Learn to Combine Linguistic and Symbolic Information for Table-based Fact Verification (2020)

Abstract: Table-based fact verification is expected to perform both linguistic reasoning and symbolic reasoning. Existing methods lack attention to take advantage of the combination of linguistic information and symbolic information. In this work, we propose HeterTFV, a graph-based reasoning approach, that learns to combine linguistic information and symbolic information effectively. We first construct a program graph to encode programs, a kind of LISP-like logical form, to learn the semantic compositionality of the programs. Then we construct a heterogeneous graph to incorporate both linguistic information and symbolic information by introducing program nodes into the heterogeneous graph. Finally, we propose a graph-based reasoning approach to reason over the multiple types of nodes to make an effective combination of both types of information. Experimental results on a large-scale benchmark dataset TABFACT illustrate the effect of our approach.

## introduction fact verification aims to verify whether a fact is entailed or refuted by the given evidence, which has attracted increasing attention. recent researches mainly focus on the unstructured text as the evidence and ignoring the evidence with the structured or semi-structured format. a recently proposed dataset tabfact (wenhu chen and wang, 2020) fills this gap, which is designed to deal with the table-based fact verification problem, namely, verifying whether a statement is correct by the given semi-structured table evidence. it is well accepted that symbolic information (such as count and only) plays a great role in understanding semi-structured evidence based statements @xcite . however, most existing approaches for fact verification @xcite @xcite @xcite focus on the understanding of natural language, namely, linguistic reasoning, but fail to consider symbolic information, which plays an important role in complex reasoning @xcite @xcite . due to the diversity of natural language expressions, it is difficult to capture symbolic information effectively from natural language directly. consequently, how to leverage symbolic information effectively becomes a crucial problem. to alleviate this problem, @xcite propose a graph module network that concatenates graphenhanced linguistic-level representations and program-guided symbolic-level representations together to predict the labels. however, their method focuses on the representation of symbolic information, rather than take advantage of the combination of both types of information. more specifically, we believe that the concatenation operation between two types of representations is not effective enough to leverage the linguistic information and symbolic information to perform reasoning. in recent studies, graph neural networks show their powerful ability in dealing with semi-structured data @xcite . under this consideration, we propose to use graph neural networks that learn to combine linguistic information and symbolic information in a simultaneous fashion. since the representations of different types of information fall in different embedding spaces, date result score brazil scorers competition may 11, 1919 w 6 -0 friedenreich, neco, haroldo south american championship may 18, 1919 w 3 -1 heitor, amilcar, millon south american championship may 26, 1919 d 2 -2 neco south american championship may 29, 1919 w 1 -0 friedenreich south american championship june 1, 1919 d 3 -3 haroldo, arlindo taca roberto cherry 4 of 5 game be for the south american championship entailed 1. eq { 5 ; count { filter_eq { all_rows ; competition ; south american championship } } } 2. eq { 4 ; count { filter_eq { all_rows ; competition ; south american championship } } } 3. and { eq { 4 ; count { all_rows } } ; eq { 5 ; count { filter_eq { all_rows ; competition ; south american championship } } } } 4. and { eq { 5 ; count { all_rows } } ; eq { 4 ; count { filter_eq { all_rows ; competition ; south american championship } } } } table selected programs label statement figure 1: example of the tabfact dataset, which are expected to combine both linguistic information in the statement and the table and symbolic information in the programs. given a table and a statement, the goal is to predict whether the label is entailed or refuted. program is a kind of lisp-like logical form. the program synthesis and selection process are described in section 3.2. a heterogeneous graph structure is suitable to reason and aggregate over different types of nodes to combine different types of information. in this paper, we propose a heterogeneous graph-based neural network for table-based fact verification named hetertfv, to learn to combine linguistic information and symbolic information. given a statement and a table, we first generate programs with the latent program algorithm (lpa) algorithm proposed by @xcite . after that, we construct a program graph to capture the inner structure in the program and use gated graph neural network to encode the programs to learn the semantic compositionality. then a heterogeneous graph is constructed with statement nodes, table nodes, and program nodes to incorporate both linguistic information and symbolic information, which is expected to exploit the structure in the table and build connections among the statement, table, and programs. finally, a graph-based neural network is proposed to reason over the constructed heterogeneous graph, which enables the message passing processes of different types of nodes to achieve the purpose to combine linguistic information and symbolic information. we conduct experiments on the tabfact (wenhu chen and wang, 2020), a large-scale benchmark dataset for table-based fact verification. experimental results show that our model outperforms all baselines and achieves state-of-the-art performance. in summary, the main contributions of this paper are three-fold: given a statement and a table, our goal is to verify whether a textual statement is entailed or refuted by the given semi-structured table evidence. we evaluate our model on the tabfact dataset (wenhu chen and wang, 2020), a large-scale benchmark dataset for table-based fact verification. figure 1 shows an taking the statement, function names (such as eq, count, filter eq, and so on) and the table as input, our approach first constructs a program graph to encode programs, and then constructs a heterogeneous graph among different types of nodes. finally, a graph-based reasoning network is applied on the constructed heterogeneous graph. blue, yellow, and purple nodes stand for table nodes, statement nodes, and program nodes, respectively. ## hetertfv in this paper, we propose a graph-based approach for table-based fact verification task, which takes advantage of both linguistic information and symbolic information. we first generate programs from the statement and table, construct a program graph, and encode each program in a bottom-up manner to learn semantic compositionality (section 3.2). after that, we construct a heterogeneous graph with the statement, table, and program nodes to enable to reason over multiple types of nodes (section 3.3). finally, we propose a graph-based neural network to reason over the constructed heterogeneous graph (section 3.4). figure 2 shows the architecture of the proposed graph-based approach. ## conclusion in this work, we focus on the table-based fact verification task, propose hetertfv, a graph-based approach that learns to combine linguistic information and symbolic information effectively by reasoning over the constructed heterogeneous graph. specifically, we first construct a program graph to encode programs. then we construct a heterogeneous graph among tables, statements, and programs to incorporate linguistic information and symbolic information. finally, we propose a heterogeneous graph-based neural network to perform reasoning to learn to combine both types of information. we conduct experiments on the tabfact dataset. experimental results illustrate that our model outperforms all the baseline systems with considerable increment and achieves state-of-the-art performance. in the future, we will do more attempt to combine linguistic information and symbolic information on the other tasks, such as knowledge graph reasoning or text reasoning.