Large language models (LLMs) have achieved unprecedented performance by leveraging vast pretraining corpora, yet their performance remains suboptimal in knowledge-intensive domains such as medicine and scientific research, where high factual precision is required. While synthetic data provides a promising avenue for augmenting domain knowledge, existing methods frequently generate redundant samples that do not align with the model's true knowledge gaps. To overcome this limitation, we propose a novel Structural Entropy-guided Knowledge Navigator (SENATOR) framework that addresses the intrinsic knowledge deficiencies of LLMs. Our approach employs the Structure Entropy (SE) metric to quantify uncertainty along knowledge graph paths and leverages Monte Carlo Tree Search (MCTS) to selectively explore regions where the model lacks domain-specific knowledge. Guided by these insights, the framework generates targeted synthetic data for supervised fine-tuning, enabling continuous self-improvement. Experimental results on LLaMA-3 and Qwen2 across multiple domain-specific benchmarks show that SENATOR effectively detects and repairs knowledge deficiencies, achieving notable performance improvements. The code and data for our methods and experiments are available at https://github.com/weiyifan1023/senator.

Large Language Models (LLMs) are versatile and demonstrate impressive generalization ability by mining and learning information from extensive unlabeled text. However, they still exhibit reasoning mistakes, often stemming from knowledge deficiencies, which can affect their trustworthiness and reliability. Although users can provide diverse and comprehensive queries, obtaining sufficient and effective feedback is demanding. Furthermore, evaluating LLMs comprehensively with limited labeled samples is difficult. This makes it a challenge to diagnose and remedy the deficiencies of LLMs through rich label-free user queries. To tackle this challenge, we propose a label-free curricular meaningful learning framework (LaMer). LaMer first employs relative entropy to automatically diagnose and quantify the knowledge deficiencies of LLMs in a label-free setting. Next, to remedy the diagnosed knowledge deficiencies, we apply curricular meaningful learning: first, we adopt meaningful learning to adaptively synthesize augmentation data according to the severity of the deficiencies, and then design a curricular deficiency remedy strategy to remedy the knowledge deficiencies of LLMs progressively. Experiments show that LaMer efficiently and effectively diagnoses and remedies knowledge deficiencies in LLMs, improving various LLMs across seven out-of-distribution (OOD) reasoning and language understanding benchmarks, achieving comparable results to baselines with just 40\% training data. LaMer even surpasses methods that rely on labeled datasets for deficiency diagnosis. In application, our label-free method can offer an effective knowledge deficiency diagnostic tool for efficient LLM development.

As world knowledge evolves and new task paradigms emerge, Continual Learning (CL) is crucial for keeping Large Language Models (LLMs) up-to-date and addressing their shortcomings. In practical applications, LLMs often require both continual instruction tuning (CIT) and continual pre-training (CPT) to adapt to new task paradigms and acquire necessary knowledge for task-solving. However, it remains challenging to collect CPT data that addresses the knowledge deficiencies in models while maintaining adequate volume, and improving the efficiency of utilizing this data also presents significant difficulties. Inspired by the 'summarizing mistakes' learning skill, we propose the Continue Evolving from Mistakes (CEM) method, aiming to provide a data-efficient approach for collecting CPT data and continually improving LLMs' performance through iterative evaluation and supplementation with mistake-relevant knowledge. To efficiently utilize these CPT data and mitigate forgetting, we design a novel CL training set construction paradigm that integrates parallel CIT and CPT data. Extensive experiments demonstrate the efficacy of the CEM method, achieving up to a 17% improvement in accuracy in the best case. Furthermore, additional experiments confirm the potential of combining CEM with catastrophic forgetting mitigation methods, enabling iterative and continual model evolution.