Despite decades of work, gaining a first-principles understanding of amorphous materials
remains an extremely challenging problem. However, recent theoretical breakthroughs have …

In 1989, Sir Sam Edwards made the visionary proposition to treat jammed granular materials
using a volume ensemble of equiprobable jammed states in analogy to thermal equilibrium …

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 …

The low-frequency vibrational and low-temperature thermal properties of amorphous solids
are markedly different from those of crystalline solids. This situation is counterintuitive …

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 …

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 …

Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from
universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding …

Unusual features of the vibrational density of states D (ω) of glasses allow one to rationalize
their peculiar low-temperature properties. Simulational studies of D (ω) have been restricted …

Low-frequency vibrational modes play a central role in determining various basic properties
of glasses, yet their statistical and mechanical properties are not fully understood. Using …

A remarkable feature of disordered solids distinct from crystals is the violation of the Debye
scaling law of the low-frequency vibrational density of states. Because the low-frequency …