Keywords: disorderd systems, glass transition, jamming, avalanche statistics, replica symmetry breaking, neural networks, deep learning.

I had the chance to start working with the Simons Collaboration on Cracking the glass problem during my Ph.D., where I have studied the statistical physics of disordered systems, with focus on the glass transition in spin- (link) and structural-glasses (link) and on the jamming transition (link) in random packings of spheres.

In particular, I studied the statistics of the response of systems of hard spheres under a small shear-strain — figure (a); such response is random (sample-dependent) and jerky (discontinuous) — figure (b). The distribution of the response can be computed analytically in infinite dimensions via an approach based on the RSB theory — figure (c), — and in this case it displays critical properties, namely a power-law behaviour. Remarkably, this mean-field prediction holds true in finite dimensions as well! The details of my work can be found in my Ph.D. thesis and here.

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I have recently started a joint postdoc affiliated with the Simons Collaboration that takes place between the EPFL (Lausanne, Switzerland) and the CEA (Paris, France). Now my research consists in studying the properties of the energy landscape and of the dynamics in deep neural networks.

Neural networks are, loosely speaking, algorithms that are inspired by some features of the (visual) cortex of living animals. (Supervised) neural networks can be used to do inference on data; one of the typical tasks that these algorithms can do is classification: a network can be trained on a set of pictures belonging to multiple categories, in such a way that when presented with a new image there is a high chance that it will be able to correctly classify the category the image belongs to. Training is characterized as a process where some error function is minimized, with respect to the parameters of the model; the error is defined as a measure of mismatch between the predicted category of a picture and the true one

In order to achieve good results on complex datasets, these networks need to be fairly deep (millions of tunable parameters to be inferred). There are several reason to think that the energy landscape, as a function of the parameters, is rough and complex, as one finds in disordered glassy systems, but it turns out that it might be much smoother. The goal of my research is to characterize this landscape and the salient features of the dynamics that the system undergoes while learning (i.e. during training).