SlowGuess/ACL_2020_OCR huggingface dataset:
It illustrates the effectiveness of KGAT among graph based reasoning models. With BERT based sentence retrieval, our KGAT also outperforms BERT (Base) (Soleimani et al., 2019) by almost  $1\%$  FEVER score, showing consistent effectiveness with different sentence retrieval models. When using BERT (Large) as the encoder, KGAT also outperforms the corresponding version of Soleimani et al. (2019). KGAT with RoBERTa performs the best compared with all previously published research on all evaluation metrics. CorefBERT (Ye et al., 2020) extends our KGAT architecture and explicitly models co-referring relationship in context for better performance.
The sentence retrieval performances of ESIM and BERT are compared in Table 3. The BERT sentence retrieval outperforms ESIM sentence retrieval significantly, thus also helps improve KGAT's reasoning accuracy. Nevertheless, for more fair comparisons, our following experiments are all based on ESIM sentence retrieval, which is the one used by GEAR, our main baseline (Zhou et al., 2019).
5.2 Performance on Different Scenarios
This experiment studies the effectiveness of kernel on multiple and single evidence reasoning scenarios, as well as the contribution of kernels.
The verifiable instances are separated (except instances with "NOT ENOUGH INFO" label) into two groups according to the golden evidence labels. If more than one evidence pieces are required, the claim is considered as requiring multi-evidence reasoning. The single evidence reasoning set and the multiple evidence reasoning set contain 11,372  $(85.3\%)$  and 1,960  $(14.7\%)$  instances, respectively. We also evaluate two additional KGAT variations: KGAT-Node which only uses kernels on the node, with the edge kernels replaced by standard dot-production attention, and KGAT-Edge which only uses kernels on the edge. The results of these systems on the two scenarios are shown in Table 4.
KGAT-Node outperforms GAT by more than  $0.3\%$  on both single and multiple reasoning sce
4https://github.com/huggingface/pytorch-transformers
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Reasoning	Model	LA	GFEVER	FEVER
Multiple	GEAR	66.38	n.a.	37.96	-0.25%
GAT	66.12	84.39	38.21	-
KGAT-Node	65.51	83.88	38.52	0.31%
KGAT-Edge	65.87	84.90	39.08	0.87%
KGAT-Full	65.92	85.15	39.23	1.02%
Single	GEAR	78.14	n.a.	75.73	-1.69%
GAT	79.79	81.96	77.42	-
KGAT-Node	79.92	82.29	77.73	0.31%
KGAT-Edge	79.90	82.41	77.58	0.16%
KGAT-Full	80.33	82.62	78.07	0.65%
Table 4: Claim Verification Accuracy on Claims that requires Multiple and Single evidence Pieces. Standard GAT with no kernel (GAT), with only node kernel (KGAT-Node), with only edge kernel (KGAT-Edge) and the full model (KGAT-Full) are compared.
narios. As expected, it does not help much on GFEVER, because the golden evidence is given and node selection is not required. It illustrates KGAT-Node mainly focuses on choosing appropriate evidence and assigning accurate combining weights in the readout.
KGAT-Edge outperforms GAT by more than  $0.8\%$  and  $0.1\%$  on multiple and single evidence reasoning scenarios, respectively. Its effectiveness is mostly on combining the information from multiple evidence pieces.
The multiple and single evidence reasoning scenarios evaluate the reasoning ability from different aspects. The single evidence reasoning mainly focuses on selecting the most relevant evidence and inference with single evidence. It mainly evaluates model de-noising ability with the retrieved evidence. The multiple evidence reasoning is a harder and more complex scenario, requiring models to summarize necessary clues and reason over multiple evidence. It emphasizes to evaluate the evidence interactions for the joint reasoning. KGAT-Node shows consistent improvement on both two reasoning scenarios, which demonstrates the important role of evidence selection. KGAT-Edge, on the other hand, is more effective on multiple reasoning scenarios as the Edge Kernels help better propagate information along the edges.
5.3 Effectiveness of Kernel in KGAT
This set of experiments further illustrate the influences of kernels in KGAT.
More Concentrated Attention. This experiment studies kernel attentions by their entropy, which reflects whether the learned attention weights are focused or scattered. The entropy of the kernel attentions in KGAT, the dot-product at
(a) Edge Attention.
(b) Node Attention.
Figure 3: Attention Weight Entropy on Evidence Graph, from KGAT and GAT, of graph edges and nodes. Uniform weights' entropy is also shown for comparison. Less entropy shows more concentrated attention.
Figure 4: Evidence Selection Effectiveness of KGAT and GAT. Fig 4(a) shows the distribution of attention weights on evidence nodes  $p(n^p)$ , sorted by their weights; Fig 4(b) evaluates the recall of selecting the golden standard evidence nodes at different depths.
(a) Attention Distribution.
(b) Evidence Recall.
tentions in GAT, and the uniform attentions are shown in Figure 3.
The entropy of Edge attention is shown in Figure 3(a). Both GAT and KGAT show a smaller entropy of the token attention than the uniform distribution. It illustrates that GAT and KGAT have the ability to assign more weight to some important tokens with both dot product based and kernel based attentions. Compared to the dot-product attentions in GAT, KGAT's Edge attention focuses on fewer tokens and has a smaller entropy.
The entropy of Node attentions are plotted in Figure 3(b). GAT's attentions distribute almost the same with the uniform distribution, while KGAT has concentrated Node attentions on a few evidence sentences. As shown in the next experiment, the kernel based node attentions focus on the correct evidence pieces and de-noises the retrieved sentences, which are useful for claim verification.
More Accurate Evidence Selection. This experiment evaluates the effectiveness of KGAT-Node through attention distribution and evidence recall. The results are shown in Figure 4.
We first obtain the node attention score in the evidence graph from KGAT or GAT, and calcu
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(a) GAT.
(b) KGAT.
late the statistics of the maximum one for each claim, as most of which only require single evidence to verify. The attention score of the highest attended evidence node for each claim is plotted in Figure 4(a). As expected, KGAT concentrates its weight to select evidence nodes and provides a focused attention.
Then the evidence selection accuracy is evaluated by their evidence recall. We first rank all evidence pieces for each claim. Then the evidence recall with different ranking depths is plotted in Figure 4(b). KGAT achieves a much higher recall on top ranking positions—only the first ranked sentence covers nearly  $80\%$  of ground truth evidence, showing the node kernels' ability to select correct evidence. This also indicates the potential of the node kernels in the sentence retrieval stage, which we reserve for future work as this paper focuses on the reasoning stage.
Fine-Grained Evidence Propagation. The third analysis studies the distribution of KGAT-Edge's attention which is used to propagate the evidence clues in the evidence graph.
Figure 5 plots the attention weight distribution of the edge attention scores in KGAT and GAT, one from kernels and one from dot-products. The kernel attentions again are more concentrated: KGAT focuses fewer words while GAT's dot-product attentions are almost equally distributed among all words. This observation of the scattered dot-product attention is consistent with previous research (Clark et al., 2019). As shown in the next case study, the edge kernels provide a fine-grained and intuitive attention pattern when combining evidence clues from multiple pieces.
Figure 5: The Attention Weight Distribution from GAT and KGAT on evidence sentence tokens. Top  $10\%$  tokens are presented. The rest follows standard long tail distributions.
Figure 6: Edge Attention Weights on Evidence Tokens. Darker red indicates higher attention weights.
Claim: Al Jardine is an American rhythm guitarist.
(1) [Al Jardine] Alan Charles Jardine (born September 3, 1942) is an American musician, singer and songwriter who co-founded the Beach Boys.
(2) [Al Jardine] He is best known as the band's rhythm guitarist, and for occasionally singing lead vocals on singles such as "Help Me, Rhonda" (1965), "Then I Kissed Her" (1965) and "Come Go with Me" (1978).
(3) [Al Jardine] In 2010, Jardine released his debut solo studio album, A Postcard from California.
(4) [Al Jardine] In 1988, Jardine was inducted into the Rock and Roll Hall of Fame as a member of the Beach Boys.
(5) [Jardine] Ray Jardine American rock climber, lightweight backpacker, inventor, author and global adventurer.
Label: SUPPORT
Table 5: An example claim (Zhou et al., 2019) whose verification requires multiple pieces of evidence.
6 Case Study
Table 5 shows the example claim used in GEAR (Zhou et al., 2019) and the evidence sentences retrieved by ESIM, among which the first two are required evidence pieces. Figure 6 presents the distribution of attentions from the first evidence to the tokens in the second evidence  $(\alpha_{i}^{2\rightarrow 1})$  in KGAT (Edge Kernel) and GAT (dot-product).
The first evidence verifies that "Al Jardine is an American musician" but does not enough information about whether "Al Jardine is a rhythm guitarist". The edge kernels from KGAT accurately pick up the additional information evidence (1) required from evidence (2): "rhythm guitarist". It effectively fills the missing information and completes the reasoning chain. Interesting, "Al Jardine" also receives more attention, which helps to verify if the information in the second evidence is about the correct person. This kernel attention pattern is more intuitive and effective than the dot-product attention in GAT. The later one scatters almost uniformly across all tokens and hard to explain how the joint reasoning is conducted. This seems to be
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a common challenge of the dot-product attention in Transformers (Clark et al., 2019).
This paper presents KGAT, which uses kernels in Graph Neural Networks to conduct more accurate evidence selection and fine-grained joint reasoning. Our experiments show that kernels lead to the more accurate fact verification. Our studies illustrate the two kernels play different roles and contribute to different aspects crucial for fact verification. While the dot-product attentions are rather scattered and hard to explain, the kernel-based attentions show intuitive and effective attention patterns: the node kernels focus more on the correct evidence pieces; the edge kernels accurately gather the necessary information from one node to the other to complete the reasoning chain. In the future, we will further study this properties of kernel-based attentions in neural networks, both in the effectiveness front and also the explainability front.
This research is jointly supported by the NSFC project under the grant no. 61661146007, the funds of Beijing Advanced Innovation Center for Language Resources (No. TYZ19005), and the NExT++ project, the National Research Foundation, Prime Ministers Office, Singapore under its IRC@Singapore Funding Initiative.
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