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MACM: Utilizing a Multi-Agent System for Condition Mining in Solving Complex Mathematical Problems

2024-04-06 · Bin Lei, Yi Zhang, Shan Zuo, Ali Payani, Caiwen Ding

Recent advancements in large language models, such as GPT-4, have demonstrated remarkable capabilities in processing standard queries. Despite these advancements, their performance substantially declines in \textbf{advanced mathematical problems requiring complex, multi-step logical reasoning}. To enhance their inferential capabilities, current research has delved into \textit{prompting engineering}, exemplified by methodologies such as the Tree of Thought and Graph of Thought. Nonetheless, these existing approaches encounter two significant limitations. Firstly, their effectiveness in tackling complex mathematical problems is somewhat constrained. Secondly, the necessity to design distinct prompts for individual problems hampers their generalizability. In response to these limitations, this paper introduces the \textit{Multi-Agent System for conditional Mining} (\textbf{MACM}) prompting method. It not only resolves intricate mathematical problems but also demonstrates strong generalization capabilities across various mathematical contexts. With the assistance of MACM, the accuracy of GPT-4 Turbo on the most challenging level five mathematical problems in the MATH dataset increase from $\mathbf{54.68\%} \text{ to } \mathbf{76.73\%}$. The code is available in \url{https://github.com/bin123apple/MACM}.

📄 PDF Abstract BibTeX arXiv:2404.04735

Code (1)

bin123apple/macm 공식 구현

Tasks

Logical ReasoningMathMath Word Problem Solving

Methods 이 논문이 사용한 방법론

Attention 설명 없음
Softmax The Softmax output function transforms a previous layer's output into a vector of probabilities. It is commonly used for multiclass classification. Given an input vector $x$…
Linear Layer A Linear Layer is a projection $\mathbf{XW + b}$.
Layer Normalization Unlike batch normalization, Layer Normalization directly estimates the normalization statistics from the summed inputs…
Dense Connections Dense Connections, or Fully Connected Connections, are a type of layer in a deep neural network that use a linear operation where every input is connected to every output…
Label Smoothing Label Smoothing is a regularization technique that introduces noise for the labels. This accounts for the fact that datasets may have mistakes in them, so maximizing the…
Residual Connection 설명 없음
Dropout Dropout is a regularization technique for neural networks that drops a unit (along with connections) at training time with a specified probability $p$ (a common value is…

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