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Quantitative CLTs in Deep Neural Networks
We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$.
Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees
In this article, we prove intrinsic versions of the OSSS and Schramm-Steif inequalities for functionals of a general Poisson process, and apply these new estimates to deduce sufficient conditions - expressed in terms of randomized stopping sets - yielding sharp phase transitions, quantitative noise sensitivity, exceptional times and bounds on critical windows for monotonic Boolean Poisson functions.
Probability Mathematical Physics Combinatorics Mathematical Physics 60D05, 60G55, 68W20, 60J25, 60H99, 82B43
