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Clustering of solutions in the symmetric binary perceptron
Carlo Baldassi, Riccardo Della Vecchia, Carlo Lucibello +1
The geometrical features of the (non-convex) loss landscape of neural network models are crucial in ensuring successful optimization and, most importantly, the capability to genera…
Natural representation of composite data with replicated autoencoders
Matteo Negri, Davide Bergamini, Carlo Baldassi +2
Generative processes in biology and other fields often produce data that can be regarded as resulting from a composition of basic features. Here we present an unsupervised method b…
Properties of the geometry of solutions and capacity of multi-layer neural networks with Rectified Linear Units activations
Carlo Baldassi, Enrico M. Malatesta, Riccardo Zecchina
Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for…
Shaping the learning landscape in neural networks around wide flat minima
Carlo Baldassi, Fabrizio Pittorino, Riccardo Zecchina
Learning in Deep Neural Networks (DNN) takes place by minimizing a non-convex high-dimensional loss function, typically by a stochastic gradient descent (SGD) strategy. The learnin…