Quantifying Concentration Phenomena of Mean-Field Transformers in the Low-Temperature Regime
Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models. In this paper, we study the evolution of tokens in deep encoder-only transformers at inference time which is described in the large-token limit by a mean-field continuity equation. Leveraging ideas from the convergence analysis of interacting multi-particle systems, with particles corresponding to tokens, we prove that the token distribution rapidly concentrates onto the push-forward of the initial distribution under a projection map induced by the key, query, and value matrices, and remains metastable for moderate times. Specifically, we s...
| Authors | Albert Alcalde, Leon Bungert, Konstantin Riedl et al. |
|---|---|
| Primary category | math.AP |
| Published | 11 May 2026 |
| Last updated at source | 11 May 2026 |
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