Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems (1811.00720v2)

Abstract: Solving math word problems is a challenging task that requires accurate natural language understanding to bridge natural language texts and math expressions. Motivated by the intuition about how human generates the equations given the problem texts, this paper presents a neural approach to automatically solve math word problems by operating symbols according to their semantic meanings in texts. This paper views the process of generating equation as a bridge between the semantic world and the symbolic world, where the proposed neural math solver is based on an encoder-decoder framework. In the proposed model, the encoder is designed to understand the semantics of problems, and the decoder focuses on tracking semantic meanings of the generated symbols and then deciding which symbol to generate next. The preliminary experiments are conducted in a dataset Math23K, and our model significantly outperforms both the state-of-the-art single model and the best non-retrieval-based model over about 10% accuracy, demonstrating the effectiveness of bridging the symbolic and semantic worlds from math word problems.

Review of "Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems"

The paper by Ting-Rui Chiang and Yun-Nung Chen addresses the complex task of solving math word problems, an area that tests both natural language understanding and mathematical reasoning. The authors propose a sophisticated neural approach based on an encoder-decoder framework that focuses on mapping natural language text to mathematical expressions through semantically-aligned equation generation.

Core Methodology

The proposed model operates under the premise that mathematical symbols in an equation must be directly semantically linked to the corresponding components within the problem text. To this end, the encoder is tasked with deriving semantic representations for numerical entities within the problem, while the decoder is responsible for maintaining these semantic links as it outputs mathematical symbols.

One of the core innovations of this work is the use of a stack in the decoding process to manage semantic representation tracking, which mimics the cognitive process humans undergo when translating word problems into equations. This approach employs stack actions reminiscent of human symbolic manipulation, thereby attempting to maintain cognitive analogy in the generation of equations.

Numerical Results and Performance

The experimental evaluation performed on the Math23K dataset demonstrates the efficacy of the proposed approach. The model outperforms existing models by approximately 10% in accuracy. Notably, the performance improvement is achieved without relying on retrieval-based methods, which often lack generalizability due to their dependency on template matching.

Implications and Future Directions

The model's ability to offer interpretable steps in the reasoning and solving process is significant both practically and theoretically. It addresses shortcomings of previous models that required extensive human knowledge to define equation templates, thereby making strides toward a more autonomous solution capability in AI.

The research highlights the importance of semantic understanding in bridging the gap between natural language and mathematical computational logic. It paves the way for further exploration of generalized symbol manipulation frameworks in AI, which could extend to more complex domains beyond arithmetic, such as algebraic and geometric problem-solving.

Moreover, the methodology could have far-reaching implications in educational technology, where automated problem-solving systems could support student learning by providing step-by-step reasoning for solutions.

Conclusion

Chiang and Chen's work is a significant contribution to the field of solving math word problems through AI. By focusing on semantic alignment between text and symbols, the proposed neural math solver model sets a new precedence in performance and interpretability. As AI-driven methods continue to evolve, models like this lay the groundwork for more comprehensive systems capable of understanding and solving increasingly complex linguistic and symbolic challenges.