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Functional Large Deviations for Wide Deep Neural Networks with Gaussian Initialization and Lipschitz Activations
Claudio Macci, Barbara Pacchiarotti, Katerina Papagiannouli +2
We establish a functional large deviation principle for fully connected multi-layer perceptrons with i.i.d. Gaussian weights (LeCun initialization) and general Lipschitz activation…
Wasserstein asymptotics for empirical measures of diffusions on four dimensional closed manifolds
Dario Trevisan, Feng-Yu Wang, Jie-Xiang Zhu
We identify the leading term in the asymptotics of the quadratic Wasserstein distance between the invariant measure and empirical measures for diffusion processes on closed weighte…
Asymptotics for Random Quadratic Transportation Costs
Martin Huesmann, Michael Goldman, Dario Trevisan
We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclid…