We introduce MAmmoTH, a series of open-source large language models (LLMs)
specifically tailored for general math problem-solving. The MAmmoTH models are
trained on MathInstruct, our meticulously curated instruction tuning dataset.
MathInstruct is compiled from 13 math datasets with intermediate rationales,
six of which have rationales newly curated by us. It presents a unique hybrid
of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also
ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT
not only unleashes the potential of tool use but also allows different thought
processes for different math problems. As a result, the MAmmoTH series
substantially outperform existing open-source models on nine mathematical
reasoning datasets across all scales with an average accuracy gain between 13%
and 29%. Remarkably, our MAmmoTH-7B model reaches 35% on MATH (a
competition-level dataset), which exceeds the best open-source 7B model
(WizardMath) by 25%, and the MAmmoTH-34B model achieves 46% accuracy on MATH,
even surpassing GPT-4's CoT result. Our work underscores the importance of
diverse problem coverage and the use of hybrid rationales in developing
superior math generalist models.

MAmmoTH 是一系列为数学问题解决而特别定制的开源大型语言模型，通过混合的证明链和思考程序的理论，提供了广泛的数学领域覆盖，取得了显著的性能提升。

MAmmoTH: 通过混合指导调整构建数学通才模型

MAmmoTH: Building Math Generalist Models through Hybrid Instruction  Tuning

Large Language Models (LLMs) have demonstrated significant progress in
utilizing external APIs as tools for various tasks. However, their tool-using
ability is limited by the availability of suitable APIs and the instability of
implicit reasoning, particularly when simultaneously engaging in reasoning
about plans and actual calculations. To address these limitations, we propose
CREATOR, a novel framework that empowers LLMs to create their own tools through
documentation and code realization. CREATOR disentangles the LLM's ability into
two distinct phases: abstract tool creation and concrete decision execution,
which results in improved LLM performance. We evaluate CREATOR on two
established benchmarks: MATH, which consists of challenging math competition
problems, and TabMWP, which includes diverse tabular contents for
problem-solving. Remarkably, CREATOR significantly outperforms existing
chain-of-thought (CoT), program-of-thought (PoT), and tool-using baselines on
these two benchmarks. Additionally, we present a new dataset, Creation
Challenge, comprising 2K diverse questions, to highlight the necessity and
benefits of LLMs' tool creation ability in effectively addressing these
problems. Furthermore, our research reveals that leveraging LLMs as tool
creators facilitates knowledge transfer, and LLMs exhibit varying levels of
tool creation abilities, enabling them to flexibly tackle diverse situations.
Our study represents a promising avenue for maximizing the potential of LLMs
and advancing toward truly intelligent and adaptable AI systems.

CREATOR 是一种新颖的框架，使大型语言模型创建自己的工具变得容易，该方法在数学问题求解方面的表现显著优于现有方法，并有助于知识转移和提高模型的适应性。