<ul><li>Using entropic inequalities from information theory, new bounds on the total variation and 2-Wasserstein distances between conditionally Gaussian and Gaussian laws are provided.</li><li>The results are applied to quantify the convergence speed of a randomly initialized fully connected neural network and its derivatives to Gaussian distributions.</li><li>The findings improve and extend previous research studies on the subject.</li><li>Cumulant estimates and activation function assumptions play a crucial role in the results.</li></ul>

Entropic bounds for conditionally Gaussian vectors and applications to neural networks

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