Large language models (LLMs) have developed impressive performance and strong explainability across various reasoning scenarios, marking a significant stride towards mimicking human-like intelligence. Despite this, when tasked with several simple questions supported by a generic fact, LLMs often struggle to abstract and apply the generic fact to provide consistent and precise answers, revealing a deficiency in abstract reasoning abilities. This has sparked a vigorous debate about whether LLMs are genuinely reasoning or merely memorizing. In light of this, we design a preliminary study to quantify and delve into the abstract reasoning abilities of existing LLMs. Our findings reveal a substantial discrepancy between their general reasoning and abstract reasoning performances.

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.