Session F53: Marginal Stability in Amorphous Materials and Beyond

Aging, Jamming and the Mechanisms of Marginal Stability in Amorphous Solids

The random first order transition theory of glasses provides a route to understanding not only the dynamics of the supercooled liquid state, but also the history dependent properties of nonequilibrium amorphous states, i.e., glasses. I will review its implications for preparing marginally stable amorphous packings as well as the dynamic implications of the competing existence of thermodynamically stable periodic crystals for obtaining such amorphous assemblies.   

Jamming of particles and machine learning models

In this talk I will describe the analogy between hard spheres in high dimension and some machine learning problems focusing on the properties of their landscape and their jamming transition. I will highlight how marginal stability emerges in both cases and what are its consequences.   

Marginally stable phases in structural glasses

A novel form of amorphous matter characterized by marginal stability was recently discovered in the mean-field theory of structural glasses. In the marginally stable phase, structural glasses inherit the richness of spin-glass physics characterized by ergodicity breaking transitions, complex free energy landscapes, rejuvenation and memory effects. We study analytically and numerically Weeks-Chandler-Andersen glasses. By changing external parameters, we continuously explore physical regimes relevant to granular matter, foams, emulsions, hard and soft colloids, and molecular glasses. Our results suggest that marginal phases should be observable for colloidal and non-Brownian particles near jamming. In this regime, we numerically observe rejuvenation and memory effects. By contrast, we find that molecular glasses do not present marginally stable phases, but our study reveals instead the presence of localised excitations presumably relevant for mechanical and vibrational properties of structural glasses.   

A jamming transition controls the landscape in deep learning

Deep learning has been immensely successful at a variety of tasks, ranging from classification to AI. Learning corresponds to fitting training data, which is implemented by descending a very high-dimensional loss function. Understanding under which conditions neural networks do not get stuck in poor minima of the loss, and how the landscape of that loss evolves as depth is increased remains a challenge. Here we predict, and test empirically, an analogy between this landscape and the energy landscape of repulsive ellipses. We argue that infully-connected networks a phase transition delimits the over- and under-parametrized regimes where fitting can or cannot be achieved. In the vicinity of this transition, properties of the curvature of the minima of the loss are critical. This transition shares direct similarities with the jamming transition by which particles form a disordered solid as the density is increased, which also occurs in certain classes of computational optimization and learning problems such as the perceptron. Our analysis gives a simple explanation as to why poor minima of the loss cannot be encountered in the overparametrized regime, and puts forward the surprising result that the ability of fully connected networks to fit random data is independent of their depth. Our observations suggests that this independence also holds for real data. We also study a quantity Δ which characterizes how well (Δ<0) or badly (Δ>0) a datum is learned. At the critical point it appears to be power-law distributed, suggesting that near the transition the loss landscape has a hierarchical structure and that the learning dynamics is prone to avalanche-like dynamics, with abrupt changes in the set of patterns that are learned.   

Marginal stability in finite dimensions

Glassy materials are omnipresent in everyday life from windows to plastics to piles of sand. Yet our understanding of both their (equilibrium) liquid and (out-of-equilibrium) solid phases lags far behind that of crystalline counterparts. Recent advances are rapidly changing the ways in which we understand these common-yet-physically-enigmatic materials. This talk overviews one such advance -- the discovery of the Gardner phase transition from normal to marginally-stable glasses. Our work in particular indicates that such a transition, first found in abstract infinite-dimensional models, can survive down to the three-dimensional world. This transition reinforces the overriding role of rugged free-energy landscapes that dictate physics of glassy systems, with tangible consequences on jamming, yielding, and beyond.