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•We sayfislocallyL 1-Lipschitzif for every bounded subsetV ⊂ Xthere exists a function LV ∈L 1 loc(I)such that for a.e.t∈Iit holds: ∀x, y∈ V,∥f(t, x)−f(t, y)∥ ≤L V(t)∥x−y∥

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Training Infinitely Deep and Wide Transformers

math.OC · 2026-05-17 · unverdicted · novelty 8.0

Develops a mean-field neural PDE model for transformer training, proves forward-pass well-posedness via function-space ODEs, derives conditional Wasserstein gradients, and shows global convergence of gradient flow under an NTK injectivity condition equivalent to linear independence of log-sum-exp fu

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  • Training Infinitely Deep and Wide Transformers math.OC · 2026-05-17 · unverdicted · none · ref 53

    Develops a mean-field neural PDE model for transformer training, proves forward-pass well-posedness via function-space ODEs, derives conditional Wasserstein gradients, and shows global convergence of gradient flow under an NTK injectivity condition equivalent to linear independence of log-sum-exp fu