Modeling Transformers as complex networks to analyze learning dynamics

• URL: http://arxiv.org/abs/2509.15269v1
• Date: Thu, 18 Sep 2025 10:20:26 GMT
• Title: Modeling Transformers as complex networks to analyze learning dynamics
• Authors: Elisabetta Rocchetti,
• Abstract summary: This project investigates whether learning dynamics can be characterized through the lens of Complex Network Theory.<n>I introduce a novel methodology to represent a Transformer-based model as a directed, weighted graph where nodes are the model's computational components.<n>I analyze a suite of graph-theoretic metrics to reveal that the network's structure evolves through distinct phases of exploration, consolidation, and refinement.
• Score: 0.2538209532048867
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The process by which Large Language Models (LLMs) acquire complex capabilities during training remains a key open question in mechanistic interpretability. This project investigates whether these learning dynamics can be characterized through the lens of Complex Network Theory (CNT). I introduce a novel methodology to represent a Transformer-based LLM as a directed, weighted graph where nodes are the model's computational components (attention heads and MLPs) and edges represent causal influence, measured via an intervention-based ablation technique. By tracking the evolution of this component-graph across 143 training checkpoints of the Pythia-14M model on a canonical induction task, I analyze a suite of graph-theoretic metrics. The results reveal that the network's structure evolves through distinct phases of exploration, consolidation, and refinement. Specifically, I identify the emergence of a stable hierarchy of information spreader components and a dynamic set of information gatherer components, whose roles reconfigure at key learning junctures. This work demonstrates that a component-level network perspective offers a powerful macroscopic lens for visualizing and understanding the self-organizing principles that drive the formation of functional circuits in LLMs.

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