Mathematical reasoning is one of the core capabilities for Large Language Models (LLMs). Yet, existing approaches often rely on static heuristics or pre-determined reasoning strategies, limiting their ability to adapt to different intermediate states. To address this limitation, we propose FLAIR (Fuzzy-Logic-AssIsted Reasoner), an adaptive framework that integrates fuzzy theory into LLM-based mathematical reasoning. Specifically, FLAIR characterizes intermediate problem-solving states using fuzzy memberships and employs a parameterized fuzzy rule system to conditionally activate subsequent actions. These rule parameters are further adjusted via Reinforcement Learning using solution-level feedback as the reward signal, enabling adaptive and iterative refinement without reliance on a fixed strategy. To the best of our knowledge, this work is the first to integrate fuzzy theory into LLM-based mathematical reasoning. Extensive experiments across multiple benchmarks demonstrate that FLAIR consistently outperforms recent state-of-the-art baselines, while offering effective and interpretable diagnostics of intermediate problem-solving states.

Reinforcement learning (RL) has emerged as a powerful post-training paradigm for enhancing the reasoning capabilities of large language models (LLMs). However, reinforcement learning for LLMs faces substantial data scarcity challenges, including the limited availability of high-quality external supervision and the constrained volume of model-generated experience. These limitations make data-efficient reinforcement learning a critical research direction. In this survey, we present the first systematic review of reinforcement learning for LLMs under data scarcity. We propose a bottom-up hierarchical framework built around three complementary perspectives: the data-centric perspective, the training-centric perspective, and the framework-centric perspective. We develop a taxonomy of existing methods, summarize representative approaches in each category, and analyze their strengths and limitations. Our taxonomy aims to provide a clear conceptual foundation for understanding the design space of data-efficient RL for LLMs and to guide researchers working in this emerging area. We hope this survey offers a comprehensive roadmap for future research and inspires new directions toward more efficient and scalable reinforcement learning post-training for LLMs.

Adversarial attack aims to perturb input sequences and mislead a trained model for false predictions. To enhance the model robustness, defensing methods are accordingly employed by either data augmentation (involving adversarial samples) or model enhancement (modifying the training loss and/or model architecture). In contrast to previous work, this paper revisits the masked language modeling (MLM) and presents a simple yet efficient algorithm against adversarial attacks, termed [MASK] insertion for defensing (MI4D). Specifically, MI4D simply inserts [MASK] tokens to input sequences during training and inference, maximizing the intersection of the new convex hull (MI4D creates) with the original one (the clean input forms). As neither additional adversarial samples nor the model modification is required, MI4D is as computationally efficient as traditional fine-tuning. Comprehensive experiments have been conducted using three benchmark datasets and four attacking methods. MI4D yields a significant improvement (on average) of the accuracy between 3.2 and 11.1 absolute points when compared with six state-of-the-art defensing baselines.

Given a context knowledge base (KB) and a corresponding question, the Knowledge Base Question Answering task aims to retrieve correct answer entities from this KB. Despite sophisticated retrieval algorithms, the impact of the low-resource (incomplete) KB is not fully exploited, where contributing components (. key entities and/or relations) may be absent for question answering. To effectively address this problem, we propose a contrastive regularization based method, which is motivated by the learn-by-analogy capability from human readers. Specifically, the proposed work includes two major modules: the knowledge extension and sMoCo module. The former aims at exploiting the latent knowledge from the context KB and generating auxiliary information in the form of question-answer pairs. The later module utilizes those additional pairs and applies the contrastive regularization to learn informative representations, that making hard positive pairs attracted and hard negative pairs separated. Empirically, we achieved the state-of-the-art performance on the WebQuestionsSP dataset and the effectiveness of proposed modules is also evaluated.