Evaluating Mathematical Reasoning of Large Language Models: A Focus on Error Identification and Correction

The rapid advancement of Large Language Models (LLMs) in the realm of mathematical reasoning necessitates comprehensive evaluations to gauge progress and inspire future directions. Existing assessments predominantly focus on problem-solving from the examinee perspective, overlooking a dual perspective of examiner regarding error identification and correction. From the examiner perspective, we define four evaluation tasks for error identification and correction along with a new dataset with annotated error types and steps. We also design diverse prompts to thoroughly evaluate eleven representative LLMs. Our principal findings indicate that GPT-4 outperforms all models, while open-source model LLaMA-2-7B demonstrates comparable abilities to closed-source models GPT-3.5 and Gemini Pro. Notably, calculation error proves the most challenging error type. Moreover, prompting LLMs with the error types can improve the average correction accuracy by 47.9\%. These results reveal potential directions for developing the mathematical reasoning abilities of LLMs. Our code and dataset is available on https://github.com/LittleCirc1e/EIC.

Self-Paced Neutral Expression-Disentangled Learning for Facial Expression Recognition

The accuracy of facial expression recognition is typically affected by the following factors: high similarities across different expressions, disturbing factors, and micro-facial movement of rapid and subtle changes. One potentially viable solution for addressing these barriers is to exploit the neutral information concealed in neutral expression images. To this end, in this paper we propose a self-Paced Neutral Expression-Disentangled Learning (SPNDL) model. SPNDL disentangles neutral information from facial expressions, making it easier to extract key and deviation features. Specifically, it allows to capture discriminative information among similar expressions and perceive micro-facial movements. In order to better learn these neutral expression-disentangled features (NDFs) and to alleviate the non-convex optimization problem, a self-paced learning (SPL) strategy based on NDFs is proposed in the training stage. SPL learns samples from easy to complex by increasing the number of samples selected into the training process, which enables to effectively suppress the negative impacts introduced by low-quality samples and inconsistently distributed NDFs. Experiments on three popular databases (i.e., CK+, Oulu-CASIA, and RAF-DB) show the effectiveness of our proposed method.