Solving General Arithmetic Word Problems (1608.01413v2)

Abstract: This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional annotations or predefined templates. We develop a theory for expression trees that can be used to represent and evaluate the target arithmetic expressions; we use it to uniquely decompose the target arithmetic problem to multiple classification problems; we then compose an expression tree, combining these with world knowledge through a constrained inference framework. Our classifiers gain from the use of {\em quantity schemas} that supports better extraction of features. Experimental results show that our method outperforms existing systems, achieving state of the art performance on benchmark datasets of arithmetic word problems.

Solving General Arithmetic Word Problems: A Summary

This paper introduces a novel approach to automatically tackling arithmetic word problems, a subset of natural language processing challenges that necessitate the combination of numerical values with basic arithmetic operations. The method proposed is unique in its breadth, able to solve arithmetic problems that require multiple steps and operations without resorting to predefined templates or additional annotated data. The approach centers around a theoretical framework and computational implementation that builds upon the notion of expression trees.

Core Contributions

A significant contribution of this research is the development of a theory around monotonic expression trees. The authors propose that arithmetic expressions can be uniformly represented using such trees, which ensures unique decomposition of the problem. This theoretical foundation enables the decomposition of the natural language problem into simpler classification tasks, where each task involves predicting the lowest common ancestor operation between pairs of numerical quantities mentioned in the problem text.

The paper also introduces a new concept called "quantity schemas," which are utilized for effective feature extraction. Quantity schemas help the classifiers isolate relevant information from surrounding noise in the text, thereby improving the accuracy of classification.

Methodology

The authors' approach entails several stages:

1. Quantity Detection and Schema Extraction: Extract quantity schemas from text to capture contextual information relevant to each number mentioned.
2. Expression Tree Framework: Represent the problem as an expression tree where each arithmetic operation corresponds to an internal node and quantities form the leaves.
3. Classification and Inference: Use classifiers to predict the relevance of each quantity and determine the operation at the lowest common ancestor of each quantity pair. The output from classifiers is combined using a constrained inference framework, considering world knowledge to refine the final expression tree representing the problem's solution.

Notably, constraints in the inference process (such as ensuring non-negative and integral solutions) further refine the problem-solving capability of the model.

Results

The proposed method is evaluated across several datasets, demonstrating its ability to outperform existing systems. The results show state-of-the-art performance on two benchmark datasets of arithmetic word problems. Notably, the system achieved a strong performance on a newly created dataset, specifically designed to evaluate its ability to solve multistep arithmetic problems, highlighting the algorithm's generalization capabilities.

Practical and Theoretical Implications

This work proposes a robust model for solving arithmetic word problems by leveraging advanced methods in machine learning and natural language processing. Practically, the ability to solve such problems without predefined templates extends the flexibility of AI systems in educational contexts, financial computations, and automated assistants. Theoretically, the concept of monotonic expression trees lays the groundwork for future exploration in other areas such as algebra word problems, paving the way for expanding these techniques to more complex problems involving variables.

Future Directions

One potential extension of this research lies in adapting the methodology to solve algebra word problems. By allowing leaves to represent variables, expression trees could be adapted to encompass algebraic expressions, thereby tackling a broader class of mathematical challenges. Additionally, improving quantity schema extraction and handling more diverse linguistic constructs could further enhance the system's accuracy and applicability.

Overall, the paper presents a comprehensive and well-evaluated approach that not only advances the field of automatic mathematical problem solving but also contributes a novel theoretical framework with potential applications beyond arithmetic problems.