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.
Computer Vision--ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, October 11--14, 2016, Proceedings, Part IV 14 , pages=
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A fully differentiable TensorFlow gyrokinetic code allows approximate gradients of nonlinear turbulence quantities to be used for outer-loop tasks such as profile prediction despite stochasticity.
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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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