Understanding how large language models (LLMs) acquire, retain, and apply knowledge remains an open challenge. This paper introduces a novel framework, K-(CSA)^2, which categorizes LLM knowledge along two dimensions: correctness and confidence. The framework defines six categories of knowledge, ranging from highly confident correctness to confidently held misconceptions, enabling a nuanced evaluation of model comprehension beyond binary accuracy. Using this framework, we demonstrate how techniques like chain-of-thought prompting and reinforcement learning with human feedback fundamentally alter the knowledge structures of internal (pre-trained) and external (context-dependent) knowledge in LLMs. CoT particularly enhances base model performance and shows synergistic benefits when applied to aligned LLMs. Moreover, our layer-wise analysis reveals that higher layers in LLMs encode more high-confidence knowledge, while low-confidence knowledge tends to emerge in middle-to-lower layers.
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