MathClean: A Benchmark for Synthetic Mathematical Data Cleaning

With the rapid development of large language models (LLMs), the quality of training data has become crucial. Among the various types of training data, mathematical data plays a key role in enabling LLMs to acquire strong reasoning abilities. While high-quality open-source data is important, it is often insufficient for pre-training, necessitating the addition of synthetic math problems. However, synthetic math questions and answers can introduce inaccuracies, which may degrade both the training data and web data. Therefore, an effective method for cleaning synthetic math data is essential. In this paper, we propose the MathClean benchmark to evaluate the effectiveness of math data cleaning models. The MathClean benchmark consists of 2,000 correct questions and 2,000 erroneous questions with additional 2,000 correct and erroneous answers sourced from augmented data based on GSM8K and MATH. Moreover, we also annotate error types for each question or answer, since it can assess whether models can correctly identify the error categories for future improvements. Finally, we present comprehensive evaluations using state-of-the-art (SOTA) models. Our results demonstrate that even strong models like GPT-o1 and DeepSeek-R1 perform poorly on this benchmark, highlighting the utility of MathClean. Our code and data is available at https://github.com/YuYingLi0/MathClean.

A Pairwise Probe for Understanding BERT Fine-Tuning on Machine Reading Comprehension

Pre-trained models have brought significant improvements to many NLP tasks and have been extensively analyzed. But little is known about the effect of fine-tuning on specific tasks. Intuitively, people may agree that a pre-trained model already learns semantic representations of words (e.g. synonyms are closer to each other) and fine-tuning further improves its capabilities which require more complicated reasoning (e.g. coreference resolution, entity boundary detection, etc). However, how to verify these arguments analytically and quantitatively is a challenging task and there are few works focus on this topic. In this paper, inspired by the observation that most probing tasks involve identifying matched pairs of phrases (e.g. coreference requires matching an entity and a pronoun), we propose a pairwise probe to understand BERT fine-tuning on the machine reading comprehension (MRC) task. Specifically, we identify five phenomena in MRC. According to pairwise probing tasks, we compare the performance of each layer's hidden representation of pre-trained and fine-tuned BERT. The proposed pairwise probe alleviates the problem of distraction from inaccurate model training and makes a robust and quantitative comparison. Our experimental analysis leads to highly confident conclusions: (1) Fine-tuning has little effect on the fundamental and low-level information and general semantic tasks. (2) For specific abilities required for downstream tasks, fine-tuned BERT is better than pre-trained BERT and such gaps are obvious after the fifth layer.