Physics Colloquium: Towards Conceptual Understanding of Large Language Models with Prof. Fan Yang, WFU Department of Computer Science.

Large Language Models (LLMs) have demonstrated impressive capabilities in understanding and generating human language, yet the internal mechanisms by which they encode semantic knowledge and conceptual structures remain largely opaque. In this talk, I will introduce my recent exploration in probing LLM representations, focusing on the depth-dependent emergence of conceptual understanding and the structure of learned knowledge. The first part of the talk will introduce the concept of Concept Depth, which posits that simpler concepts are captured in shallower layers while more abstract and complex ones require deeper processing. This framework is supported by probing experiments across multiple LLM architectures, shedding light on how different levels of semantic information are distributed within model layers. Building upon this, I will discuss a complementary perspective that extends beyond single vector representations to Gaussian Concept Subspaces (GCS), a novel framework that models conceptual knowledge as a distribution rather than a single fixed direction in representation space. This approach improves robustness in identifying learned concepts and has practical implications for interpretability and intervention in model behavior. Finally, I will present a vision for moving beyond empirical characterization toward physical interpretations of LLMs, drawing connections between deep learning representations and theoretical modeling of dynamical systems. This future perspective invites interdisciplinary collaboration in physics, neuroscience, and AI, aiming to ground the emergent behaviors of LLMs in a more principled framework.