  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.
