Scaling Limits of Long-Context Transformers
We study the long-context limit of softmax self-attention with a fixed query and a random context of $n$ i.i.d. keys on the sphere, viewing the inverse temperature $β_n$ as the scaling parameter that decides whether attention degenerates into uniform averaging or collapses onto the single closest key. We show that the critical scale at which selectivity emerges is determined by the local exponent of the distance-to-query distribution near zero rather than by global features of the context, and scales like $β_n^\ast \asymp n^{2/(d-1)}$ for uniform keys on $\mathbb{S}^{d-1}$. Furthermore, we characterize the limiting laws of the ordered attention weights and of the attention output across a...
| Authors | Giuseppe Bruno, Shi Chen, Zhengjiang Lin et al. |
|---|---|
| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 8 May 2026 |
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