We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights. These networks have been introduced to alleviate the drawbacks due to a Gaussian initialization. In a Bayesian framework, when the likelihood is Gaussian, we identify the posterior distribution of the output in the sequential wide-width limit and, in the shallow case, we compute explicitly the posterior distribution of these models.
The talk is based on a joint work with Nicola Apollonio and Giovanni Franzina.

See HERE for the full abstract.