A constrained Wasserstein steepest-ascent flow computes E-optimal designs by solving convex SDPs at each step and converges to first-order stationary points with an exact energy identity.
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Models multi-head transformer data flow as time-dependent Wasserstein gradient flows of an attention-capturing interaction energy, with proofs on omega-limit stationary points and stability under weight and input perturbations.
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Gradient flow for finding E-optimal designs
A constrained Wasserstein steepest-ascent flow computes E-optimal designs by solving convex SDPs at each step and converges to first-order stationary points with an exact energy identity.
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Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows
Models multi-head transformer data flow as time-dependent Wasserstein gradient flows of an attention-capturing interaction energy, with proofs on omega-limit stationary points and stability under weight and input perturbations.