Math Question Solving via Formula Relationship Mapping
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Solution Overview
Problem
Existing large language models (LLMs) struggle to accurately understand and solve mathematical questions due to their inability to interpret and reason with exact answers, necessitating an explainable and reliable method for automatic solving and interpretation of such questions.
Innovation Solution
A method that decomposes mathematical questions into sentences, converts formula sentences into corresponding formulas, establishes a formula relationship map, and calculates variable values, with error detection and interactive explanations, using neural networks for classification and inference.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If large language models are used to answer mathematical questions, then the system can process natural language input, but the model cannot accurately understand and solve mathematical questions requiring exact answers
Solution Approach 1:
The patent segments the mathematical question processing into distinct components: natural language understanding module, mathematical formula conversion module, reasoning module, and calculation module. This segmentation allows each component to specialize in specific tasks, with the formula conversion module transforming natural language into precise mathematical representations that can be reliably solved, thereby resolving the contradiction between processing versatility and answer accuracy.
Solution Approach 2:
The patent introduces mathematical formulas as an intermediary representation between natural language questions and final answers. The formula conversion module acts as a mediator that translates ambiguous natural language into precise mathematical notation, enabling accurate reasoning and calculation while maintaining the ability to process diverse natural language inputs.
2Loss of information
If the system provides detailed step-by-step reasoning for mathematical solutions, then the explainability improves, but the complexity of the system increases
Solution Approach 1:
The patent segments the reasoning process into discrete, manageable steps that correspond to different modules in the system. Each module handles a specific aspect of the reasoning process, making the overall system more explainable while keeping individual components relatively simple. The step-by-step reasoning is generated by coordinating these segmented modules rather than requiring a single complex reasoning engine.
3Adaptability or versatility
If the system handles complex mathematical questions with multiple graphs and formulas, then the scope of solvable questions expands, but the processing time increases
Solution Approach 1:
The patent segments the processing of complex mathematical questions into parallel operations across multiple specialized modules. The natural language understanding, formula conversion, reasoning, and calculation modules can operate in parallel where possible, reducing overall processing time while maintaining the ability to handle complex questions with multiple graphs and formulas.
Solution Approach 2:
The patent performs preliminary actions by pre-processing the mathematical question into standardized formulas and representations before the main reasoning and calculation process. This preliminary conversion step organizes the information in a way that facilitates faster subsequent processing, reducing the time required to solve complex mathematical problems.
Data Source
AI summary
A method of machine solving mathematical question is provided. The method comprises receiving a mathematical question described in a natural language; decomposing the mathematical question into multiple sentences, wherein the multiple sentences include one question sentence; establishing a relationship map of formula according to the relations of the one or more variables included each of the sentences; and calculating, sequentially, values of the one or more variables according to the relationship map of formula until a value of the variable included in the formula of the question sentence is calculated as an answer.