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Local entropic loss functions provide a versatile framework to define architecture-aware regularization procedures. Besides the possibility of being anisotropic in the synaptic space, the local entropic smoothening of the loss function can vary during training, thus yielding a tunable model complexity. A scoping protocol where the regularization is strong in the early-stage of the training and then fades progressively away constitutes an alternative to standard initialization procedures for deep convolutional neural networks, nonetheless, it has wider applicability. We analyze anisotropic, local entropic smoothenings in the language of statistical physics and information theory, providing insight into both their interpretation and workings. We comment some aspects related to the physics of renormalization and the spacetime structure of convolutional networks.
We study both classical and quantum algorithms to solve a hard optimization problem, namely 3-XORSAT on 3-regular random graphs. By introducing a new quasi-greedy algorithm that is not allowed to jump over large energy barriers, we show that the prob
We study the distribution of the minimum free energy (MFE) for the Turner model of pseudoknot free RNA secondary structures over ensembles of random RNA sequences. In particular, we are interested in those rare and intermediate events of unexpected l
We study link-diluted $pm J$ Ising spin glass models on the hierarchical lattice and on a three-dimensional lattice close to the percolation threshold. We show that previously computed zero temperature fixed points are unstable with respect to temper
We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the synaptic
It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an otherwise Anderson localized Hamiltonian leads