This paper presents an in-depth examination of the evolution and interplay of cognitive and expressive capabilities in large language models (LLMs), with a specific focus on Baichuan-7B and Baichuan-33B, an advanced bilingual (Chinese and English) LLM series. We define and explore the model's cognitive and expressive capabilities through linear representations across three critical phases: Pretraining, Supervised Fine-Tuning (SFT), and Reinforcement Learning from Human Feedback (RLHF). Cognitive capability is defined as the quantity and quality of information conveyed by the neuron output vectors within the network, similar to the neural signal processing in human cognition. Expressive capability is defined as the model’s capability to produce word-level output. Our findings unveil a sequential development pattern, where cognitive abilities are largely established during Pretraining, whereas expressive abilities predominantly advance during SFT and RLHF. Statistical analyses confirm a significant correlation between the two capabilities, suggesting that cognitive capacity may limit expressive potential. The paper also explores the theoretical underpinnings of these divergent developmental trajectories and their connection to the LLMs' architectural design. Moreover, we evaluate various optimization-independent strategies, such as few-shot learning and repeated sampling, which bridge the gap between cognitive and expressive capabilities. This research reveals the potential connection between the hidden space and the output space, contributing valuable insights into the interpretability and controllability of their training processes.