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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2 Pith papers cite this work. Polarity classification is still indexing.
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Derives exact closed-form effect of adversarial kicks on the order parameter in Kuramoto networks, showing coupling-independent increments even at weak synchronization and explaining amplification near criticality.
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Analytical foundation for adversarial synchronization control in oscillator networks
Derives exact closed-form effect of adversarial kicks on the order parameter in Kuramoto networks, showing coupling-independent increments even at weak synchronization and explaining amplification near criticality.