Deep learning algorithms are responsible for a technological revolution in a variety of tasks
including image recognition or Go playing. Yet, why they work is not understood. Ultimately …

Supervised deep learning involves the training of neural networks with a large number N of
parameters. For large enough N, in the so-called over-parametrized regime, one can …

Deep learning has been immensely successful at a variety of tasks, ranging from
classification to artificial intelligence. Learning corresponds to fitting training data, which is …

We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for
a single layer neural network classifying a high-dimensional Gaussian mixture where each …

``Self-Organised Criticality''(SOC) is the mechanism by which complex systems
spontaneously settle close to a* critical point*, at the edge between stability and chaos, and …

The bias-variance trade-off is a central concept in supervised learning. In classical statistics,
increasing the complexity of a model (eg, number of parameters) reduces bias but also …

Stochastic gradient descent (SGD) is the workhorse algorithm of deep learning technology.
At each step of the training phase, a mini batch of samples is drawn from the training dataset …

The frequency scaling exponent of low-frequency excitations in microscopically small
glasses, which do not allow for the existence of waves (phonons), has been in the focus of …

We consider the Ising perceptron model with N spins and M= N* alpha patterns, with a
general activation function U that is bounded above. For U bounded away from zero, or U a …

We start with a few concise definitions of the most important concepts discussed in this entry.
Glass transition For molecular liquids, the glass transition denotes a crossover from a …