studying hallucination in LLMs (Tang et al., 2024). It contains summaries (AggreFact and TofuEval), responses to search queries (ClaimVerify, LFQA, ExpertQA, Reveal, and FactCheck-GPT), as well as Wikipedia claims (Wice). In our experiments, we treat their negative label as hallucination, and we use only the test set for a fair comparison.

4.3 Experiments on SummaC Benchmarks

Table 1 shows the balanced accuracies of HaluMap as well as baselines on the SummaC benchmarks. Overall, calibrated HaluMap (75.8%) has a five-percentage-point improvement against the SummaC-zero-shot approach (70.7%), and it even achieves better performance compared to ChatGPT with CoT prompting. Comparing HaluMap with calibrated HaluMap, they achieve very similar performance and the main difference is in the Polytype and FactCC datasets, where calibrated HaluMap has around three percentage points improvement on both datasets. Given that these two datasets are the most skewed ones (93.4% hallucination and 15% hallucination), it suggests that the calibrated HaluMap is more robust on the imbalanced distributed datasets.
<table>
  <tr>
    <th>Model Name</th>
    <th colspan="2">AggreFact</th>
    <th colspan="2">TofuEval</th>
    <th>Wice</th>
    <th>Reveal</th>
    <th>Claim Verify</th>
    <th>Fact Check</th>
    <th>Expert QA</th>
    <th>LFQA</th>
    <th>Avg.</th>
  </tr>
  <tr>
    <th></th>
    <th>CNN</th>
    <th>XSum</th>
    <th>MediaS</th>
    <th>MeetB</th>
    <th></th>
    <th></th>
    <th></th>
    <th></th>
    <th></th>
    <th></th>
    <th></th>
  </tr>
  <tr>
    <td>SummaC<sub>ZS</sub></td>
    <td>51.1</td>
    <td>61.5</td>
    <td>69.5</td>
    <td>71.0</td>
    <td>62.8</td>
    <td>85.3</td>
    <td>69.7</td>
    <td>75.2</td>
    <td>55.2</td>
    <td>77.6</td>
    <td>67.9</td>
  </tr>
  <tr>
    <td>MiniCheck-FT5</td>
    <td><b>69.9</b></td>
    <td><b>74.3</b></td>
    <td><b>73.6</b></td>
    <td><b>77.3</b></td>
    <td><b>72.2</b></td>
    <td><b>86.2</b></td>
    <td><b>74.6</b></td>
    <td><b>74.7</b></td>
    <td><b>59.0</b></td>
    <td><b>85.2</b></td>
    <td><b>74.7</b></td>
  </tr>
  <tr>
    <td>HaluMap<sub>e</sub></td>
    <td>65.1</td>
    <td>60.5</td>
    <td>66.2</td>
    <td>65.8</td>
    <td>63.2</td>
    <td>81.9</td>
    <td>73.3</td>
    <td>68.9</td>
    <td>56.9</td>
    <td>76.0</td>
    <td>67.8</td>
  </tr>
  <tr>
    <td>HaluMap<sub>e</sub> (Cal.)</td>
    <td>67.7</td>
    <td>65.2</td>
    <td>65.8</td>
    <td>67.4</td>
    <td>67.1</td>
    <td>85.4</td>
    <td>73.2</td>
    <td>71.4</td>
    <td>56.3</td>
    <td>76.1</td>
    <td>69.6</td>
  </tr>
</table>

Table 4: Balanced accuracies of the SummaC, MiniCheck-FT5, and our approach (HaluMap) with the entailment values on the test set of LLM-AggreFact. Except the HaluMap results, other results are directly from the original LLM-AggreFact paper.

4.4 Experiments on HaluEval

In Table 3, we compare HaluMap with SummaC using their codebase\footnote{https://github.com/tingofurro/summac/}, ChatGPT gpt-3.5-turbo from Li et al. (2023), and Llama3-8b from Chekalina et al. (2024)—the most recent, best approach on HaluEval. Overall, HaluMap outperforms other baselines by at least 5 percentage points. However, ChatGPT outperforms HaluMap in dialogue generation. Given that ChatGPT was developed as an AI agent, it is not surprising that the developers may further focus on its abilities in dialogue generation. Comparing HaluMap with the calibrated HaluMap, they have similar performance on the three tasks, and the latter is slightly better in all three cases.

4.5 Experiments on LLM-AggreFact

In Table 4, we compare HaluMap with the best variation of MiniCheck (MiniCheck-FT5) on the LLM-AggreFact dataset. We observe a similar trend in other datasets: HaluMap performs close to SummaC<sub>ZS</sub> while the calibrated HaluMap outperforms its non-calibrated variation. Given that MiniCheck requires training, it achieves the best performance in all subsets, as expected. Still, we argue that the calibrated HaluMap is the best-performing among all the training-free models.

5 Qualitative Analysis

We conducted a qualitative analysis to gain a better insight into the calibrated HaluMap. In Figure 3, we show a vanilla HaluMap of contradiction, an average vector of self-HaluMap \( \bar{N}_{self} \), and the calibrated HaluMap where the summary is labeled as non-hallucination. We found that the sentence *Psychology can explain why somebody would turn rage inward on themselves about the fact* contradicts many other sentences in the document (Appendix A.3). These high contradiction values can be seen as the by-product of NLI models. Therefore, calibrating these values can further improve the pooling process when computing the overall hallucination strength. It can also benefit in spotting the possible hallucination sentences in the document. In this example, using vanilla HaluMap would wrongly get a high contradiction due to some high values in the map. On the other hand, calibrated HaluMap has a lower overall contradiction value after pooling.

![Three bar plots showing HaluMap vectors for different conditions](page_1012_682_388_246.png)

Figure 3: (a) The vanilla contradiction HaluMap of a non-hallucination document-summary pair. (b) The average self-HaluMap of contradiction shows that a few sentences (especially the second-to-last sentence) have a very high average contradiction against other sentences. (c) The calibrated HaluMap shows there is almost no contradiction in any place. More red indicates hallucinations.

6 Conclusion

We introduced HaluMap, a post-hoc framework that enhances explainability in hallucination detection. HaluMap is a metric based on an informed calibration of NLI outcomes and it outperforms existing NLI-based methods with improved hallucination detection performance as well as a clearer visual interpretation. By providing interpretable explanations without requiring model access, HaluMap serves as a practical tool for verifying model outputs across various NLP tasks.
7 Limitations

This paper only studies one certain type of hallucination: faithfulness. There exists also factuality (Augenstein et al., 2024), and intrinsic or extrinsic hallucinations (Maynez et al., 2020). We expect the proposed method to also apply to these definitions of hallucinations as long as we can define the entailment and/or the contradiction relation in these definitions. The scope of this paper covers a limited number of tasks, namely summarization, question answering, and dialogue generation. Hallucination also exists in other text generation tasks, for which this study can be extended if suitable datasets become available.

8 Ethical Concerns

The hallucination in LLMs itself draws the attention of ethical concerns in using LLMs. However, this paper focuses on how to better combat and explain hallucinations with interpretable methods. With the proposed method, we hope to better reveal the hallucinations in specific text segments, contribute to a better understanding of hallucinations, and therefore, help to mitigate the ethical concerns of using LLMs.

Acknowledgments

This work was conducted during Zhixue Zhao’s research visit to the Lamarr Institute for Machine Learning and Artificial Intelligence. We would like to especially thank our colleagues Ipek Baris Schlicht, Shaina Ashraf, and Tianyi Zhang, for their discussions in shaping the idea of this paper. This work was partially supported by the AISafety Project, funded by the BMBF under the grant proposal 05D23PD1, and by the state of North Rhine-Westphalia as part of the Lamarr Institute for Machine Learning and Artificial Intelligence.

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Figure 4: Self-HaluMap of contradiction showing many contradictions (red) in one document.

A Appendix

A.1 Different Pooling Operations
The performance of using different combinations of operations can be in Table 5 and Table 6.

<table>
  <tr>
    <th rowspan="2">2nd Operation</th>
    <th colspan="3">1st Operation</th>
  </tr>
  <tr>
    <th>Max</th>
    <th>Mean</th>
    <th>Min</th>
  </tr>
  <tr>
    <td>Max</td>
    <td>57.6</td>
    <td><b>75.8</b></td>
    <td>62.9</td>
  </tr>
  <tr>
    <td>Mean</td>
    <td>58.9</td>
    <td>61.0</td>
    <td>60.0</td>
  </tr>
  <tr>
    <td>Min</td>
    <td>61.0</td>
    <td>61.3</td>
    <td>58.6</td>
  </tr>
</table>

Table 5: The performance of different pooling operations by using entailment value in SummaC benchmarks.

<table>
  <tr>
    <th rowspan="2">2nd Operation</th>
    <th colspan="3">1st Operation</th>
  </tr>
  <tr>
    <th>Max</th>
    <th>Mean</th>
    <th>Min</th>
  </tr>
  <tr>
    <td>Max</td>
    <td>74.9</td>
    <td>63.8</td>
    <td>50.4</td>
  </tr>
  <tr>
    <td>Mean</td>
    <td>74.1</td>
    <td>65.3</td>
    <td>50.3</td>
  </tr>
  <tr>
    <td>Min</td>
    <td>73.6</td>
    <td>66.8</td>
    <td>50.3</td>
  </tr>
</table>

Table 6: The performance of different pooling operations by using contradiction value in SummaC benchmarks.

A.2 Self-HaluMap
The contradiction values of a self-HaluMap can be found in Figure 4.

A.3 Full Text in the Qualitative Analysis
Table 7 shows the full text in Sec5, including the document, right summary and the hallucinated summary.
Document:
Marseille, France (CNN)The French prosecutor leading an investigation into the crash of Germanwings Flight 9525 insisted Wednesday that he was not aware of any video footage from on board the plane. Marseille prosecutor Brice Robin told CNN that "so far no videos were used in the crash investigation." He added, "A person who has such a video needs to immediately give it to the investigators." Robin's comments follow claims by two magazines, German daily Bild and French Paris Match, of a cell phone video showing the harrowing final seconds from on board Germanwings Flight 9525 as it crashed into the French Alps. All 150 on board were killed. Paris Match and Bild reported that the video was recovered from a phone at the wreckage site. The two publications described the supposed video, but did not post it on their websites. The publications said that they watched the video, which was found by a source close to the investigation. "One can hear cries of 'My God' in several languages," Paris Match reported. "Metallic banging can also be heard more than three times, perhaps of the pilot trying to open the cockpit door with a heavy object. Towards the end, after a heavy shake, stronger than the others, the screaming intensifies. Then nothing." "It is a very disturbing scene," said Julian Reichelt, editor-in-chief of Bild online. An official with France’s accident investigation agency, the BEA, said the agency is not aware of any such video. Lt. Col. Jean-Marc Menichini, a French Gendarmerie spokesman in charge of communications on rescue efforts around the Germanwings crash site, told CNN that the reports were "completely wrong" and "unwanted." "Cell phones have been collected at the site, he said, but that they 'hadn’t been exploited yet.' Menichini said he believed the cell phones would need to be sent to the Criminal Research Institute in Rosny sous-Bois, near Paris, in order to be analyzed by specialized technicians working hand-in-hand with investigators. But none of the cell phones found so far have been sent to the institute. Menichini asked. Asked whether staff involved in the search could have leaked a memory card to the media, Menichini answered with a categorical "no." Reichelt told "Erin Burnett: Outfront" that he had watched the video and stood by the report, saying Bild and Paris Match are "very confident" that the clip is real. He noted that investigators only revealed they’d recovered cell phones from the crash site after Bild and Paris Match published their reports. "That is something we did not know before... Overall we can say many things of the investigation weren’t revealed by the investigation at the beginning," he said. What was mental state of Germanwings co-pilot? German airline Lufthansa confirmed Tuesday that co-pilot Andreas Lubitz had battled depression years before he took the controls of Germanwings Flight 9525, which he’s accused of deliberately crashing last week in the French Alps. Lubitz told his Lufthansa flight training school in 2009 that he had a “previous episode of severe depression,” the airline said Tuesday. Email correspondence between Lubitz and the school discovered in an internal investigation. Lufthansa said, included medical documents he submitted in connection with resuming his flight training. The announcement indicates that Lufthansa, the parent company of Germanwings, knew of Lubitz’s battle with depression, allowed him to continue training and ultimately put him in the cockpit. Lufthansa, whose CEO Carsten Spohr previously said Lubitz was 100% fit to fly, described its statement Tuesday as a “swift and seamless clarification” and said it was sharing the information and documents – including training and medical records – with public prosecutors. Spohr traveled to the crash site Wednesday, where recovery teams have been working for the past week to recover human remains and plane debris scattered across a steep mountainside. He saw the crisis center set up in Seyne-les-Alpes, laid a wreath in the village of Le Vernet, closer to the crash site, where grieving families have left flowers at a simple stone memorial. Menichini told CNN late Tuesday that no visible human remains were left at the site but recovery teams would keep searching. French President Francois Hollande, speaking Tuesday, said that it should be possible to identify all the victims using DNA analysis by the end of the week, sooner than authorities had previously suggested. In the meantime, the recovery of the victims’ personal belongings will start Wednesday, Menichini said. Among those personal belongings could be more cell phones belonging to the 144 passengers and six crew on board. Check out the latest from our correspondents. The details about Lubitz’s correspondence with the flight school during his training were among several developments as investigators continued to delve into what caused the crash and Lubitz’s possible motive for downing the jet. A Lufthansa spokesperson told CNN on Tuesday that Lubitz had a valid medical certificate, had passed all his examinations and “held all the licenses required.” Earlier, a spokesman for the prosecutor’s office in Dusseldorf, Christoph Kumpa, said medical records reveal Lubitz suffered from suicidal tendencies at some point before his aviation career and underwent psychotherapy before he got his pilot’s license. Kumpa emphasized there’s no evidence suggesting Lubitz was suicidal or acting aggressively before the crash. Investigators are looking into whether Lubitz feared his medical condition would cause him to lose his pilot’s license, a European government official briefed on the investigation told CNN on Tuesday. While flying was “a big part of his life,” the source said, it’s only one theory being considered. Another source, a law enforcement official briefed on the investigation, also told CNN that authorities believe the primary motive for Lubitz to bring down the plane was that he feared he would not be allowed to fly because of his medical problems. Lubitz’s girlfriend told investigators he had seen an eye doctor and a neuropsychologist, both of whom deemed him unfit to work recently and concluded he had psychological issues, the European government official said. But no matter what details emerge about his previous mental health struggles, there’s more to the story, said Brian Russell, a forensic psychologist. “Psychology can explain why somebody would turn rage inward on themselves about the fact that maybe they weren’t going to keep doing their job and they’re upset about that and so they’re suicidal,” he said. “But there is no mental illness that explains why somebody then feels entitled to also take that rage and turn it outward on 149 other people who had nothing to do with the person’s problems.” Germanwings crash compensation: What we know. Who was the captain of Germanwings Flight 9525? CNN’s Margot Haddad reported from Marseille and Pamela Brown from Dusseldorf, while Laura Smith-Spark wrote from London. CNN’s Frederik Pleitgen, Pamela Boykoff, Antonia Mortensen, Sandrine Amiel and Anna-Maja Rappard contributed to this report.

Right Summary:
Marseille prosecutor says "so far no videos were used in the crash investigation" despite media reports. Journalists at Bild and Paris Match are "very confident" the video clip is real, an editor says. Andreas Lubitz had informed his Lufthansa training school of an episode of severe depression, airline says.

Hallucination Summary:
A video showing the final moments of Germanwings Flight 9525 has been recovered by investigators from the wreckage site. Marseille prosecutor Brice Robin urged anyone who might have more footage to turn it over immediately. Andreas Lubitz, the co-pilot accused of deliberately crashing the plane, had a history of severe depression and suicidal tendencies.

Table 7: The full document used in Sec 5.

Reviewer paper summaries: This paper proposes a novel method for detecting faithfulness hallucinations using an NLI model. The novel contribution consists in an extra step, where entailment and contradiction scores are calibrated to achieve higher accuracy. An extensive experimental evaluation shows that the method improve over previous NLI-based detection methods.

The paper proposed a post-hoc, training-free and model-agnostic hallucination detection method HaluMap. It calculates the consistency score between each pair of sentences from the generated summary and the document, and the consistency between each pair of sentences within the document. The experimental results and the visualisation analysis demonstrate the effectiveness of the proposed method.
Summary of strengths: - Novel variation on using NLI models to detect faithfulness hallucinations.
- Experimental results demonstrating an improvement over previous approaches.

1. The proposed method is simple and effective.
2. The method is well motivated, and the writing is clear and easy to read.
3. The experimental results on various tasks and datasets demonstrate the effectiveness of the method.
Summary of weaknesses: - Lack of a precise definition of faithfulness hallucination.
- Superficial analysis of the experimental results.

No major weakness that I can spot, and here are some minor questions:
1. The computational cost could be expensive if the documents contain many sentences since it needs to compare the NLI score between each pair of sentences within documents.
2. There could be different approaches to separate the document instead of sentences, e.g., chunks with a fixed length. They may lead to more self-consistent results, not like Figure 4, which would be more reasonable because documents won't always have such low quality.
Comments, suggestions and typos: The term "hallucination" is used in different ways in the literature, and although the authors specify that they are concerned with "faithfulness hallucinations" (as opposed to "factuality hallucinations"), they do not provide a precise definition. Given the method explored in the paper, it would be interesting to know, for example, whether notions of entailment and contradiction are part of the definition. It would also be interesting to know whether the data sets used for evaluation are based on the same definition, or whether there is variation.

The qualitative analysis in Section 5 is somewhat disappointing, as it consists mainly of a figure illustrating uncalibrated and calibrated NLI scores from a single example, and we have no way of knowing how representative this example is. Given that some of the data sets contain different error types, one could at least expect a breakdown of scores over error types, or some other insightful error analysis.

Minor comments:
- It is slightly confusing that the symbol "s" (presumably for "summary") is used in Figure 2, illustrating the method, while the symbol "t" (for "text") is used for the same thing (?) in the text (for example, in Section 3.1).
- Typo: "handfor" -> "hand for" (page 3).

Comments after author discussion

The authors have responded to my questions in a way that has confirmed my initial assessment of the paper.

Please see weaknesses.
Overall assessment scores: 3.5

3.5
Metareview score: 3.5
Metareview: The paper introduces HaluMap, a post-hoc framework for identifying hallucinations in LLM-generated text using NLI.  Reviewers find the method promising, but raise concerns about computational cost, the scope of empirical validation, and clarity in defining "faithfulness hallucination." The authors have committed to addressing these concerns with more experiments, comparisons, and clearer explanations.
Summary of reasons to publish: The paper presents a novel and effective approach to an important problem (hallucination detection). The method is training-free, model-agnostic, and offers interpretability. The authors have committed to addressing the reviewers' concerns, which will strengthen the paper.