We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems. In this perspective, tokens are modeled as particles that interact dynamically through successive linear self-attention layers.
arXiv:2501. 18322v2 Announce Type: replace Abstract: Transformers, which are state-of-the-art in most machine learning tasks, represent the data as sequences of vectors called tokens.
By Val\'erie Castin, Pierre Ablin, Jos\'e Antonio Carrillo, Gabriel Peyr\'e
arXiv:2607. 10677v1 Announce Type: new Abstract: Self-attention is a ubiquitous primitive in modern sequence models, yet its operator-level geometry is only partially understood.
By Binbin Lin, Wei Chen, Yalun Li, Wenxiao Wang, Jieping Ye, Xiaofei He
arXiv:2512. 21113v2 Announce Type: replace Abstract: Transformers are increasingly adopted for modeling and forecasting time-series, yet their internal mechanisms remain poorly understood from a dynamical systems perspective.
By Gregory Duth\'e, Nikolaos Evangelou, Wei Liu, Ioannis G. Kevrekidis, Eleni Chatzi
arXiv:2608. 08922v1 Announce Type: cross Abstract: Transformer layers generate state-dependent interaction networks: token representations determine the attention matrix, which in turn updates the representations.
By Qucheng Gao, Zuyi Yang, Xiao Chen
arXiv:2606. 07600v1 Announce Type: cross Abstract: We formulate data propagation through the Transformer, the machine learning architecture powering large language models, as a nonlinear control system on the space of probability measures.
By Albert Alcalde, Zhengping Ji, Enrique Zuazua