Automatic math correction aims to check students' solutions to mathematical problems via artificial intelligence technologies. Most existing studies focus on judging the final answer at the problem level, while they ignore detailed feedback on each step in a math problem-solving process, which requires abilities of semantic understanding and reasoning. In this paper, we propose a reinforcement learning (RL)-based method to boost large language model (LLM) for step-level automatic math correction, named StepAMC. Particularly, we convert the step-level automatic math correction within the text classification task into an RL problem to enhance the reasoning capabilities of LLMs. Then, we design a space-constrained policy network to improve the stability of RL. Then, we introduce a fine-grained reward network to convert the binary human feedback into a continuous value. We conduct extensive experiments over two benchmark datasets and the results show that our model outperforms the eleven strong baselines.

Recently, foundation language models (LMs) have marked significant achievements in the domains of natural language processing (NLP) and computer vision (CV). Unlike traditional neural network models, foundation LMs obtain a great ability for transfer learning by acquiring rich commonsense knowledge through pre-training on extensive unsupervised datasets with a vast number of parameters. However, they still can not emulate human-like continuous learning due to catastrophic forgetting. Consequently, various continual learning (CL)-based methodologies have been developed to refine LMs, enabling them to adapt to new tasks without forgetting previous knowledge. However, a systematic taxonomy of existing approaches and a comparison of their performance are still lacking, which is the gap that our survey aims to fill. We delve into a comprehensive review, summarization, and classification of the existing literature on CL-based approaches applied to foundation language models, such as pre-trained language models (PLMs), large language models (LLMs) and vision-language models (VLMs). We divide these studies into offline CL and online CL, which consist of traditional methods, parameter-efficient-based methods, instruction tuning-based methods and continual pre-training methods. Offline CL encompasses domain-incremental learning, task-incremental learning, and class-incremental learning, while online CL is subdivided into hard task boundary and blurry task boundary settings. Additionally, we outline the typical datasets and metrics employed in CL research and provide a detailed analysis of the challenges and future work for LMs-based continual learning.