Mapping to Declarative Knowledge for Word Problem Solving
Proposes a method to map natural language to math expressions, improving arithmetic problem-solving accuracy.
Key Findings
Methodology
The study introduces a novel framework that maps natural language descriptions to math expressions using declarative knowledge. The method learns to select relevant declarative knowledge for each operation, modeling the mapping as a latent variable to avoid expensive annotations.
Key Results
- The method outperforms all other systems in biased data scenarios, demonstrating superior generalization.
- On a new dataset of 1492 problems, the model shows enhanced generalization capabilities.
- Ablation studies confirm the significant impact of declarative knowledge on model performance.
Significance
This research provides a new solution for solving math word problems, capable of handling multiple concepts and enhancing answer interpretability. It holds significant implications for fields requiring complex quantitative reasoning, such as financial news and sports results analysis.
Technical Contribution
The technical contributions include introducing declarative knowledge into math problem-solving, offering an interpretable solution without intermediate step annotations. The method reduces reliance on expensive annotations through latent variable modeling.
Novelty
This method is the first to model declarative knowledge mapping as a latent variable, offering higher interpretability and generalization compared to existing methods.
Limitations
- The model may struggle to accurately select appropriate declarative rules in complex mathematical relationships.
- Further research is needed to handle more complex algebraic problems.
Future Work
Future research directions include extending to more complex algebraic problems and improving the model to handle a wider range of natural language descriptions.
AI Executive Summary
Solving math word problems is a complex natural language understanding challenge, involving the recognition and application of various mathematical concepts. Existing methods perform poorly in biased data scenarios, limiting generalization.
This paper introduces a new framework that maps natural language descriptions to math expressions using declarative knowledge. By modeling this as a latent variable, the method avoids expensive annotations and enhances answer interpretability.
Experimental results show that the method excels on new datasets, outperforming all other systems. Future research will extend to more complex algebraic problems and improve the model to handle broader natural language descriptions.
Deep Analysis
Background
Math word problem-solving is a significant issue in NLP, involving the conversion of natural language descriptions into math expressions. Existing methods often rely on template matching or deep learning but perform poorly in biased data scenarios.
Core Problem
The core problem is accurately converting natural language descriptions into math expressions, especially in biased data scenarios. Solving this is crucial for improving model generalization.
Innovation
The paper's innovation lies in introducing declarative knowledge, modeled as a latent variable. This approach requires no expensive intermediate step annotations, offering higher interpretability and generalization.
Methodology
- �� Map natural language to math expressions
- �� Use declarative knowledge to select appropriate operations
- �� Model as latent variable to reduce annotation needs
- �� Use beam search for approximate inference
Experiments
The experimental design uses multiple datasets, including a new dataset of 1492 problems. The model excels in biased data scenarios, outperforming all other systems.
Results
Results show the method excels on new datasets, outperforming all other systems. Ablation studies confirm the significant impact of declarative knowledge on model performance.
Applications
This method can be applied in fields like financial news analysis and sports result interpretation, requiring complex quantitative reasoning.
Limitations & Outlook
The model may have limitations in handling complex mathematical relationships, requiring further research to extend to more complex algebraic problems.
Plain Language Accessible to non-experts
Imagine you're in a kitchen cooking. You have apples and oranges and want to know the total number of fruits. You need to add apples and oranges together. This is like adding different numbers in a math problem to get a total. Our model is like a smart assistant helping you decide whether to use addition or another method to solve the problem.
ELI14 Explained like you're 14
Imagine you're playing a game where you need different tools to complete tasks. Each tool has its own use. Our model is like a smart game assistant helping you choose the best tool for the task. Isn't that cool?
Glossary
Declarative Knowledge
A set of rules used to map natural language descriptions to math expressions.
Used to select appropriate mathematical operations.
Latent Variable
A variable not directly observed in the model, used to simplify complex problems.
Used to model the selection of declarative knowledge.
Arithmetic Word Problem
A problem requiring conversion of natural language to math expressions.
The main focus of the study.
Dimensional Analysis
A mathematical concept used to determine unit compatibility.
Used to select appropriate mathematical operations.
Part-Whole Relation
A mathematical concept used to determine relationships between quantities.
Used to select appropriate mathematical operations.
Open Questions Unanswered questions from this research
- 1 Handling more complex algebraic problems remains an open question.
- 2 Improving the model to handle broader natural language descriptions is needed.
Applications
Immediate Applications
Financial News Analysis
Can be used to analyze quantitative information in financial news, enhancing interpretation efficiency.
Long-term Vision
Educational Applications
In education, it can help students better understand and solve math problems.
Abstract
Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several mathematical concepts such as dimensional analysis, subset relationships, etc. In this paper, we develop declarative rules which govern the translation of natural language description of these concepts to math expressions. We then present a framework for incorporating such declarative knowledge into word problem solving. Our method learns to map arithmetic word problem text to math expressions, by learning to select the relevant declarative knowledge for each operation of the solution expression. This provides a way to handle multiple concepts in the same problem while, at the same time, support interpretability of the answer expression. Our method models the mapping to declarative knowledge as a latent variable, thus removing the need for expensive annotations. Experimental evaluation suggests that our domain knowledge based solver outperforms all other systems, and that it generalizes better in the realistic case where the training data it is exposed to is biased in a different way than the test data.