Enhancing Mathematical Reasoning in LLMs with Background Operators

• URL: http://arxiv.org/abs/2412.04110v1
• Date: Thu, 05 Dec 2024 12:24:54 GMT
• Title: Enhancing Mathematical Reasoning in LLMs with Background Operators
• Authors: Jiajun Chen, Yik-Cheung Tam,
• Abstract summary: We develop a Prolog solution that includes problem-specific predicates and intermediate predicates derived from background operators. For efficient data augmentation, we apply K-fold cross-validated self-training. Our experimental results demonstrate that 5-fold crossvalidated self-training effectively identifies new, accurate Prolog solutions.
• Score: 36.14500963096528
• License:
• Abstract: We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we develop a Prolog solution that includes problem-specific predicates and intermediate predicates derived from these background operators, ensuring that each solution adheres to the defined operator set. We introduce the MATH-Prolog corpus, which is derived from the counting and probability categories of the MATH corpus. For efficient data augmentation, we apply K-fold cross-validated self-training. This method incrementally generates new Prolog solutions for each fold, incorporating those verified as correct into the training set throughout the model training process. Our experimental results demonstrate that 5-fold crossvalidated self-training effectively identifies new, accurate Prolog solutions, achieving an accuracy of 84.6% on the cross-validated set, and 84.8% on the test set during fine-tuning the Meta-Llama-3.1-8B-Instruct model. This approach successfully uncovers new solutions with fully computable inference steps for previously unseen problems. Additionally, incorporating the background mathematical predicates into the prompt enhances solution coverage.

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