Neural Mathematical Solver with Enhanced Formula Structure

Huang, Zhenya; Liu, Qi; Gao, Weibo; Wu, Jinze; Yin, Yan; Wang, Hao; Chen, Enhong

doi:10.1145/3397271.3401227

Cited by 21 publications

(7 citation statements)

References 6 publications

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“…In Natural Language Processing (NLP), knowledge-addition methods have shown the potential to enhance problem comprehension through the utilization of explicit expert knowledge. Several recent studies [15][16][17] have focused on using additional information to aid in understanding problems. For instance, Graph2Tree [18] was introduced to capture relationships and order information among quantities.…”

Section: The Knowledge-addition Methods Solving Dir-awpmentioning

confidence: 99%

Solving Arithmetic Word Problems of Entailing Deep Implicit Relations by Qualia Syntax-Semantic Model

Meng,

Yu,

et al. 2023

CMC

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Solving arithmetic word problems that entail deep implicit relations is still a challenging problem. However, significant progress has been made in solving Arithmetic Word Problems (AWP) over the past six decades. This paper proposes to discover deep implicit relations by qualia inference to solve Arithmetic Word Problems entailing Deep Implicit Relations (DIR-AWP), such as entailing commonsense or subject-domain knowledge involved in the problem-solving process. This paper proposes to take three steps to solve DIR-AWPs, in which the first three steps are used to conduct the qualia inference process. The first step uses the prepared set of qualia-quantity models to identify qualia scenes from the explicit relations extracted by the Syntax-Semantic (S 2 ) method from the given problem. The second step adds missing entities and deep implicit relations in order using the identified qualia scenes and the qualia-quantity models, respectively. The third step distills the relations for solving the given problem by pruning the spare branches of the qualia dependency graph of all the acquired relations. The research contributes to the field by presenting a comprehensive approach combining explicit and implicit knowledge to enhance reasoning abilities. The experimental results on Math23K demonstrate hat the proposed algorithm is superior to the baseline algorithms in solving AWPs requiring deep implicit relations.

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Section: The Knowledge-addition Methods Solving Dir-awpmentioning

confidence: 99%

Solving Arithmetic Word Problems of Entailing Deep Implicit Relations by Qualia Syntax-Semantic Model

Meng,

Yu,

et al. 2023

CMC

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“…Other approaches have made a key contribution by utilizing additional knowledge such as semantic meaning. Some take advantage of structural information such as hierarchical dependency (Shen and Jin, 2020;, formula structure (Huang et al, 2020), graph-edge connection information (Zhang et al, 2020b;Wu et al, 2021;Li et al, 2020) and more Shen et al, 2021).…”

Section: Related Workmentioning

confidence: 99%

ATHENA: Mathematical Reasoning with Thought Expansion

Kim,

Hahn

et al. 2023

Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing

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Solving math word problems depends on how to articulate the problems, the lens through which models view human linguistic expressions. Real-world settings count on such a method even more due to the diverse practices of the same mathematical operations. Earlier works constrain available thinking processes by limited prediction strategies without considering their significance in acquiring mathematical knowledge. We introduce Attention-based THought Expansion Network Architecture (ATHENA) to tackle the challenges of real-world practices by mimicking human thought expansion mechanisms in the form of neural network propagation. A thought expansion recurrently generates the candidates carrying the thoughts of possible math expressions driven from the previous step and yields reasonable thoughts by selecting the valid pathways to the goal. Our experiments show that ATHENA achieves a new state-of-the-art stage toward the ideal model that is compelling in variant questions even when the informativeness in training examples is restricted. 1 Context The school playground was originally [80] meters long and [40] meters wide. Later when the school is remodeled, the length is increased by [10] meters and the width is increased by [15] meters.Train on an example of a question-solution pair under the context above.Question How many square meters is the original playground area?Solution (80 × 40)Test on variant questions that share the context above. Q0 How many times the length of the original playground was the width? DeductReasoner ATHENA UnbiasedMWP (80 + 10) × (40 + 15) − (80 × 40) (X) UnbiasedMWP (80 + 10) × (40 − 15) (X) UnbiasedMWP (1:N) 80 ÷ 40 (O) UnbiasedMWP (1:N) 80 ÷ 40 (O) Q1 How many square meters is the current playground area? DeductReasoner ATHENA UnbiasedMWP (80 + 10) × (40 + 15) − (80 × 40) (X) UnbiasedMWP (80 + 10) × (40 + 15) (O) UnbiasedMWP (1:N) 80 × 40 (X) UnbiasedMWP (1:N) (80 + 10) × (40 + 15) (O) Q2 How many square meters are increased by the current playground area compared to the original one? DeductReasoner ATHENA UnbiasedMWP (80 + 10) × (40 + 15) − (80 × 40) (O) UnbiasedMWP (80 + 10) × (40 + 15) − (80 × 40) (O) UnbiasedMWP (1:N) 80 × 40 (X) UnbiasedMWP (1:N) (80 + 10) × (40 + 15) − (80 × 40) (O) An example with a lexically similar context to that of above from the UnbiasedMWP Context The school basketball court was [20] meters long and [12] meters wide. After the renovation, the length is increased by [8] meters, and the width increases by [3] meters. Question How many square meters are increased? Solution (20 + 8) × (12 + 3) − (20 × 12

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“…To model quantity relations in problems, Zhang et al (2020) constructed graphs for quantityrelated features to enhance problem understanding. In recent years, more difficult mathematical problems were also tackled (Huang et al 2020) in addition to traditional MWP.…”

Section: Related Workmentioning

confidence: 99%

HMS: A Hierarchical Solver with Dependency-Enhanced Understanding for Math Word Problem

Lin

Huang

Zhao

et al. 2021

AAAI

Self Cite

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Automatically solving math word problems is a crucial task for exploring the intelligence levels of machines in the general AI domain. It is highly challenging since it requires not only natural language understanding but also mathematical expression inference. Existing solutions usually explore sequence-to-sequence models to generate expressions, where the problems are simply encoded sequentially. However, such models are generally far from enough for understanding problems as similar to humans and lead to incorrect answers. To this end, in this paper, we propose a novel Hierarchical Math Solver (HMS) to make deep understanding and exploitation of problems. In problem understanding, imitating human reading habits, we propose a hierarchical word-clause-problem encoder. Specifically, we first split each problem into several clauses and learn problem semantics from the local clause level to the global problem level. Then, in clause understanding, we propose a dependency-based module to enhance clause semantics with the dependency structure of the problem. Next, in expression inference, we propose a novel tree-based decoder to generate the mathematical expression for the answer. In the decoder, we apply a hierarchical attention mechanism to enhance the problem semantics with context from different levels, and a pointer-generator network to guide the model to copy existing information and infer extra knowledge. Extensive experimental results on two widely used datasets demonstrate that HMS achieves not only better answers but also more reasonable inference.

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Neural Mathematical Solver with Enhanced Formula Structure

Cited by 21 publications

References 6 publications

Solving Arithmetic Word Problems of Entailing Deep Implicit Relations by Qualia Syntax-Semantic Model

Solving Arithmetic Word Problems of Entailing Deep Implicit Relations by Qualia Syntax-Semantic Model

ATHENA: Mathematical Reasoning with Thought Expansion

HMS: A Hierarchical Solver with Dependency-Enhanced Understanding for Math Word Problem

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