Shi Chen

Shi Chen, Zhengjiang Lin, Yury Polyanskiy et al.

The evolution of tokens through a deep transformer models can be modeled as an interacting particle system that has been shown to exhibit an asymptotic clustering behavior akin to the synchronization phenomenon in Kuramoto models. In this work, we investigate the long-time clustering of mean-field transformer models. More precisely, we establish exponential rates of contraction to a Dirac point mass for any suitably regular initialization under some assumptions on the parameters of transformer models, any suitably regular mean-field initialization synchronizes exponentially fast with some quantitative rates.

Shi Chen, Zhengjiang Lin, Yury Polyanskiy et al.

As large language models scale to longer contexts, attention layers suffer from a fundamental pathology: attention scores collapse toward uniformity as context length $n$ increases, causing tokens to cluster excessively, a phenomenon known as rank-collapse. While $\textit{attention scaling}$ effectively addresses this deficiency by rescaling attention scores with a polylogarithmic factor $β_n$, theoretical justification for this approach remains lacking. We analyze a simplified yet tractable model that magnifies the effect of attention scaling. In this model, attention exhibits a phase transition governed by the scaling factor $β_n$: insufficient scaling collapses all tokens to a single direction, while excessive scaling reduces attention to identity, thereby eliminating meaningful interactions between tokens. Our main result identifies the critical scaling $β_n \asymp \log n$ and provides a rigorous justification for attention scaling in YaRN and Qwen, clarifying why logarithmic scaling maintains sparse, content-adaptive attention at large context lengths.