Kinetic theory for Transformers and the lost-in-the-middle phenomenon
We study causal self-attention dynamics -- a toy model for decoder Transformers -- which we interpret as a non-exchangeable interacting particle system. Adapting cumulant expansions to the triangular causal dependency structure of the model, and appealing to non-hierarchical methods to estimate correlations using Glauber calculus, we prove a quantitative mean-field limit result and a next-order characterization of correlations. For iid uniformly distributed tokens, the limiting correlation equation can be solved in closed form and we obtain a rigorous explanation of the empirically observed \emph{lost-in-the-middle} phenomenon: the token retrieval profile, as a function of the source posi...
| Authors | Mitia Duerinckx, Borjan Geshkovski, Stefano Rossi |
|---|---|
| Primary category | math.AP |
| Published | 9 May 2026 |
| Last updated at source | 9 May 2026 |
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