MIND: Math Informed syNthetic Dialogues for Pretraining LLMs (2410.12881v2)

Abstract: The utility of synthetic data to enhance pretraining data quality and hence to improve downstream task accuracy has been widely explored in recent LLMs. Yet, these approaches fall inadequate in complex, multi-hop and mathematical reasoning tasks as the synthetic data typically fails to add complementary knowledge to the existing raw corpus. In this work, we propose a novel large-scale and diverse Math Informed syNthetic Dialogue (MIND) generation method that improves the mathematical reasoning ability of LLMs. Specifically, using MIND, we generate synthetic conversations based on OpenWebMath (OWM), resulting in a new math corpus, MIND-OWM. Our experiments with different conversational settings reveal that incorporating knowledge gaps between dialog participants is essential for generating high-quality math data. We further identify an effective way to format and integrate synthetic and raw data during pretraining to maximize the gain in mathematical reasoning, emphasizing the need to restructure raw data rather than use it as-is. Compared to pretraining just on raw data, a model pretrained on MIND-OWM shows significant boost in mathematical reasoning (GSM8K: +13.42%, MATH: +2.30%), including superior performance in specialized knowledge (MMLU: +4.55%, MMLU-STEM: +4.28%) and general purpose reasoning tasks (GENERAL REASONING: +2.51%).

• The paper presents MIND, which enhances LLMs' mathematical reasoning by generating step-by-step synthetic dialogues from complex problems.
• It leverages a teacher-student conversational approach and decomposes tasks using data from the OpenWebMath corpus to fill reasoning gaps.
• Experiments demonstrate improvements of 13.42% on gsm8k and 2.30% on math tasks, highlighting the approach's practical impact.

An Analysis of "MIND: Math Informed syNthetic Dialogues for Pretraining LLMs"

The paper "MIND: Math Informed syNthetic Dialogues for Pretraining LLMs" introduces a novel approach to enhance the mathematical reasoning capabilities of LLMs through the generation of synthetic dialogues. The paper addresses the limitations of existing synthetic data generation methodologies in improving complex mathematical and logical reasoning tasks. It proposes a method termed MIND, which generates Math Informed syNthetic Dialogues to pretrain LLMs effectively.

Overview

The motivation behind this research is the acknowledgment that synthetic data, while beneficial in general, often lacks the depth required for enhancing multi-hop and mathematical reasoning tasks. To tackle this issue, the paper presents MIND, which leverages conversations to decompose mathematical problems into more manageable sub-problems. This method aims to restructure information directly from large corpora, enhancing the data's ability to instruct a model in reasoning processes.

Methodology

MIND involves a strategic generation of synthetic dialogues based on complex mathematical content from the OpenWebMath corpus, creating what’s referred to as the mind-owm dataset. The generated data focuses on breaking down complex problems via conversational structures that inject both step-by-step explanations and complementary reasoning. The dialogues are generated using a pretrained LLM, with prompts designed to create various conversational styles such as "teacher-student" or "problem-solving" pairs.

The authors advocate for MIND’s capability to handle knowledge gaps between dialogue participants, emphasizing its importance in generating high-quality mathematical reasoning data. The synthetic data is subsequently filtered using heuristics to ensure quality before being utilized in model pretraining.

Experimental Results

Extensive experiments demonstrate substantial improvements in mathematical reasoning benchmarks when models are pretrained on mind-owm compared to raw data alone. Specifically, models showed an increase of 13.42% on gsm8k and 2.30% on math tasks, with notable enhancements in specialized knowledge tasks as well. The findings highlight that synthetic conversational data not only improves mathematical reasoning but also benefits general reasoning tasks.

Practical and Theoretical Implications

Practically, MIND shows promise in generating high-quality synthetic data from limited raw resources, providing a scalable approach to data augmentation for LLM pretraining. This methodology can be implemented to improve mathematical reasoning in models where domain-specific data is scarce.

Theoretically, the MIND approach suggests a shift towards structured dialogue-based data formation as a viable replacement or complement to traditional pretraining datasets. This can stimulate further exploration into synthetic data generation, focusing on structured information processing.

Future Developments

The paper opens several avenues for future research in AI, particularly in exploring other domains where structured, dialogue-based synthetic data can be beneficial. Investigations into alternative conversational styles or integration with real-world data might uncover additional synergies. Moreover, exploring automated filtering methods could optimize the quality assessment process.

In conclusion, the MIND approach presents a substantial advancement in leveraging synthetic dialogues for improving the mathematical reasoning capabilities of LLMs. It underscores the potential of structured conversations in forming rich, educational input that can enhance the cognitive abilities of AI models.