Jorge Kurchan Parisi, Giorgio Zamponi, Francesco
Published in
Journal of Statistical Mechanics: Theory and Experiment

We consider the theory of the glass transition and jamming of hard spheres in the large space dimension limit. Previous investigations were based on the assumption that the probability distribution within a "cage" is Gaussian, which is not fully consistent with numerical results. Here we perform a replica calculation without making any assumption o...

Rylands, Colin Bertini, Bruno Calabrese, Pasquale
Published in
Journal of Statistical Mechanics: Theory and Experiment

We study the quench dynamics of the one-dimensional Hubbard model through the quench action formalism. We introduce a class of integrable initial states—expressed as product states over two sites—for which we can provide an exact characterisation of the late-time regime. This is achieved by finding a closed-form expression for the overlaps between ...

Queisser, Friedemann Schützhold, Ralf
Published in
Journal of Statistical Mechanics: Theory and Experiment

The hierarchy of correlations is an approximation scheme which permits the study of non-equilibrium phenomena in strongly interacting quantum many-body systems on lattices in higher dimensions (with the underlying idea being somewhat similar to dynamical mean-field theory). So far, this method was restricted to equal-time correlators such as ⟨Aˆμ(t...

Lahoche, Vincent Samary, Dine Ousmane Tamaazousti, Mohamed
Published in
Journal of Statistical Mechanics: Theory and Experiment

Some recent results showed that the renormalization group (RG) can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis (PCA) for the case of large dimensional data sets with covariance having a nearly continuous spectrum. In t...

Gerace, Federica Loureiro, Bruno Krzakala, Florent Mézard, Marc Zdeborová, Lenka
Published in
Journal of Statistical Mechanics: Theory and Experiment

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden manifold model. We consider the high-dimensional regime and using the replica method from statistical physics,...

Pellegrini, Franco Biroli, Giulio
Published in
Journal of Statistical Mechanics: Theory and Experiment

Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the training dynamics of a simple type of neural network: a single hidden layer trained to perform a classification...

Ma, Zheng Xuan, Junyu Wang, Yu Guang Li, Ming Liò, Pietro
Published in
Journal of Statistical Mechanics: Theory and Experiment

Graph neural networks (GNNs) extend the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose path integral-based GNNs (PAN) for classification and regression tasks on graphs. Specifically, we consider a...

d’Ascoli, Stéphane Sagun, Levent Biroli, Giulio
Published in
Journal of Statistical Mechanics: Theory and Experiment

A recent line of research has highlighted the existence of a ‘double descent’ phenomenon in deep learning, whereby increasing the number of training examples N causes the generalization error of neural networks (NNs) to peak when N is of the same order as the number of parameters P. In earlier works, a similar phenomenon was shown to exist in simpl...

Karakida, Ryo Osawa, Kazuki
Published in
Journal of Statistical Mechanics: Theory and Experiment

Natural gradient descent (NGD) helps to accelerate the convergence of gradient descent dynamics, but it requires approximations in large-scale deep neural networks because of its high computational cost. Empirical studies have confirmed that some NGD methods with approximate Fisher information converge sufficiently fast in practice. Nevertheless, i...

Feinauer, Christoph Lucibello, Carlo
Published in
Journal of Statistical Mechanics: Theory and Experiment

Pairwise models like the Ising model or the generalized Potts model have found many successful applications in fields like physics, biology, and economics. Closely connected is the problem of inverse statistical mechanics, where the goal is to infer the parameters of such models given observed data. An open problem in this field is the question of ...