BAG: Bi-directional Attention Entity Graph Convolutional Network for Multi-hop Reasoning Question Answering

Introduction

Question Answering (QA) and Machine Comprehension (MC) tasks have drawn significant attention during the past years. The proposal of large-scale single-document-based QA/MC datasets, such as SQuAD Rajpurkar et al. (2016), CNN/Daily mail Hermann et al. (2015), makes training available for end-to-end deep neural models, such as BiDAF Seo et al. (2016), DCN Xiong et al. (2016) and SAN Liu et al. (2017). However, gaps still exist between these datasets and real-world applications. For example, reasoning is constrained to a single paragraph, or even part of it. Extended work was done to meet practical demand, such as DrQA Chen et al. (2017) answering a SQuAD question based on the whole Wikipedia instead of single paragraph. Besides, latest large-scale datasets, e.g. TriviaQA Joshi et al. (2017) and NarrativeQA Kočiskỳ et al. (2018), address this limitation by introducing multiple documents, ensuring reasoning cannot be done within local information. Although those datasets are fairly challenging, reasoning are within one document.

In many scenarios, we need to comprehend the relationships of entities across documents before answering questions. Therefore, reading comprehension tasks with multiple hops were proposed to make it available for machine to tackle such problems, e.g. QAngaroo task Welbl et al. (2018). Each sample in QAngaroo contains multiple supporting documents, and the goal is selecting the correct answer from a set of candidates for a query. Most queries cannot be answered depending on a single document, and multi-step reasoning chains across documents are needed. Therefore, it is possible that understanding a part of paragraphs loses effectiveness for multi-hop inference, which posts a huge challenge for previous models. Some baseline models, e.g. BiDAF Seo et al. (2016) and FastQA Weissenborn et al. (2017), which are popular for single-document QA, suffer dramatical accuracy decline in this task.

In this paper, we propose a new graph-based QA model, named Bi-directional Attention Entity Graph convolutional network (BAG). Documents are transformed into a graph in which nodes are entities and edges are relationships between them. The graph is then imported into graph convolutional networks (GCNs) to learn relation-aware representation of nodes. Furthermore, we introduce a new bi-directional attention between the graph and a query with multi-level features to derive the mutual information for final prediction.

Experimental results demonstrate that BAG achieves state-of-the-art performance on the WIKIHOP dataset. Ablation test also shows BAG benefits from the bi-directional attention, multi-level features and graph convolutional networks.

Applying a bi-directional attention between graphs and queries to learn query-aware representation for reading comprehension.

Multi-level features are involved to gain comprehensive relationship representation for graph nodes during processing of GCNs.

Related Work

Recently coreference and graph-based models are studied for multi-hop QA Dhingra et al. (2018); Santoro et al. (2017). Coref-GRU Dhingra et al. (2018) uses coreferences among tokens in documents. However, it is still limited by the long-distance relation propagation capability of RNNs. Besides, graph is proved to be an efficient way to represent complex relationships among objects and derive relational information Santoro et al. (2017). MHQA-GRN Song et al. (2018) and Entity-GCN De Cao et al. (2018) construct entity graphs based on documents to learn more compact representation for multi-hop reasoning and derive answers from graph networks. However, both of them care less about input features and the attention between queries and graph nodes.

Attention has been proven to be an essential mechanism to promote the performance of NLP tasks in previous work Bahdanau et al. (2014); Sukhbaatar et al. (2015). In addition, bi-directional attention Seo et al. (2016) shows its superiority to vanilla mutual attention because it provides complementary information to each other for both contexts and queries. However, little work exploits the attention between graphs and queries.

BAG Model

We first formally define the multiple-hop QA task, taking QAngaroo Welbl et al. (2018) WIKIHOP data as an example, There is a set $S$ containing $N$ supporting documents, a query $q$ with $M$ tokens and a set of answer candidates $C$. Our goal is to find the correct answer index $a$. Giving a triple-style query $\bm{q}=(\textit{country, kepahiang})$, it means which country does kepahiang belongs to. Then answer candidates are provided, e.g. $C=\{\textit{Indonesia},\textit{Malaysia}\}$. There are multiple supporting documents but not all of them are related to reasoning, e.g. Kephiang is a regency in Bengkulu, Bengkulu is one of provinces of Indonesia, Jambi is a province of Indonesia. We can derive the correct candidate is Indonesia, i.e. $a=0$, based on reasoning hops in former two documents.

We show the proposed BAG model in Figure 1. It contains five modules: (1) entity graph construction, (2) multi-level feature layer, (3) GCN layer, (4) bi-directional attention and (5) output layer.

We construct an entity graph based on Entity-GCN De Cao et al. (2018), which means all mentions of candidates found out in documents are used as nodes in the graph. Undirected edges are defined according to positional properties of every node pair. There are two kinds of edges included: 1) cross-document edge, for every node pair with the same entity string located in different documents; 2) within-document edge, for every node pair located in the same document.

Nodes in an entity graph can be found out via simple string matching. This approach can simplify calculation as well as make sure all relevant entities are included in the graph. Picked out along possible reasoning chains during dataset generating Welbl et al. (2018), answer candidates have contained all related entities for answering. Finally, We can obtain a set of $T$ nodes ${\{n_{i}\},1\leq i\leq T}$ and corresponding edges among these nodes via above procedures.

2 Multi-level Features

We represent both nodes and queries using multi-level features as shown in Figure 1(2). We first use pretrained word embeddings to represent tokens, such as GLoVe Pennington et al. (2014) because nodes and queries are composed of tokens. Then contextual-level feature is used to offset the deficiency of GLoVe. Note that only part of tokens are remained during graph construction because we only extract entities as nodes. Thus contextual information around these entities in original document becomes essential for indicating relations between tokens and we use higher-level information for nodes except for token-level feature.

We use ELMo Peters et al. (2018) as contextualized word representations, modeling both complex word characteristics and contextual linguistic conditions. It should be noted that ELMo features for nodes are calculated based on original documents, then truncated according to the position indices of nodes. Token-level and context-level features will be concatenated and encoded to make a further comprehension. Since a node may contain more than one token, we average features among tokens to generate a feature vector for each node before encoding it. It will be transformed into the encoded node feature via a 1-layer linear network.

Different from nodes, we represent a query by directly using a bidirectional LSTM (Bi-LSTM) whose output in each step is used as encoded query features. And both linear network and LSTM have the same output dimension ${\hat{d}}$.

3 GCN Layer

Similar to Entity-GCN De Cao et al. (2018), we apply a gate on update vector $u_{i}^{l}$ and hidden state $h_{i}^{l}$ of current node by a linear transformation ${f_{s}}$,

in which $u_{i}^{l}$ can be obtained via (1) without sigmoid function. Then it will be used for updating weights for the hidden state $h_{i}^{l+1}$ of the same node in next layer,

We stack such networks for $L$ layers in which all parameters are shared. The information of each node will be propagated up to $L$-node distance away, generating $L$-hop-reasoning relation-aware representation of nodes. The initial input will be mutli-level nodes features ${{\bf{f}}_{\bf{n}}}=\{{f_{n_{i}}}\},0\leq i\leq T$ and edges ${\bf{e}}=\{{e_{ij}}\}$ in the graph.

4 Bi-directional Attention Between a Graph and a Query

Bi-directional attention is responsible for generating the mutual information between a graph and a query. In BiDAF Seo et al. (2016), attention is applied to sequence data in QA tasks such as supporting texts. However, we also find it works well between graph nodes and queries. It generates query-aware node representations that can provide more reasoning information for prediction.

where ${\rm{softma}}{{\rm{x}}_{{\rm{col}}}}$ means performing softmax function across the column, and $\cdot$ stands for matrix multiplication.

Our bi-directional attention layer is the concatenation of the original nodes feature, nodes-to-query attention, the element-wise multiplication of nodes feature and nodes-to-query attention, and multiplication of nodes feature and query-to-nodes attention. It should be noted that the relation-aware nodes representation from GCN layer is just used to calculate the similarity matrix, and original node feature is used in rest calculation to obtain more general complementary information between graph and query. Edges are not taken in account because they are discrete and combined with nodes in GCN layer. The output is defined as

5 Output layer

A 2-layer fully connect feed-forward network is employed to generate the final prediction, with $\tanh$ as the activation function in each layer. Softmax will be applied among the output. It uses query-aware representation of nodes from the attention layer as input, and its output is regarded as the probability of each node becoming answer. Since each candidate may appear several times in the graph, the probability of each candidate is the sum of all corresponding nodes. The loss function is defined as the cross entropy between the gold answer and its predicted probability.

Experiment

We used both unmasked and masked versions of the QAngaroo WIKIHOP dataset Welbl et al. (2018) and followed its basic setting, in which masked version used specific tokens such as __MASK1__ to replace original candidates tokens in documents. There are 43,738, 5,129 and 2,451 examples in the training set, the development set and the test set respectively, and test set is not public.

In addition, the number of nodes and the query length were truncated as 500 and 25 respectively for normalized computation. Dropout with rate $0.2$ was applied before GCN layer. Adam optimizer is employed with initial learning rate $2\times 10^{-4}$, which will be halved for every $5$ epochs, With batch size $32$. It took about $14$ hours for 50-epoch training on two GTX1080Ti GPUs using pre-built and pre-processed graph data generated from original corpus, which can significantly decrease the training time.

We consider the following baseline models: FastQA Weissenborn et al. (2017), BiDAF Seo et al. (2016), Coref-GRU Dhingra et al. (2018), MHQA-GRN Song et al. (2018), Entity-GCN De Cao et al. (2018). Former three models are RNN-based models, while coreference relationship is involved in Coref-GRU. The last two models are graph-based models specially designed for multi-hop QA tasks.

As shown in Table 1, we collected three kinds of results. The dev and test results stand for the original validation and test sets, noting that the test set is not public. Thus, in addition, we divide the original validation set into two parts evenly, one as a split validation set for tuning model and the other one as a split test set. The test1 results are for the split test set. And results of masked dev and test1 are also available in this table.

Our BAG model achieves state-of-the art performance on both unmasked and masked dataThe paper was written on early Dec. 2018, during that time Entity-GCN is the best public model, and only one anonymous model is better than it., with accuracy 69.0% on the test set, which is 1.4% higher in value than previous best model Entity-GCN. It is significant superior than FastQA and BiDAF due to leveraging of relationship information given by the graph and abandoning some distracting context in multiple documents. Although Coref-GRU extends GRU with coreference relationships, it is still not enough for multi-hop because hop relationships are not limited to coreference, entities with the same strings also existed across documents which can be used for reasoning. Both MHQA-GRN and Entity-GCN utilize graph networks to resolve relations among entities in documents. However, the lack of attention and complementary features limits their performance. Therefore our BAG model achieves the best performance under all data configurations. It is noticed that BAG only gets a small promotion on masked data. We argue that the reason is the attention between masks and queries generating less useful information compared to unmasked ones.

Moreover, ablation experimental results on unmasked version of the WIKIHOP dev set are given in Table 2. Once we remove the bi-directional attention and put the concatenation of nodes and queries directly into the output layer, it shows significant performance drop with more than $3\%$, proving the necessity of attention for reasoning in multi-hop QA. If we use linear-transformation-based single attention $a=h_{n}{\bf W_{a}}f_{q}$ given in Luong et al. (2015) instead of our bi-directional attention, the accuracy drops with $2\%$, which means attention bi-directionality also contributes to the performance improvement. The similar condition will appear if we remove GCN, but use raw nodes as input for the attention layer.

In addition, if edge types are no longer considered, which makes R-GCN degraded to vanilla GCN, noticeable accuracy loss about $2\%$ appears. The absence of multi-level features will also cause degradation. The removal of semantic-level features causes slight decline on the performance, including NER and POS features. Further removal of ELMo feature will causes a dramatical drop, which reflects the insufficiency of only using word embeddings as features for nodes and that contextual information is very important.

Conclusion

We propose a Bi-directional Attention entity Graph convolutional network (BAG) for multi-hop reasoning QA tasks. Regarding task characteristics, graph convolutional networks (GCNs) are efficient to handle relationships among entities in documents. We demonstrate that both bi-directional attention between nodes and queries and multi-level features are necessary for such tasks. The former one aims to obtain query-aware node representation for answering, while the latter one provides contextual comprehension of isolated nodes in graphs. Our experimental results not only demonstrate the effectiveness of two proposed modules, but also show BAG achieves state-of-the-art performance on the WIKIHOP dataset.

Our future work will be making use of more complex relations between entities and building graphs in more general way without candidates.

Acknowledgements

This work was supported by Australian Research Council Projects under grants FL-170100117, DP-280103424.

References