Nurcombe, Madeline
Published in
Journal of Statistical Mechanics: Theory and Experiment

We introduce the ghost algebra, a two-boundary generalisation of the Temperley–Lieb (TL) algebra, using a diagrammatic presentation. The existing two-boundary TL algebra has a basis of string diagrams with two boundaries, and the number of strings connected to each boundary must be even; in the ghost algebra, this number may be odd. To preserve ass...

Xie, Rongrong Marsili, Matteo
Published in
Journal of Statistical Mechanics: Theory and Experiment

We discuss the concept of probabilistic neural networks with a fixed internal representation being models for machine understanding. Here, ‘understanding’ is interpretted as the ability to map data to an already existing representation which encodes an a priori organisation of the feature space. We derive the internal representation by requiring th...

Guo, Wusong Yan, Hao Chen, Hanshuang
Published in
Journal of Statistical Mechanics: Theory and Experiment

We study the extreme value statistics of first-passage trajectories generated from a one-dimensional drifted Brownian motion subject to stochastic resetting to the starting point with a constant rate r. Each stochastic trajectory starts from a positive position x 0 and terminates whenever the particle hits the origin for the first time. We obtain a...

Loureiro, Bruno Gerbelot, Cédric Refinetti, Maria Sicuro, Gabriele Krzakala, Florent
Published in
Journal of Statistical Mechanics: Theory and Experiment

From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is therefore key to understanding robust generalisation. In this manuscript we develop a quantitative and rigorous the...

Petrini, Leonardo Cagnetta, Francesco Vanden-Eijnden, Eric Wyart, Matthieu
Published in
Journal of Statistical Mechanics: Theory and Experiment

It is widely believed that the success of deep networks lies in their ability to learn a meaningful representation of the features of the data. Yet, understanding when and how this feature learning improves performance remains a challenge. For example, it is beneficial for modern architectures to be trained to classify images, whereas it is detrime...

Veiga, Rodrigo Stephan, Ludovic Loureiro, Bruno Krzakala, Florent Zdeborová, Lenka
Published in
Journal of Statistical Mechanics: Theory and Experiment

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow networks, which tend to get stuck in badly-generalizing local minima. Here we investigate the cross-over between these two regimes in the high-dimensional ...

Plyukhin, Alex V
Published in
Journal of Statistical Mechanics: Theory and Experiment

We consider a classical Brownian oscillator of mass m driven from an arbitrary initial state by varying the stiffness k(t) of the harmonic potential according to the protocol k(t)=k0+aδ(t) , involving the Dirac delta function. The microscopic work performed on the oscillator is shown to be W=(a2/2m)q2−aqv , where q and v are the coordinate and velo...

Daniels, Max Gerbelot, Cédric Krzakala, Florent Zdeborová, Lenka
Published in
Journal of Statistical Mechanics: Theory and Experiment

Signal recovery under generative neural network priors has emerged as a promising direction in statistical inference and computational imaging. Theoretical analysis of reconstruction algorithms under generative priors is, however, challenging. For generative priors with fully connected layers and Gaussian i.i.d. weights, this was achieved by the mu...

Mukherjee, Sukanta Pareek, Puneet Barma, Mustansir Kumar Nandi, Saroj
Published in
Journal of Statistical Mechanics: Theory and Experiment

The autocorrelation function in many complex systems shows a crossover in the form of its decay: from a stretched exponential relaxation (SER) at short times to a power law at long times. Studies of the mechanisms leading to such multiple relaxation patterns are rare. Additionally, the inherent complexity of these systems makes it hard to understan...

Mabillard, Joël Gaspard, Pierre
Published in
Journal of Statistical Mechanics: Theory and Experiment

Within the framework of the local equilibrium approach, the equilibrium and nonequilibrium properties relevant to the hydrodynamics of the perfect hard-sphere crystal were obtained through molecular dynamics simulations using the Helfand moments associated with momentum and energy transport. Because this crystal is face-centered cubic, the hydrodyn...