Multi-Evidence based Fact Verification via A Confidential Graph Neural Network

Previous research on the fact verification task adapts existing Natural Language Inference (NLI) models to predict the label of the given claim [23, 35, 36, 37, 38, 39, 40, 24, 41]. The NLI task aims to classify the relationship between a pair of premises and hypotheses as entailment, contradiction, or neutral, similar to the fact verification task. One of the most commonly used models is the Enhanced Sequential Inference Model (ESIM) [42] and its variants.

Recently, pre-trained language models (PLMs) [43, 25, 44, 45, 46] have shown their strong effectiveness in fact verification [47, 48]. Some researchers directly use language models to verify claims without any evidence [49]. Other researchers use the Retrieval-augmented generation (RAG) methods for fact verification tasks [50, 51]. They use a retriever to retrieve claim-related evidence, and then integrate the claim and evidence knowledge into the generation task to verify the claim. Then, some researchers use data augmentation methods to train on the generated datasets based on the FEVER dataset to improve the effectiveness of claim verification [52, 53]. Most fact verification systems use pre-trained language models to encode the claim and the evidence [54, 55]. Then they combine attention mechanisms [55, 56] or some neural network architectures [54, 57] to construct classification layers for label prediction.

In addition, some claim verification models are formulated based on logical rules of language. LOREN [28] decomposes the claim into a series of phrases and then uses the logical aggregation rules to validate the phrases and predict the claim label. ProoFVer [58] uses a seq2seq model to generate a natural logic proof to verify the claim. CLEVER [57] utilizes counterfactual theory to achieve claim verification by mitigating bias introduced from solely relying on claims for prediction during the inference stage.

Other works adopt graph-based modeling methods for multi-evidence reasoning. An early attempt to use a graph-based reasoning model for fact verification is GEAR [27], which regards the evidence-claim pair as a graph node to construct a fully connected evidence graph. It proposes an evidence reasoning network, similar to a graph attention neural network [32] to propagate evidence information. Then, KGAT [26] proposes a fine-grained fact verification model based on a kernel graph attention neural network. It utilizes both token-level and sentence-level kernel attention mechanisms to capture fine-grained evidence information for claim verification. EvidenceNet [59] utilizes the evidence fusion network to capture different levels of global contextual information filtered by the gating mechanism. ICMI [60] is inspired by the multi-relational graph convolutional network and then uses dual evidence fusion graphs to capture multi-view information within and between documents, thereby solving the problem of multi-hop fact verification. CGAT [61] constructs a phrase-level graph by introducing a knowledge graph to obtain a node representation with detailed semantic information and then uses the graph attention network (GAT) model for inference. FACTKG [18] creates a dataset by using a knowledge graph, which provides an evidence graph composed of entities and entity relations. It uses GEAR [27] for factual verification reasoning.

In addition, some work introduces semantic graphs for factual verification. It uses the semantic role labeling (SRL) toolkit to parse the evidence sentences into $n$ structural relation triples as the nodes. DREAM [62] constructs semantic graphs for claim and evidence, which encodes them using the XLNET model [46]. Meanwhile, it uses graph convolutional network (GNN) [63] and the GAT model to propagate and aggregate evidence information. GLAF [64] constructs an evidence graph based on triple-level nodes. It combines the local fission reasoning layer and global evidence aggregation layer to establish logical relations between clues, share information, and exchange evidence clues for claim verification. RoEG [65] uses an entity recognizer to extract entities from the evidence. It then constructs an entity graph to capture fine-grained evidence features and semantic relations. SISER [29] incorporates sentence-level graph reasoning, sequence reasoning, and semantic graph reasoning to verify the claim.

The CO-GAT model uses the retrieved evidence $E=\{e_{1},e_{2},\dots,e_{i}\}$ and the given claim $c$ to construct the evidence reasoning graph $G$ for the fact verification task.

Node Encoding. The node representation is initialized by feeding the concatenated sequence to the pre-trained language models, such as ELECTRA [66] and RoBERTa [43].

where $\circ$ denotes the concatenation operation. As shown in Fig. 2, $e_{p}$ contains the retrieved evidence sentence and the document (Wiki) title. Both “[CLS]” and “[SEP]” are special tokens in the pre-trained language models, such as ELECTRA and RoBERTa. We take the last hidden state of the “[CLS]” token as the initial node representation $h_{p}$ of the node $n_{p}$.

Graph Reasoning. Following the previous work [27, 32], the evidence reasoning graph uses the edge attention mechanism to propagate evidence information and the node attention mechanism to aggregate node information for claim prediction.

For the edge attention mechanism, each node receives attention from neighbor nodes and uses this attention score to aggregate semantic information from neighbor nodes to update the node representation. CO-GAT utilizes the multi-head attention mechanism [67] to construct the edge attention mechanism. Specifically, the scaled dot product attention model is used to calculate the edge attention:

where $\alpha_{i}^{q\rightarrow p}$ represents the $i$-th head edge attention that the node $n_{q}$ receives from the node $n_{p}$. The weight matrix $W_{i}^{Q},W_{i}^{K}\in\mathcal{R}^{d_{m}\times d_{k}}$. $d_{k}$ represents the dimension of each head, which is calculated by Eq. 3. $d_{m}$ denotes the hidden size of the pre-trained language models. $\#head$ represents the number of attention heads.

Subsequently, the node $n_{p}$ uses the edge attention score $\alpha_{i}^{q\rightarrow p}$ to aggregate the semantic information from neighbor nodes. CO-GAT concatenates the node representation $v^{i}(h_{p})$ obtained from each attention head as the updated node representation $v(h_{p})$:

where $W_{i}^{V}\in\mathcal{R}^{d_{m}\times d_{k}}$. Through the edge attention mechanism, each node obtains semantic information from the neighbor nodes. Consequently, the node attention mechanism assigns each node with an attention weight to aggregate the semantic information of graph nodes for claim verification. We use the Eq. 6 to calculate the node attention score $\beta_{p}$ of the node $n_{p}$:

Then, we employ the node aggregator to gather the semantic information from all graph nodes to get the final hidden state $V$:

Label Prediction. The factual classification label $y_{c}$ of the given claim $c$ is predicted according to the probability $P(y_{c}|c,E)$:

where the labels $y_{c}$ are categorized into three classes: 0, 1, and 2, representing SUPPORTS, REFUTES, and NOT ENOUGH INFO, respectively. These labels signify whether the provided evidence supports, refutes, or lacks sufficient information to predict the claim.

Next, in Sec. III-B, we introduce a node masking mechanism to erase the noise semantic information before feeding the node representations to graph reasoning. Subsequently, we employ the multi-task modeling method outlined in Section III-C to train the CO-GAT model.

The task of fact verification requires the utilization of multiple pieces of evidence for reasoning. However, the retrieval evidence pieces inevitably contain noise information. As the attention layer deepens, the node representation tends to become homogeneous [68, 69]. Therefore, the noise semantic information is easily captured by other nodes during graph reasoning, consequently affecting the representation learning of the graph nodes. Therefore, the CO-GAT model proposes a node masking mechanism to erase the noise information from the initial node representations and alleviate the noisy semantic information propagated in the graph neural network.

The model assesses the confidence score (CO-SCO) of nodes and adjusts the information flow of blank nodes according to this score. This process aims to conduct the denoised node presentation $\widetilde{h}_{p}$ of the node $n_{p}$ by adding the representation of blank node to the initial node representations using CO-SCO:

where $h_{b}$ is the node representation of the blank node $n_{b}$. The blank node $n_{b}$ only contains the claim $c$ without any evidence. Similarity to Eq. 1, we utilize the same pre-trained language model for encoding the node $n_{b}$.

The confidence score (CO-SCO) can be calculated:

where $\text{CO-SCO}\in[0,1]$. The $y_{e_{p}}=1$ indicates that the model recognizes the given evidence $e_{p}$ as the golden evidence for the claim $c$. CO-SCO represents the relevance between the claim $c$ and evidence $e_{p}$. A higher confidence score indicates that the evidence piece is more effective in supporting or refuting the claim, indicating the necessity to retain more semantic information from the initial node representation.

The CO-GAT model utilizes a multi-task training strategy, in which the final loss function $L$ consists of two loss functions: the cross entropy loss function $L_{fact}$ for claim verification, and the cross entropy loss function $L_{evi}$ for node prediction:

Claim Verification Loss. The claim verification model can be trained by minimizing the cross entropy loss with the claim prediction label $y_{c}$:

where $y_{c}^{*}$ is the ground truth verification label for the given claim $c$. The labels $y_{c}^{*}$ and $y_{c}$ can categorized into three classes, representing SUPPORTS, REFUTES, and NOT ENOUGH INFO, respectively.

To obtain the prediction label $y_{c}$, CO-GAT employs the graph attention network as the reasoning model to integrate the evidence information:

The final hidden state $\widetilde{V}$ of the evidence graph is obtained by Eq. 7 using the denoised node representation $\widetilde{h}_{p}$ (Eq. 9):

Node Prediction Loss. For each node in the evidence graph, we predict its confidential label $y_{e}$. we minimize the node prediction loss $L_{evi}$ to help language models judge the relevance between claims-evidence pair and predict the node confidence score:

where $y_{e_{p}}^{*}$ denotes the ground truth confidence label for the graph node $n_{p}$. $y_{e_{p}}^{*}$ and $y_{e_{p}}$ can be categorized into two groups: 0 and 1, signifying whether the provided evidence can provide sufficient clues to verify the claim. The claim-evidence relevance probability is calculated:

where $h_{p}$ denotes the initial node representation of node $n_{p}$.

In our experiments, we leverage the FEVER [70] dataset and SCIFACT [8] dataset, which focuses on the general domain and the science-specific domain, respectively. They are publicly available collections for the fact verification task. FEVER employs Wikipedia as its trustworthy corpus for claim verification. It comprises 185,455 annotated claims classified into SUPPORTS, REFUTES, or NOT ENOUGH INFO categories. SCIFACT comprises 1,409 annotated claims sourced from 5,183 scientific articles. These claims are categorized as SUPPORT, CONTRADICT, or NOT ENOUGH INFO. The data statistics of the FEVER dataset and the SCIFACT dataset are shown in TABLE I.

Similar to the previous fact verification systems [28, 29], our experiment employs the identical experimental configuration as KGAT [26] on the FEVER dataset. We directly employ the document retrieval model and evidence retrieval model from KGAT. During the TEST stage, we need to submit our results to the designated website²²2https://codalab.lisn.upsaclay.fr/competitions/7308 for blind evaluation. We utilize the same experimental configuration as SCIKGAT [71] on the SCIFACT dataset. we also submit our results to the designated website³³3https://leaderboard.allenai.org/scifact/submissions/public for blind evaluation. The experimental data can be obtained via GitHub⁴⁴4https://github.com/thunlp/KernelGAT.

FEVER: The same as the previous research [49, 26], CO-GAT uses the official evaluation metrics⁵⁵5https://github.com/sheffieldnlp/fever-scorer FEVER score (FEVER) and Label Accuracy (ACC) to estimate the label prediction performance of model on the FEVER dataset. FEVER score is the primary evaluation metric of the CO-GAT model on the FEVER dataset, which offers a more comprehensive reflection of the inference capability.

SCIFACT: Precision, Recall, and F1 score are employed to assess the performance of the CO-GAT model on the SCIFACT dataset. It is evaluated at abstract and sentence levels.

In our experiments, we compare the CO-GAT model with some fact verification work that focuses on graph reasoning or achieves fine performance on the FEVER dataset and SCIFACT dataset.

Athene [24], UNC NLP [23] and UCL MRG [30] are three top models in FEVER 1.0 shared task [16]. They are based on the NLI model to establish factual reasoning models. In addition, they use attention mechanisms to focus on the semantic information of the claim and evidence.

The prevalence of pre-trained language models and graph neural network architectures has led to their integration into fact verification tasks, resulting in notable performance improvements. GEAR [27] represents an early attempt to establish a reasoning model for fact verification based on the graph neural network. It utilizes the graph-based evidence reasoning network to aggregate evidence information. The BERT model [25] is used to encode the claim and evidence sentence pairs. Subsequently, KGAT [26] proposes a fine-grained graph inference model with a kernel-based graph attention network. It can utilize BERT [25], RoBERTa [43], and CorefRoBERTa [72] models to encode graph nodes. KGAT employs both the token-level and sentence-level kernel attention mechanisms to capture fine-grained evidence information. EvidenceNet [59] employs the gating mechanism to filter redundant evidence information and utilizes the evidence fusion network to capture global contextual information from different levels of evidence. ICMI [60] uses the graph neural network to integrate multi-view contextual information for fact verification, which includes the intra-document context of evidence sentences from the same document and the inter-document context of sentences from other documents. DREAM [62] is different from previous work, which establishes a semantic graph by employing a semantic role labeler to decompose claims and evidence sentences. Crucially, we build a graph-based baseline model MHA-GAT as our main baseline. It only uses the multi-head attention mechanism [67] to establish a graph attention model to aggregate evidence information.

Different from the graph-based inference models, MLA [55] proposes a sequence inference model. It utilizes both token-level and sentence-level self-attentions to capture information and incorporates the static positional encoding mechanism into the input of the multi-head attention mechanism. LOREN [28] propose an interpretable fact verification at the phrase level. The veracity of the phrases serves as an explanation and is aggregated into the final verdict according to the logical rules.

The rest of this section describes the implementation details of the CO-GAT model on the FEVER dataset and SCIFACT dataset.

The fact verification performance of CO-GAT on the FEVER dataset and SCIFACT dataset are compared with several baseline models. The results are shown in TABLE III.

Overall, CO-GAT confirms its effectiveness by achieving a 73.59% FEVER score on the blind test set. Compared to these graph-based claim verification models [27, 62, 26], our CO-GAT model achieves a 3.35% improvement. It shows that our node masking mechanism is effective in enhancing the graph reasoning process and does not change the vanilla graph modeling architecture. Compared with the MHA-GAT model, CO-GAT achieves a 1.03% improvement by keeping the same graph reasoning module as the MHA-GAT model. It shows that the node masking mechanism can help filter out the noise information and conduct more calibrated node representations before feeding the node representations to the reasoning graph. Furthermore, CO-GAT also demonstrates its effectiveness by keeping the vanilla GAT architecture for graph reasoning and conducting competitive performance with EvidenceNET and IMCI models. CO-GAT avoids conducting repetitive encoding [59] and building an additional reasoning graph in the fact verification model [60].

Besides the FEVER dataset, we also conduct experiments on the SCIFACT dataset, which focuses on scientific claim verification. CO-GAT also outperforms baseline models on the SCIFACT dataset, which also confirms its effectiveness. The better fact verification results show the generalization ability of CO-GAT by broadening its effectiveness to the science-specific domain.

This section investigates the effectiveness of different modules and backbone models of the CO-GAT model through ablation studies.

In Fig. 3, we conduct two experiments: the initial experiment investigates the correlation between NEI label prediction probability and the cross entropy score; the subsequent one analyses the NEI prediction ratio of the cases that belong to SUPPORT and REFUTE.

As shown in Fig. 3a, when the cross entropy is low, both MHA-GAT and CO-GAT exhibit a similar probability distribution in predicting the claim label as NEI. However, different from the MHA-GAT model, the CO-GAT model conducts a notably higher probability of predicting the claim label as NEI when the cross entropy score increases, which indicates that the CO-GAT model prefers to predict the claim label as NEI when the cross entropy is higher. Such a phenomenon demonstrates that the reasoning ability of CO-GAT relies more on sufficient information and calibrates the uncertain predictions to the NEI, making CO-GAT conduct more reliable predictions.

Furthermore, we analyze the NEI prediction ratios of the cases that belong to the SUPPORT and REFUTE classes. As shown in Fig. 3b, the results indicate that, in comparison to the MHA-GAT model, CO-GAT exhibits a higher tendency to predict the claim label as NEI. This further confirms the calibration behavior of our CO-GAT model, which predicts some confusing cases as the NEI label.

In Fig. 4, we scale the confidence score to explore the effectiveness of the confidence score in controlling the semantic information flow from the node representations to the graph reasoning module.

As shown in Fig. 4a, we scale the CO-SCO by multiplying it with a coefficient $\alpha$, which changes from 1.0 to 0.0 results with the interval of 0.2. As the confidence score decreases, more evidence information flows from blank nodes into the graph nodes. In this case, the reasoning model lacks sufficient evidence information to make a correct fact verification prediction, leading to the tendency of the NEI prediction of CO-GAT. Nonetheless, as shown in Fig. 4b, the label accuracy exhibits only a slight decrease while the scaling factor varies from 1.0 to 0.4. Despite inevitable errors in node confidence assessment, it ensures that CO-GAT can preserve useful semantic information of node representations and feed them to the reasoning graph, indicating its strong tolerance of the CO-SCO prediction in our node masking mechanism.

As shown in Fig. 4c, we analyze the change of cross entropy scores by scaling the CO-SCO to control the information flow from the blank node to these initial node representations. The lower attention entropy score indicates a more concentrated attention mechanism. The evaluation results show that, as the scaling coefficient decreases from 1.0 to 0.0, the edge attention entropy gradually increases, which illustrates that the semantic information gradually flows from blank nodes to vanilla nodes. In this case, the node representations tend to become more homogeneous, making the edge attention mechanism unable to identify these useful nodes. On the contrary, the node attention entropy remains relatively stable regardless of changes in the scaling coefficient. It demonstrates that the node representations become more homogenized after multi-layer graph attention encoding. This indicates that the edge attention mechanism is primarily responsible for node selection and the node attention mechanism does not pay attention to node selection. This further demonstrates the necessity of utilizing the node masking mechanism to erase noise information before the graph reasoning, preventing its impact on the learned representations of other nodes during graph reasoning.

In this experiment, we investigate the comparison of the attention mechanisms between the CO-GAT model and the MHA-GAT model.

As shown in Fig. 5a, the node attention entropy scores of MHA-GAT and CO-GAT are almost the same, which indicates that both of them have a similar node attention distribution. This shows that CO-GAT has little effect on node attention. On the contrary, the edge attention entropy of CO-GAT is notably smaller than that of MHA-GAT. It demonstrates that the edge attention mechanism of CO-GAT helps to conduct a more concentrated distribution while using edge attention to encode node representations. The main reason may lie in that the node masking mechanism has the ability to erase some unnecessary information from the initial node representations, make these node representations more distinguished, and finally conduct a more concentrated attention distribution.

Furthermore, we analyze the attention distribution of edge attention and node attention by sorting the attention weights. As shown in Fig. 5b, during the graph reasoning process, CO-GAT assigns more attention weights to some nodes, which demonstrates that our attention masking mechanism can expose the valuable node representations by alleviating the effect of noise node representations. As shown in Fig. 5c, it illustrates that the node attention weights of the CO-GAT model are more stable, compared to the MHA-GAT model. These encoded node representations become more homogeneous after edge attention based encoding, which thrives on erasing the noise information from the initial node representations.

TABLE V shows three claim examples in the FEVER dataset.

In the first case, “CHIPs” is ambiguous, which indicates two meanings: movies and TV dramas. However, this claim does not specify which was mentioned. The MHA-GAT model assigns approximately 0.3 edge attention weight to $E_{3}$ and $E_{5}$. Yet, $E_{3}$ states “CHIPs aired from September 15, 1977, to May 1, 1983”, $E_{5}$ declares “ CHIPs began on October 21, 2015”. The timing of these two pieces of evidence is different from the “2017” in the claim. The presence of interference information “1977” and “2015” leads to incorrect prediction results in the MHA-GAT model, which predicts the claim label as “REFUTES”. On the contrary, although the CO-GAT model assigns more edge attention weight to the $E_{5}$, it predicts the confidence score of $E_{5}$ to be 0.28. It erases the majority of noise information based on confidence scores and makes it more inclined to the blank node. Due to the lack of sufficient information remaining in the reasoning model, the CO-GAT model correctly predicts that the label of this claim is “NEI”.

As shown in the second case, the MHA-GAT model pays more attention weight to the evidence $E_{1}$ and the other four pieces of evidence receive similar attention weights. $E_{1}$ indicates that “Aphrodite is the daughter of Dione, as mentioned in Homer’s Iliad”. $E_{2}$ illustrates that “Dione is an oracular Titaness primarily known from Book V of Homer’s Iliad”. $E_{1}$ and $E_{2}$ can jointly infer that the label of this claim should be “SUPPORTS”. However, in the MHA-GAT model, the $E_{2}$ obtains a minimal node attention weight, which is only 0.02. It leads to the MHA-GAT model not obtaining sufficient effective information for claim verification. Meanwhile, $E_{3}$ and $E_{5}$ have a higher node attention weight compared to the $E_{2}$, which indicates “Aphrodite” is a “mother”. This introduces additional noise semantic information, resulting in the MHA-GAT model predicting that the claim label is “REFUTES”. In contrast, the $E_{1}$ and $E_{2}$ in the CO-GAT model have high confidence scores, which allows them to retain more useful information. Furthermore, $E_{1}$ and $E_{2}$ receive higher edge attention weights than the other evidence pieces, thus CO-GAT predicts the correct label “SUPPORTS”.

In the third case, the MHA-GAT model and the CO-GAT model pay more attention to the golden evidence $E_{1}$. The evidence $E_{1}$ states “The Nice Guys is a 2016 American action comedy film”. Consequently, the MHA-GAT model predicts the claim label as “REFUTES”. However, the CO-GAT model mistakenly evaluates the correlation between $E_{1}$ and the claim, leading to erasing the majority of its semantic information. Thus, the CO-GAT model makes a mistake prediction of the claim label as “NEI”.