Evolution is a blind fitting process by which organisms become adapted to their
environment. Does the brain use similar brute-force fitting processes to learn how to …

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 …

In this paper we first recall the recent result that in deep networks a phase transition,
analogous to the jamming transition of granular media, delimits the over-and under …

Construction faces many safety accidents with urbanization, particularly in hoisting.
However, there is a lack of systematic review studies in this area. This paper explored the …

We argue that in fully-connected networks a phase transition delimits the over-and under-
parametrized regimes where fitting can or cannot be achieved. Under some general …

We study how neural networks compress uninformative input space in models where data
lie in d dimensions, but the labels of which only vary within a linear manifold of dimension …

We consider the problem of training a neural network to store a set of patterns with maximal
noise robustness. A solution, in terms of optimal weights and state update rules, is derived …

By using the viewpoint of modern computational algebraic geometry, we explore properties
of the optimization landscapes of deep linear neural network models. After providing …

Descent methods for deep networks are notoriously capricious: they require careful tuning of
step size, momentum and weight decay, and which method will work best on a new …

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