M. Xu

Erxin Yu, Jing Li, Ming Liao et al.

Although large language models demonstrate strong performance across various domains, they still struggle with numerous bad cases in mathematical reasoning. Previous approaches to learning from errors synthesize training data by solely extrapolating from isolated bad cases, thereby failing to generalize the extensive patterns inherent within these cases. This paper presents Self-Error-Instruct (SEI), a framework that addresses these model weaknesses and synthesizes more generalized targeted training data. Specifically, we explore a target model on two mathematical datasets, GSM8K and MATH, to pinpoint bad cases. Then, we generate error keyphrases for these cases based on the instructor model's (GPT-4o) analysis and identify error types by clustering these keyphrases. Next, we sample a few bad cases during each generation for each identified error type and input them into the instructor model, which synthesizes additional training data using a self-instruct approach. This new data is refined through a one-shot learning process to ensure that only the most effective examples are kept. Finally, we use these curated data to fine-tune the target model, iteratively repeating the process to enhance performance. We apply our framework to various models and observe improvements in their reasoning abilities across both in-domain and out-of-domain mathematics datasets. These results demonstrate the effectiveness of self-error instruction in improving LLMs' mathematical reasoning through error generalization.

Zige Wang, Qi Zhu, Fei Mi et al.

Gradient-based data influence approximation has been leveraged to select useful data samples in the supervised fine-tuning of large language models. However, the computation of gradients throughout the fine-tuning process requires too many resources to be feasible in practice. In this paper, we propose an efficient gradient-based data selection framework with clustering and a modified Upper Confidence Bound (UCB) algorithm. Based on the intuition that data samples with similar gradient features will have similar influences, we first perform clustering on the training data pool. Then, we frame the inter-cluster data selection as a constrained computing budget allocation problem and consider it a multi-armed bandit problem. A modified UCB algorithm is leveraged to solve this problem. Specifically, during the iterative sampling process, historical data influence information is recorded to directly estimate the distributions of each cluster, and a cold start is adopted to balance exploration and exploitation. Experimental results on various benchmarks show that our proposed framework, ClusterUCB, can achieve comparable results to the original gradient-based data selection methods while greatly reducing computing consumption.