The regularized Transformer loss satisfies Villani's coercive energy criteria, yielding log-Sobolev constants C_LS ≤ λ^{-1} + d/λ² and finite-time convergence bounds for noisy SGD.
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Weight-Decay Turns Transformer Loss Landscapes Villani: Functional-Analytic Foundations for Optimization and Generalization
The regularized Transformer loss satisfies Villani's coercive energy criteria, yielding log-Sobolev constants C_LS ≤ λ^{-1} + d/λ² and finite-time convergence bounds for noisy SGD.