On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers

תקציר מקורי באנגליתarXiv:2607.18584v1 Announce Type: new Abstract: 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. We show that in embedding dimension two, for any key, query, and value matrices, the dynamics can be reformulated as a generalized Kuramoto-type model with pure second-harmonic coupling. This formulation is amenable to Watanabe--Strogatz theory which reveals the dynamics are intrinsically low-dimensional regardless of the parameter matrices. For a class of token initializations associated with the Ott--Antonsen (OA) manifold, we show that the parameter matrices induce a diverse variety of lo