For uniform keys on the d-dimensional sphere, softmax attention becomes selective at inverse temperature scaling β_n* ≍ n^{2/(d-1)}, with explicit limiting laws for attention weights and outputs in each regime.
IEEE Transactions on Information Theory , year=
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Establishes robustness of distribution support for guided diffusion processes under exact score access across DDIM, DDPM, and exponential integrator discretizations.
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Scaling Limits of Long-Context Transformers
For uniform keys on the d-dimensional sphere, softmax attention becomes selective at inverse temperature scaling β_n* ≍ n^{2/(d-1)}, with explicit limiting laws for attention weights and outputs in each regime.
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On the Robustness of Distribution Support under Diffusion Guidance
Establishes robustness of distribution support for guided diffusion processes under exact score access across DDIM, DDPM, and exponential integrator discretizations.