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
Micchelli, Yuesheng Xu, and Haizhang Zhang
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Proves first UATs for k-times differentiable nonlinear operators and their derivatives via OL architectures uniformly on compact sets in weighted Bastiani-Sobolev spaces on general Banach spaces.
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Training Infinitely Deep and Wide Transformers
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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Universal Approximation of Nonlinear Operators and Their Derivatives
Proves first UATs for k-times differentiable nonlinear operators and their derivatives via OL architectures uniformly on compact sets in weighted Bastiani-Sobolev spaces on general Banach spaces.