This paper presents a tag-based statistical math word problem solver with understanding, reasoning, and explanation. It analyzes the text and transforms both body and question parts into their tag-based logic forms, and then performs inference on them. The proposed tag-based approach provides the flexibility for annotating an extracted math quantity with its associated syntactic and semantic information, which can be used to identify the desired operand and filter out irrelevant quantities. The proposed approach is thus less sensitive to the irrelevant information and could provide the answer more precisely. Also, it can handle much more problem types other than addition and subtraction.

In this paper, an objective qtumtitative quality measure is proposed to evaluate tile performance of machiue translation systems. The proposed method is to compare the raw translation output of an MT system with the final revised version lor the customers, and then compute the editing efforts required to convert the raw translation to the final version. In contrast to the other prolx)sals, the evaluatiral process can he (lone quickly and automatically. Itence, it can provide a quick response on any system change. A system designer can thus quickly lind the advantages or faults of a particular performanceimproving strategy aml improve system performance dynamieally. Application of such a measure to improve the system performance on-line on a parameterized and feedback-controlled system will be demonstrated. Furthermore, because the revised versiou is used directly as a reference, tile perfoInunice lneasnre can reflect tile real quality gap between the system performance and customer expectation. A system designer can thus concentrate on practically impo~ult topics rather than ml theoretically interesting issues. Based on the above problems with human inspection, some automatic approaches were proposed to eval

We present ASDiv (Academia Sinica Diverse MWP Dataset), a diverse (in terms of both language patterns and problem types) English math word problem (MWP) corpus for evaluating the capability of various MWP solvers. Existing MWP corpora for studying AI progress remain limited either in language usage patterns or in problem types. We thus present a new English MWP corpus with 2,305 MWPs that cover more text patterns and most problem types taught in elementary school. Each MWP is annotated with its problem type and grade level (for indicating the level of difficulty). Furthermore, we propose a metric to measure the lexicon usage diversity of a given MWP corpus, and demonstrate that ASDiv is more diverse than existing corpora. Experiments show that our proposed corpus reflects the true capability of MWP solvers more faithfully.

We introduce MeSys, a meaning-based approach, for solving English math word problems (MWPs) via understanding and reasoning in this paper. It first analyzes the text, transforms both body and question parts into their corresponding logic forms, and then performs inference on them. The associated context of each quantity is represented with proposed role-tags (e.g., nsubj, verb, etc.), which provides the flexibility for annotating an extracted math quantity with its associated context information (i.e., the physical meaning of this quantity). Statistical models are proposed to select the operator and operands. A noisy dataset is designed to assess if a solver solves MWPs mainly via understanding or mechanical pattern matching. Experimental results show that our approach outperforms existing systems on both benchmark datasets and the noisy dataset, which demonstrates that the proposed approach understands the meaning of each quantity in the text more.

In this article, an integrated model is derived that jointly identifies and aligns bilingual named entities (NEs) between Chinese and English. The model is motivated by the following observations: (1) whether an NE is translated semantically or phonetically depends greatly on its entity type, (2) entities within an aligned pair should share the same type, and (3) the initially detected NEs can act as anchors and provide further information while selecting NE candidates. Based on these observations, this article proposes a translation mode ratio feature (defined as the proportion of NE internal tokens that are semantically translated), enforces an entity type consistency constraint, and utilizes additional new NE likelihoods (based on the initially detected NE anchors).Experiments show that this novel method significantly outperforms the baseline. The typeinsensitive F-score of identified NE pairs increases from 78.4% to 88.0% (12.2% relative improvement) in our Chinese-English NE alignment task, and the type-sensitive F-score increases from 68.4% to 83.0% (21.3% relative improvement). Furthermore, the proposed model demonstrates its robustness when it is tested across different domains. Finally, when semi-supervised learning is conducted to train the adopted English NE recognition model, the proposed model also significantly boosts the English NE recognition type-sensitive F-score.