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Dual Instruction Tuning Strategy for Mathematical Reasoning with Large Language Models


Core Concepts
Proposing a dual instruction tuning strategy to enhance mathematical reasoning with large language models.
Abstract
Recent advancements in instruction tuning with large language models (LLMs) for mathematical reasoning tasks. Challenges of incorrect, missing, and redundant steps in Chain-of-Thought (CoT) data. Proposal of a dual instruction tuning strategy for forward and reverse reasoning. Introduction of Intermediate Reasoning State Prediction and Instruction Reconstruction tasks. Multi-task fine-tuning using existing and newly created data. Validation of the strategy's effectiveness and domain generalization through experiments. Comparison of performance with baseline models on various mathematical reasoning tasks. Ablation study on the components of the dual instruction tuning strategy. Limitations and future directions for enhancing mathematical reasoning with LLMs.
Stats
"In one semester, how many hours does Kimo spend attending classes? Let's write a program." - Prediction: 208, Answer: 272 "If Katarina has 68 cookies, how many cookies do they have in total? Let's write a program." - Prediction: 237, Answer: 298 "If Becky ate 10 slices, how many total slices did they eat? Let's write a program." - Prediction: 1, Answer: 31
Quotes
"The proposed strategy improves the reasoning abilities and domain generalization of the model." "The 13B model surpasses LLMs with 175B+ parameters in performance on the MATH task." "The proposed strategy enables the model to accurately learn the relationship between each instruction clause and thought."

Deeper Inquiries

How can the dual instruction tuning strategy be adapted for other domains beyond mathematics?

The dual instruction tuning strategy proposed in the context for mathematical reasoning can be adapted for other domains by modifying the tasks and datasets to suit the specific domain requirements. For instance, in the domain of natural language processing, the tasks could involve text generation, sentiment analysis, or language translation. The IRSP task could be tailored to predict the next word in a sentence or generate a coherent paragraph based on a given prompt. The IR task could focus on reconstructing missing information in a text or completing incomplete sentences. By adjusting the tasks and datasets to align with the specific domain, the dual instruction tuning strategy can be effectively applied to a wide range of domains beyond mathematics.

What are the potential drawbacks of relying on large language models for mathematical reasoning?

While large language models (LLMs) have shown significant advancements in mathematical reasoning tasks, there are several potential drawbacks to relying solely on them for such tasks. One drawback is the lack of interpretability in the reasoning process of LLMs, making it challenging to understand how they arrive at their answers. This lack of transparency can be a significant limitation, especially in educational settings where explanations and step-by-step reasoning are crucial. Another drawback is the potential for bias in the training data of LLMs, which can lead to biased or inaccurate results in mathematical reasoning tasks. Additionally, the computational resources required to train and fine-tune large language models for mathematical reasoning can be substantial, making it inaccessible for some users or organizations with limited resources. Furthermore, the generalization of LLMs to new or unseen mathematical problems may be limited, as they may struggle with complex or novel problem-solving scenarios that were not adequately covered in the training data. This limitation can hinder the adaptability of LLMs to a wide range of mathematical reasoning tasks.

How can the findings of this study be applied to enhance human understanding of mathematical concepts?

The findings of this study can be applied to enhance human understanding of mathematical concepts by improving the explanation and reasoning processes in educational settings. By incorporating the dual instruction tuning strategy into educational tools and platforms, students can receive more detailed and accurate explanations for mathematical problems. This can help students better grasp the underlying concepts and reasoning steps involved in solving mathematical problems. Additionally, the insights gained from the study can be used to develop interactive learning environments that provide real-time feedback and guidance to students as they work through mathematical exercises. By integrating the dual instruction tuning strategy into educational technology, students can receive personalized support and tailored explanations based on their individual learning needs. Moreover, the study's findings can inform the design of educational curricula and teaching methodologies to emphasize the importance of understanding and executing instructions in mathematical reasoning. By highlighting the significance of intermediate reasoning states and instruction reconstruction, educators can enhance students' problem-solving skills and critical thinking abilities in mathematics.
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