Arithmetic Reasoning with LLM: Prolog Generation & Permutation
Summary
Paper digest
What problem does the paper attempt to solve? Is this a new problem?
The paper aims to enhance the reasoning performance of Large Language Models (LLMs) by using Prolog generation and permutation to solve mathematical questions . This paper addresses the challenge of improving LLMs' ability to solve mathematical problems involving arithmetic, commonsense, and symbolic reasoning, which are areas where LLMs typically struggle . The approach of generating Prolog programs to solve mathematical questions is a novel method proposed in the paper to improve the performance of LLMs in arithmetic reasoning tasks .
What scientific hypothesis does this paper seek to validate?
This paper aims to validate the scientific hypothesis that instructing large language models (LLMs) to focus on extracting predicates and generating symbolic formulas from math problem descriptions, rather than generating a sequence of arithmetic calculations, can lead to improved arithmetic problem-solving by using Prolog programs . The hypothesis suggests that by leveraging Prolog-based arithmetic problem-solving, LLMs can outperform traditional approaches like Chain-of-Thought (CoT) generation in solving mathematical questions . Additionally, the paper proposes a data augmentation method called PROPER specifically designed for Prolog code generation to enhance the model's accuracy and mitigate early convergence during training .
What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?
The paper proposes several innovative ideas, methods, and models in the field of arithmetic reasoning with Large Language Models (LLMs) . One key proposal is to shift the focus of LLMs from generating sequences of arithmetic calculations to extracting predicates and generating symbolic formulas from math problem descriptions. This approach aims to enhance reasoning performance by allowing an external code interpreter to handle the underlying calculations based on the symbolic formulas generated by the LLMs .
Additionally, the paper introduces the use of Prolog programs generated by LLMs to solve mathematical questions. Experimental results demonstrate that this Prolog-based arithmetic problem-solving method outperforms the Chain of Thought (CoT) generation approach in the GSM8K benchmark across different LLMs . This shift towards Prolog-based solutions showcases improved performance in arithmetic reasoning tasks.
Furthermore, the paper suggests a data augmentation technique involving the permutation of ground truth predicates to enhance the robustness of LLM training. By permuting the predicates in Prolog, the training process becomes more resilient, allowing models to learn to extract predicates from mathematical questions regardless of their ordering. This approach aims to provide more precise reflections of the nature of mathematical problems and improve the overall performance of LLMs in arithmetic reasoning tasks . The paper introduces novel characteristics and advantages compared to previous methods in arithmetic reasoning with Large Language Models (LLMs) . One key characteristic is the shift in focus from generating sequences of arithmetic calculations to extracting predicates and generating symbolic formulas from math problem descriptions. This approach allows an external code interpreter to handle the underlying calculations based on the symbolic formulas generated by the LLMs, enhancing reasoning performance .
Furthermore, the paper proposes the use of Prolog programs generated by LLMs to solve mathematical questions, showcasing improved performance compared to the Chain-of-Thought (CoT) generation approach across different LLMs . The Prolog-based arithmetic problem-solving method consistently outperforms CoT, demonstrating a 10.9% margin over the CoT baseline on average across all models on the GSM8K dataset .
Additionally, the paper introduces PROPER, a data augmentation method specifically designed for Prolog code generation. PROPER enables finetuned models to learn the non-sequential nature of Prolog predicates, improving accuracy on the GSM8K-Prolog dataset and mitigating early convergence during training . This data augmentation technique enhances the robustness of LLM training by permuting ground truth predicates, allowing models to learn to extract predicates regardless of their ordering .
Moreover, the paper highlights the use of the PySwip library as a Prolog interpreter to produce final answers, showcasing the practical implementation of Prolog-based arithmetic reasoning with LLMs . The Prolog generation approach consistently outperforms CoT across different LLMs, indicating exceptional superiority over CoT in solving arithmetic reasoning problems . This shift towards Prolog-based solutions and the utilization of data augmentation techniques contribute to enhanced performance and accuracy in arithmetic reasoning tasks compared to previous methods .
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 studies exist in the field of arithmetic reasoning with large language models (LLMs). Noteworthy researchers in this area include Zheng Yuan, Hongyi Yuan, Chengpeng Li, Guanting Dong, Chuanqi Tan, Chang Zhou, Yifan Zhang, Jingqin Yang, Andrew Chi-Chih Yao, Denny Zhou, Nathanael Schärli, Le Hou, Jason Wei, Nathan Scales, Xuezhi Wang, Dale Schuurmans, Claire Cui, Olivier Bousquet, Quoc Le, Ed Chi, Xinyu Zhu, Junjie Wang, Lin Zhang, Yuxiang Zhang, Yongfeng Huang, Ruyi Gan, Jiaxing Zhang, Yujiu Yang, Thibaut Lavril, Thomas Wang, Timothée Lacroix, William El Sayed, Tian Liang, Zhiwei He, Wenxiang Jiao, Xing Wang, Yan Wang, Rui Wang, Zhaopeng Tu, Shuming Shi, Jieyi Long, Qing Lyu, Shreya Havaldar, Adam Stein, Li Zhang, Delip Rao, Eric Wong, Marianna Apidianaki, Chris Callison-Burch, Swaroop Mishra, Matthew Finlayson, Pan Lu, Leonard Tang, Sean Welleck, Chitta Baral, Tanmay Rajpurohit, Oyvind Tafjord, Ashish Sabharwal, Peter Clark, Ashwin Kalyan, Arvind Neelakantan, Quoc V. Le, Martin Abadi, Andrew McCallum, Dario Amodei, Maxwell Nye, Michael Henry Tessler, Joshua B. Tenenbaum, Brenden M. Lake, Liangming Pan, Alon Albalak, Xinyi Wang, William Yang Wang, Jack W Rae, Sebastian Borgeaud, Trevor Cai, Katie Millican, Jordan Hoffmann, Francis Song, John Aslanides, Sarah Henderson, Roman Ring, Susannah Young, among others .
The key to the solution mentioned in the paper involves instructing large language models (LLMs) to focus on extracting predicates and generating symbolic formulas from math problem descriptions. This approach allows the LLMs to generate Prolog programs to solve mathematical questions. Experimental results have shown that this Prolog-based arithmetic problem-solving method outperforms the Chain of Thought (CoT) generation approach in the GSM8K benchmark across different LLMs. Additionally, the paper proposes a data augmentation method called PROPER, designed specifically for Prolog code generation, to enhance model accuracy and mitigate early convergence during training .
How were the experiments in the paper designed?
The experiments in the paper were designed by conducting training and evaluation processes using different Large Language Models (LLMs) such as Llama2, CodeLlama, and Mistral on the GSM8K and GSM-HARD datasets . The training involved experimenting with various settings, including different LoRA rank and alpha configurations, with the most effective setting being r = 32, α = 64 . During training, the models were fine-tuned using 8-bit quantization and LoRA to optimize performance efficiently . At inference time, beam search with a beam size of 4 was used to generate Prolog code, and the PySwip library was employed as the Prolog interpreter for producing the final answer . The evaluation metric used was accuracy, comparing the performance of Prolog generation against the CoT baseline, showing a significant improvement in accuracy with Prolog generation across all models on the GSM8K and GSM-HARD datasets .
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-Prolog dataset, which is a high-quality Prolog-annotated version of the GSM8K dataset . The code for creating this dataset is open source, as it was contributed to the research community with the MIT license .
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 study conducted experiments using different Large Language Models (LLMs) such as Llama2, CodeLlama, and Mistral, and compared the performance of Prolog generation against the Chain-of-Thought (CoT) baseline . The results consistently showed that Prolog generation outperformed CoT across all three models, demonstrating a significant improvement in accuracy, with a margin of 10.9% on average across all models on the GSM8K dataset and expanding to 22.6% on the challenging GSM-HARD dataset . This indicates the exceptional superiority of Prolog generation over CoT in solving arithmetic reasoning tasks.
Furthermore, the study introduced a data augmentation method called PROPER specifically designed for Prolog code generation. PROPER aimed to help the finetuned models learn the non-sequential nature of Prolog predicates, leading to improved accuracy on the GSM8K-Prolog dataset and mitigating early convergence during training . The results showed that PROPER enhanced the model's performance, highlighting the effectiveness of this augmentation technique in enhancing the model's learning capabilities.
Moreover, the study suggested using validation accuracy instead of validation loss to select the best checkpoint for the models. By choosing checkpoints based on validation accuracy, the performance of the Prolog and PROPER methods significantly improved compared to the CoT baseline, indicating a divergence between the objective of cross-entropy loss and the ultimate accuracy of Prolog generation . This recommendation based on the analysis of validation accuracy contributes to refining the training process and improving the overall performance of the models.
In conclusion, the experiments and results presented in the paper provide robust evidence supporting the scientific hypotheses under investigation. The study's methodology, experimental setup, and analysis of results offer valuable insights into the effectiveness of Prolog generation, the impact of data augmentation techniques like PROPER, and the importance of selecting checkpoints based on validation accuracy for enhancing the performance of Large Language Models in solving arithmetic reasoning tasks .
What are the contributions of this paper?
The paper makes several contributions:
- It explores the use of Large Language Models (LLMs) to generate Prolog programs for solving mathematical questions, outperforming the Chain of Thought (CoT) generation in the GSM8K benchmark across three distinct LLMs .
- The paper proposes permuting the ground truth predicates to enhance LLM training robustness through data augmentation .
- It discusses the limitations of the experimental results due to the limited size of the original corpus and the impact of model scaling on the performance of Prolog code generation for arithmetic reasoning .
- The paper aims to enhance the reasoning performance of LLMs by generating Prolog predicates from mathematical question descriptions and using an external Prolog interpreter to process the queries .
- It contributes to the field of arithmetic reasoning by leveraging LLMs to generate symbolic formulas and predicates for solving mathematical problems, focusing on extracting predicates from the problem description to improve calculation accuracy .
What work can be continued in depth?
Further research in this field can delve deeper into several areas to enhance the performance of large language models (LLMs) in arithmetic reasoning:
- Dataset Augmentation: Future studies can explore preparing a larger and more diverse corpus specifically tailored for Prolog code generation to improve the reasoning performance of LLMs .
- Model Scaling Impact: Investigating the impact of scaling the base model to more than 7 billion parameters on the performance of Prolog code generation for arithmetic reasoning could provide valuable insights .
- Expanding Domain: Expanding the domain by using other interpreting tools beyond PySwip to handle questions with non-integer answers could broaden the scope of solvable questions and improve the versatility of LLMs in arithmetic reasoning tasks .