Year: 2026
Type: preprint
Abstract: We study the dynamical behavior of tokens in transformers from a control-theoretic perspective. Our model includes the feed-forward layer present after the self-attention mechanism, with the self-attention mechanism interpreted as an interacting particle system and the feed-forward layer as an independent control. Our main theoretical result establishes that the feed-forward network can steer the tokens arbitrarily close to consensus regardless of the key, query, and value matrices. Our result are easily extended to convergence to many clusters and to multi-head attention. We conduct numerical experiments to verify our results, and compare thresholding behavior from our theory to real-world LLMs.
Source: arXiv (Cornell University)
Institution: University of Maryland, College Park
Language: English
Topic: Topic Modeling
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214948618