Research on automatically solving mathematical word problems (MWP) has a long history. Most recent works adopt Seq2Seq approach to predict the result equations as a sequence of quantities and operators. Although result equations can be written as a sequence, it is essentially a structure. More precisely, it is a Direct Acyclic Graph (DAG) whose leaf nodes are the quantities, and internal and root nodes are arithmetic or comparison operators. In this paper, we propose a novel Seq2DAG approach to extract the equation set directly as a DAG structure. It is extracted in a bottom-up fashion by aggregating quantities and sub-expressions layer by layer iteratively. The advantages of our approach approach are three-fold: it is intrinsically suitable to solve multivariate problems, it always outputs valid structure, and its computation satisfies commutative law for +, x and =. Experimental results on Math23K and DRAW1K demonstrate that our model outperforms state-of-the-art deep learning methods. We also conduct detailed analysis on the results to show the strengths and limitations of our approach.

Table, widely used in documents from various vertical domains, is a compact representation of data. There is always some strong demand to automatically extract key information from tables for further analysis. In addition, the set of keys that need to be extracted information is usually time-varying, which arises the issue of zero-shot keys in this situation. To increase the efficiency of these knowledge workers, in this study we aim to extract the values of a given set of keys from tables. Previous table-related studies mainly focus on relational, entity, and matrix tables. However, their methods fail on mixed-style tables, in which table headers might exist in any non-merged or merged cell, and the spatial relationships between headers and corresponding values are diverse. Here, we address this problem while taking mixed-style tables into account. To this end, we propose an end-to-end neural-based model, called Information Extraction in Mixed-style Table (IEMT). IEMT first uses BERT to extract textual semantics of the given key and the words in each cell. Then, it uses multi-layer CNN to capture the spatial and textual interactions among adjacent cells. Furthermore, to improve the accuracy on zero-shot keys, we pre-train IEMT on a dataset constructed on 0.4 million tables from Wikipedia and 140 million triplets from Ownthink. Experiments with the fine-tuning step on 26,869 financial tables show that the proposed model achieves 0.9323 accuracy for zero-shot keys, obtaining more than 8% increase compared with the model without pre-training.

Claims over the numerical relationships among some measures are commonly expressed in tabular forms, and widely exist in the published documents on the Web. This paper introduces the problem of numerical formula recognition from tables, namely recognizing all numerical formulas inside a given table. It can well support many interesting downstream applications, such as numerical error correction in tables, formula recommendation in tables. Here, we emphasize that table is a kind of language that adopts a different linguistic paradigm from natural language. It uses visual grammar like visual layout and visual settings (e.g., indentation, font style) to express the grammatical relationships among the table cells. Understanding tables and recognizing formulas require decoding the visual grammar while simultaneously understanding the textual information. Another challenge is that formulas are complicated in terms of diverse math functions and variable-length of arguments. To address these challenges, we convert this task into a uniform framework, extracting relations of table cell pairs in a table. A two-channel neural network model TaFor is proposed to embed both the textual and visual features for a table cell. Our framework achieves the formula-level F1-score = 0.90 on a real-world dataset of 190179 tables while a retrieval-based method achieves F1-score = 0.72. We also perform extensive experiments to demonstrate the effectiveness of each component in our model, and conduct a case study to discuss the limits of the proposed model. With our published data this study also aims to attract the community's interest in deep semantic understanding over tables.

Tabular forms of numerical facts widely exist in the disclosure documents of vertical domains, especially the financial fields. It is also quite common that the same fact might be mentioned multiple times in different tables with diverse tabular presentation. Firm's disclosure documents are the main source of accounting information for individual investors. Its authenticity is crucial for both firms' development and investors' investment decisions. However, due to large volumes of tables, frequent updates during editing, and limited time for manual cross-checking, these facts might be inconsistent with each other even after official publishing. Such errors may bring about huge reputational risk, and even economic losses even if the mistakes are made unintentionally instead of deliberately. Hence, it creates an opportunity for Automatic Numerical Cross-Checking over Tables. This paper introduces the key module of such a system, which aims to identify whether a pair of table cells are semantically equivalent, namely referring to the same fact. We observed that due to tabular presentation diversity the facts in tabular forms are difficult to be parsed into relational tuples. Thus, we present an end-to-end solution of binary classification over each pair of table cells, which does not involve with explicit semantic parsing over tables. Also, we discuss the design of this neural model to compromise between prediction accuracy and inference time for a large number of table cell pairs, and propose some practical techniques to address the issue of extreme classification imbalance among pairs. Experiments show that our model achieves macro F1 = 0.8297 in linking semantically equivalent table cells from the IPO prospectus. Finally, an auditing tool is built to support guided cross-checking over financial documents, reducing work hours by 52% ~ 68%. This system has received wide recognition in the Chinese financial community. Nine of the top ten Chinese security brokers have adopted this system to support their business of investment banking.

Natural language is used to describe objective facts, including simple relations like ""Jobs was the CEO of Apple"", and complex relations like ""the GDP of the United States in 2018 grew 2.9% compared with 2017". For the latter example, the growth rate relation is between two other relations. Due to the complex nature of language, this kind of nested relations is expressed frequently, especially in professional documents in fields like economics, finance, and biomedicine. But extracting nested relations is challenging, and research on this problem is almost vacant. In this paper, we formally formulate the nested relation extraction problem, and come up with a solution using Iterative Neural Network. Specifically, we observe that the nested relation structures can be expressed as a Directed Acyclic Graph (DAG), and propose the model to simultaneously consider the word sequence of natural language in the horizontal direction and the DAG structure in the vertical direction. Based on two nested relation extraction tasks, namely semantic causality relation extraction and formula extraction, we show that the proposed model works well on them. Moreover, we speed up the DAG-LSTM training significantly by a simple parallelization solution.

Verbal descriptions over the numerical relationships among some objective measures widely exist in the published documents on Web, especially in the financial fields. However, due to large volumes of documents and limited time for manual cross-check, these claims might be inconsistent with the original structured data of the related indicators even after official publishing. Such errors can seriously affect investors' assessment of the company and may cause them to undervalue the firm even if the mistakes are made unintentionally instead of deliberately. It creates an opportunity for automated Numerical Cross-Checking (NCC) systems. This paper introduces the key component of such a system, formula extractor, which extracts formulas from verbal descriptions of numerical claims. Specifically, we formulate this task as a DAG-structure prediction problem, and propose an iterative relation extraction model to address it. In our model, we apply a bi-directional LSTM followed by a DAG-structured LSTM to extract formulas layer by layer iteratively. Then, the model is built using a human-labeled dataset of tens of thousands of sentences. The evaluation shows that this model is effective in formula extraction. At the relation level, the model achieves a 97.78% precision and 98.33% recall. At the sentence level, the predictions over 92.02% of sentences are perfect. Overall, the project for NCC has received wide recognition in the Chinese financial community.