MathDivide: Improved mathematical reasoning by large language models

Saksham Sahai Srivastava, Ashutosh Gandhi·May 12, 2024

Summary

The paper "MathDivide: Improved Mathematical Reasoning by Large Language Models" introduces a novel technique that enhances large language models' (LLMs) ability to solve math problems. By breaking down complex problems into simpler sub-problems, converting them into algebraic expressions, and using Python code execution, MathDivide improves performance compared to existing methods like MathPrompter. The study tests the approach on various LLMs, including proprietary models (GPT-3.5-turbo and GPT-4) and open-source ones (Llama2 and Llama3), using the GSM8K dataset. MathDivide, with human feedback for refinement, shows superior accuracy, especially in the case of proprietary models. However, the research is limited by the dataset size and the need for further testing on diverse data. The study also touches upon the potential of LLMs in logical reasoning and the importance of responsible research practices. Other papers in the collection explore related advancements, such as code generation, few-shot learning, and the role of prompts and supervision in improving mathematical reasoning.

Key findings

2

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to address the challenge of enhancing the mathematical reasoning capability of large language models (LLMs) through a novel prompting technique called MathDivide. This technique involves breaking down complex mathematical problems into smaller, more manageable sub-problems, leveraging human feedback-based refinement loops to improve accuracy, and structuring the problem-solving process in a step-by-step manner . This problem of improving mathematical reasoning in LLMs is not entirely new, as previous research has explored different prompting techniques to enhance the reasoning abilities of these models .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate the scientific hypothesis that the proposed prompting technique called MathDivide significantly enhances the mathematical reasoning capability of large language models by breaking down complex mathematical problems into smaller and simpler sub-problems, leveraging a human-feedback-based refinement loop to improve accuracy, and outperforming leading prompting techniques like Mathprompter . The study focuses on improving the mathematical reasoning ability of pre-trained large language models by structuring the problem-solving process similar to how a student solves a mathematical problem step-by-step, demonstrating the potential of breaking down problems into smaller subproblems to enhance performance .


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

I would be happy to help analyze the new ideas, methods, or models proposed in a paper. Please provide me with the specific details or key points from the paper that you would like me to focus on for analysis. The paper "MathDivide: Improved mathematical reasoning by large language models" proposes a novel prompting technique called MathDivide that enhances the mathematical reasoning capability of large language models . This technique breaks down complex mathematical problems into smaller, simpler sub-problems and leverages a human-feedback-based refinement loop to improve accuracy . Compared to previous methods, MathDivide outperformed the leading prompting technique Mathprompter, showcasing the significance of structured problem-solving in mathematics .

One key advantage of MathDivide is its structured approach, where the mathematical problem is decomposed into manageable sub-problems formulated as algebraic expressions . This method allows the large language models to solve each sub-problem sequentially, leading to a more systematic and accurate problem-solving process . Additionally, MathDivide incorporates a human-based feedback mechanism for refinement, ensuring context-aware and accurate corrections .

Furthermore, the paper emphasizes the ethical implications of the research by ensuring fairness in comparisons with existing techniques, transparency in methodology descriptions, and accountability in the research processes . This commitment to ethical standards enhances the credibility and reliability of the proposed MathDivide technique .


Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

Several related research works exist in the field of improving mathematical reasoning using large language models. Noteworthy researchers in this field include Noorbakhsh et al., Yuan et al., Yamauchi et al., Imani et al., and many others . The key to the solution mentioned in the paper is a novel prompting technique called MathDivide, which significantly enhances the mathematical reasoning capability of large language models by breaking down complex mathematical problems into smaller and simpler sub-problems. This technique leverages a human-feedback-based refinement loop to further enhance accuracy and beat the performance of existing prompting techniques .


How were the experiments in the paper designed?

The experiments in the paper were designed by utilizing a prompting technique called MathDivide to enhance the mathematical reasoning capability of large language models . The experimentation involved conducting tests with both proprietary models like GPT-3.5-turbo and GPT-4, as well as open-source LLM models such as Llama2 and Llama3 . The experiments focused on solving math word problems from the GSM8K dataset using the Mathprompter technique, which was evaluated on the MultiArith dataset . The MathDivide technique was assessed on the same LLM models and dataset to ensure a fair and direct comparison . The experiments also involved running the Llama2 and Llama3 models using an open-source project called Ollama, which provides memory-quantized versions of various LLMs through an API . Additionally, a Python script was implemented to parse the GSM8K dataset, append custom prompts to questions, and call the Ollama API to obtain LLM responses for evaluation .


What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study is the GSM8K dataset . The code used in the experimentation is open source, as it was run using an open-source project called Ollama, which provides a memory-quantized version of many open-sourced LLMs through an API .


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide strong support for the scientific hypotheses that needed verification. The paper introduces a novel prompting technique called MathDivide, which significantly enhances the mathematical reasoning capability of large language models (LLMs) by breaking down complex problems into simpler sub-problems and incorporating human feedback-based refinement loops . The experiments conducted with different LLM models, such as GPT-3.5-turbo, GPT-4, Llama2, and Llama3, demonstrate the effectiveness of the MathDivide technique in improving accuracy in solving mathematical word problems .

The study compares the performance of MathDivide with the Mathprompter technique on the same LLM models and dataset, showcasing that MathDivide outperformed Mathprompter, which had previously shown better accuracy compared to the state-of-the-art zero-shot-CoT prompting approach . By utilizing a structured problem decomposition approach, precise computation, and iterative refinement based on human feedback, MathDivide successfully guides the LLMs towards correct answers, showcasing the effectiveness of the proposed technique .

Furthermore, the paper addresses the ethical implications of the research by ensuring fairness in comparisons, transparency in methods and datasets used, and accountability in the research processes . This commitment to ethical standards enhances the credibility and reliability of the study's findings, supporting the scientific hypotheses and conclusions drawn from the experiments conducted .

In conclusion, the experiments and results presented in the paper provide robust evidence supporting the scientific hypotheses put forth by demonstrating the efficacy of the MathDivide prompting technique in enhancing the mathematical reasoning capabilities of large language models through structured problem-solving approaches and human feedback-based refinements .


What are the contributions of this paper?

The paper "MathDivide: Improved mathematical reasoning by large language models" makes several significant contributions:

  • Introducing a novel prompting technique called MathDivide that enhances the mathematical reasoning capability of large language models by breaking down complex problems into smaller sub-problems and leveraging human-feedback-based refinement to improve accuracy .
  • Demonstrating the importance of solving math problems in a structured manner and outperforming leading prompting techniques like Mathprompter .
  • Addressing the ethical implications of the research by ensuring fairness in comparisons, transparency in methods and datasets used, and avoiding adverse social implications .
  • Providing detailed descriptions of methods and datasets for replication and verification by other researchers, promoting accountability in the research process .
  • Combining a chain-of-thoughts approach with algebraic expression formulation, problem decomposition, precise computation using Python code snippets, and human feedback-based refinement to mimic human problem-solving strategies .
  • Contributing to the field of mathematical reasoning by improving the capabilities of pre-trained large language models through innovative prompting techniques and structured problem-solving approaches .

What work can be continued in depth?

Further research in the field of mathematical reasoning by large language models can be extended in several ways:

  • Exploration of Automated Refinement Techniques: Investigating automated techniques for refining prompts in math word problem-solving tasks could enhance scalability and efficiency in experimentation .
  • Real-Time Learning and Adaptation: Studying how large language models learn and adapt in real-time scenarios can provide insights into their continuous improvement without the need for additional supervised data or training .
  • Comparative Studies: Conducting comprehensive studies comparing the performance of different prompting techniques on diverse datasets, including real-world complex math word problems, can offer a deeper understanding of the robustness and generalizability of these techniques .
  • Enhancing Human Feedback Mechanisms: Improving the effectiveness of human-based feedback mechanisms to drive large language models towards correct answers by providing in-context learning opportunities and error corrections .
  • Innovative Prompting Techniques: Developing novel prompting techniques that leverage human feedback loops, structured problem decomposition, precise computation, and iterative refinement to enhance the analytical and logical reasoning capabilities of large language models .

Introduction
Background
Evolution of large language models in math problem-solving
Limitations of existing methods like MathPrompter
Objective
To enhance LLMs' mathematical reasoning capabilities
Introduce MathDivide technique and its benefits
Method
Data Collection
GSM8K dataset: Selection and description
Range of LLMs tested (proprietary and open-source)
Comparison with baseline methods
Data Preprocessing
Problem decomposition strategy
Conversion to algebraic expressions
Integration of Python code execution
Model Evaluation
Performance metrics: Accuracy and improvements over existing methods
Human feedback for refinement and its impact
Results and Analysis
Superior accuracy of MathDivide, especially in proprietary models
Limitations: Dataset size and need for diverse data testing
Case studies: Success stories and challenging examples
Performance Breakdown
Proprietary models (GPT-3.5-turbo, GPT-4) vs open-source models (Llama2, Llama3)
Error Analysis
Common misconceptions and areas for improvement
Ethical Considerations and Responsible Research
The role of LLMs in logical reasoning and education
Implications for responsible use and bias mitigation
Related Advances
Code generation and few-shot learning in math problem-solving
The impact of prompts and supervision on mathematical reasoning
Conclusion
Summary of findings and contributions
Future directions for research and potential real-world applications
References
List of papers and resources discussed in the collection
Basic info
papers
computation and language
artificial intelligence
Advanced features
Insights
What technique does the paper "MathDivide" introduce to enhance LLMs' math problem-solving abilities?
Which LLMs are tested in the study, and what dataset is used for evaluating MathDivide's performance?
How does MathDivide differ from existing methods like MathPrompter in solving math problems?
What are the limitations mentioned in the paper regarding the approach and the need for further research?

MathDivide: Improved mathematical reasoning by large language models

Saksham Sahai Srivastava, Ashutosh Gandhi·May 12, 2024

Summary

The paper "MathDivide: Improved Mathematical Reasoning by Large Language Models" introduces a novel technique that enhances large language models' (LLMs) ability to solve math problems. By breaking down complex problems into simpler sub-problems, converting them into algebraic expressions, and using Python code execution, MathDivide improves performance compared to existing methods like MathPrompter. The study tests the approach on various LLMs, including proprietary models (GPT-3.5-turbo and GPT-4) and open-source ones (Llama2 and Llama3), using the GSM8K dataset. MathDivide, with human feedback for refinement, shows superior accuracy, especially in the case of proprietary models. However, the research is limited by the dataset size and the need for further testing on diverse data. The study also touches upon the potential of LLMs in logical reasoning and the importance of responsible research practices. Other papers in the collection explore related advancements, such as code generation, few-shot learning, and the role of prompts and supervision in improving mathematical reasoning.
Mind map
Common misconceptions and areas for improvement
Proprietary models (GPT-3.5-turbo, GPT-4) vs open-source models (Llama2, Llama3)
Human feedback for refinement and its impact
Performance metrics: Accuracy and improvements over existing methods
Integration of Python code execution
Conversion to algebraic expressions
Problem decomposition strategy
Comparison with baseline methods
Range of LLMs tested (proprietary and open-source)
GSM8K dataset: Selection and description
Introduce MathDivide technique and its benefits
To enhance LLMs' mathematical reasoning capabilities
Limitations of existing methods like MathPrompter
Evolution of large language models in math problem-solving
List of papers and resources discussed in the collection
Future directions for research and potential real-world applications
Summary of findings and contributions
The impact of prompts and supervision on mathematical reasoning
Code generation and few-shot learning in math problem-solving
Implications for responsible use and bias mitigation
The role of LLMs in logical reasoning and education
Error Analysis
Performance Breakdown
Model Evaluation
Data Preprocessing
Data Collection
Objective
Background
References
Conclusion
Related Advances
Ethical Considerations and Responsible Research
Results and Analysis
Method
Introduction
Outline
Introduction
Background
Evolution of large language models in math problem-solving
Limitations of existing methods like MathPrompter
Objective
To enhance LLMs' mathematical reasoning capabilities
Introduce MathDivide technique and its benefits
Method
Data Collection
GSM8K dataset: Selection and description
Range of LLMs tested (proprietary and open-source)
Comparison with baseline methods
Data Preprocessing
Problem decomposition strategy
Conversion to algebraic expressions
Integration of Python code execution
Model Evaluation
Performance metrics: Accuracy and improvements over existing methods
Human feedback for refinement and its impact
Results and Analysis
Superior accuracy of MathDivide, especially in proprietary models
Limitations: Dataset size and need for diverse data testing
Case studies: Success stories and challenging examples
Performance Breakdown
Proprietary models (GPT-3.5-turbo, GPT-4) vs open-source models (Llama2, Llama3)
Error Analysis
Common misconceptions and areas for improvement
Ethical Considerations and Responsible Research
The role of LLMs in logical reasoning and education
Implications for responsible use and bias mitigation
Related Advances
Code generation and few-shot learning in math problem-solving
The impact of prompts and supervision on mathematical reasoning
Conclusion
Summary of findings and contributions
Future directions for research and potential real-world applications
References
List of papers and resources discussed in the collection
Key findings
2

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to address the challenge of enhancing the mathematical reasoning capability of large language models (LLMs) through a novel prompting technique called MathDivide. This technique involves breaking down complex mathematical problems into smaller, more manageable sub-problems, leveraging human feedback-based refinement loops to improve accuracy, and structuring the problem-solving process in a step-by-step manner . This problem of improving mathematical reasoning in LLMs is not entirely new, as previous research has explored different prompting techniques to enhance the reasoning abilities of these models .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate the scientific hypothesis that the proposed prompting technique called MathDivide significantly enhances the mathematical reasoning capability of large language models by breaking down complex mathematical problems into smaller and simpler sub-problems, leveraging a human-feedback-based refinement loop to improve accuracy, and outperforming leading prompting techniques like Mathprompter . The study focuses on improving the mathematical reasoning ability of pre-trained large language models by structuring the problem-solving process similar to how a student solves a mathematical problem step-by-step, demonstrating the potential of breaking down problems into smaller subproblems to enhance performance .


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

I would be happy to help analyze the new ideas, methods, or models proposed in a paper. Please provide me with the specific details or key points from the paper that you would like me to focus on for analysis. The paper "MathDivide: Improved mathematical reasoning by large language models" proposes a novel prompting technique called MathDivide that enhances the mathematical reasoning capability of large language models . This technique breaks down complex mathematical problems into smaller, simpler sub-problems and leverages a human-feedback-based refinement loop to improve accuracy . Compared to previous methods, MathDivide outperformed the leading prompting technique Mathprompter, showcasing the significance of structured problem-solving in mathematics .

One key advantage of MathDivide is its structured approach, where the mathematical problem is decomposed into manageable sub-problems formulated as algebraic expressions . This method allows the large language models to solve each sub-problem sequentially, leading to a more systematic and accurate problem-solving process . Additionally, MathDivide incorporates a human-based feedback mechanism for refinement, ensuring context-aware and accurate corrections .

Furthermore, the paper emphasizes the ethical implications of the research by ensuring fairness in comparisons with existing techniques, transparency in methodology descriptions, and accountability in the research processes . This commitment to ethical standards enhances the credibility and reliability of the proposed MathDivide technique .


Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

Several related research works exist in the field of improving mathematical reasoning using large language models. Noteworthy researchers in this field include Noorbakhsh et al., Yuan et al., Yamauchi et al., Imani et al., and many others . The key to the solution mentioned in the paper is a novel prompting technique called MathDivide, which significantly enhances the mathematical reasoning capability of large language models by breaking down complex mathematical problems into smaller and simpler sub-problems. This technique leverages a human-feedback-based refinement loop to further enhance accuracy and beat the performance of existing prompting techniques .


How were the experiments in the paper designed?

The experiments in the paper were designed by utilizing a prompting technique called MathDivide to enhance the mathematical reasoning capability of large language models . The experimentation involved conducting tests with both proprietary models like GPT-3.5-turbo and GPT-4, as well as open-source LLM models such as Llama2 and Llama3 . The experiments focused on solving math word problems from the GSM8K dataset using the Mathprompter technique, which was evaluated on the MultiArith dataset . The MathDivide technique was assessed on the same LLM models and dataset to ensure a fair and direct comparison . The experiments also involved running the Llama2 and Llama3 models using an open-source project called Ollama, which provides memory-quantized versions of various LLMs through an API . Additionally, a Python script was implemented to parse the GSM8K dataset, append custom prompts to questions, and call the Ollama API to obtain LLM responses for evaluation .


What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study is the GSM8K dataset . The code used in the experimentation is open source, as it was run using an open-source project called Ollama, which provides a memory-quantized version of many open-sourced LLMs through an API .


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide strong support for the scientific hypotheses that needed verification. The paper introduces a novel prompting technique called MathDivide, which significantly enhances the mathematical reasoning capability of large language models (LLMs) by breaking down complex problems into simpler sub-problems and incorporating human feedback-based refinement loops . The experiments conducted with different LLM models, such as GPT-3.5-turbo, GPT-4, Llama2, and Llama3, demonstrate the effectiveness of the MathDivide technique in improving accuracy in solving mathematical word problems .

The study compares the performance of MathDivide with the Mathprompter technique on the same LLM models and dataset, showcasing that MathDivide outperformed Mathprompter, which had previously shown better accuracy compared to the state-of-the-art zero-shot-CoT prompting approach . By utilizing a structured problem decomposition approach, precise computation, and iterative refinement based on human feedback, MathDivide successfully guides the LLMs towards correct answers, showcasing the effectiveness of the proposed technique .

Furthermore, the paper addresses the ethical implications of the research by ensuring fairness in comparisons, transparency in methods and datasets used, and accountability in the research processes . This commitment to ethical standards enhances the credibility and reliability of the study's findings, supporting the scientific hypotheses and conclusions drawn from the experiments conducted .

In conclusion, the experiments and results presented in the paper provide robust evidence supporting the scientific hypotheses put forth by demonstrating the efficacy of the MathDivide prompting technique in enhancing the mathematical reasoning capabilities of large language models through structured problem-solving approaches and human feedback-based refinements .


What are the contributions of this paper?

The paper "MathDivide: Improved mathematical reasoning by large language models" makes several significant contributions:

  • Introducing a novel prompting technique called MathDivide that enhances the mathematical reasoning capability of large language models by breaking down complex problems into smaller sub-problems and leveraging human-feedback-based refinement to improve accuracy .
  • Demonstrating the importance of solving math problems in a structured manner and outperforming leading prompting techniques like Mathprompter .
  • Addressing the ethical implications of the research by ensuring fairness in comparisons, transparency in methods and datasets used, and avoiding adverse social implications .
  • Providing detailed descriptions of methods and datasets for replication and verification by other researchers, promoting accountability in the research process .
  • Combining a chain-of-thoughts approach with algebraic expression formulation, problem decomposition, precise computation using Python code snippets, and human feedback-based refinement to mimic human problem-solving strategies .
  • Contributing to the field of mathematical reasoning by improving the capabilities of pre-trained large language models through innovative prompting techniques and structured problem-solving approaches .

What work can be continued in depth?

Further research in the field of mathematical reasoning by large language models can be extended in several ways:

  • Exploration of Automated Refinement Techniques: Investigating automated techniques for refining prompts in math word problem-solving tasks could enhance scalability and efficiency in experimentation .
  • Real-Time Learning and Adaptation: Studying how large language models learn and adapt in real-time scenarios can provide insights into their continuous improvement without the need for additional supervised data or training .
  • Comparative Studies: Conducting comprehensive studies comparing the performance of different prompting techniques on diverse datasets, including real-world complex math word problems, can offer a deeper understanding of the robustness and generalizability of these techniques .
  • Enhancing Human Feedback Mechanisms: Improving the effectiveness of human-based feedback mechanisms to drive large language models towards correct answers by providing in-context learning opportunities and error corrections .
  • Innovative Prompting Techniques: Developing novel prompting techniques that leverage human feedback loops, structured problem decomposition, precise computation, and iterative refinement to enhance the analytical and logical reasoning capabilities of large language models .
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