# Modeling Transformers as complex networks to analyze learning dynamics

arXiv: https://arxiv.org/abs/2509.15269 · HTML: https://mlsanity.com/paper/2509.15269/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge and representations inside LLMs, one of 13 directions in Mechanistic interpretability.
- Builds on 5 of its 9 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Placed in

- Mechanistic interpretability / [Knowledge and representations inside LLMs](https://mlsanity.com/mechinterp/knowledge-and-representations-inside-llms/)

## Builds on (most cited first, 5 of 5)

- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Graph Structure of Neural Networks](https://mlsanity.com/paper/2007.06559/) (2020)
- [Structure and Performance of Fully Connected Neural Networks: Emerging Complex Network Properties](https://mlsanity.com/paper/2107.14062/) (2021)
- [Characterizing Learning Dynamics of Deep Neural Networks via Complex Networks](https://mlsanity.com/paper/2110.02628/) (2021)

## Abstract (arXiv)

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.