Related papers: Exploring high-dimensional random landscapes: from…
In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov Chain. [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi…
Our theoretical understanding of glassy dynamics is notoriously incomplete, and it is even more so when the glassy systems are driven out of equilibrium. An extreme way to drive a system out of equilibrium is to introduce nonequilibrium…
Understanding how frustration and disorder shape relaxation in complex systems is a central problem in statistical physics and quantum annealing. Spin-glass models provide a natural framework to explore this connection, as their energy…
In these lecture notes we present different methods and concepts developed in statistical physics to analyze gradient descent dynamics in high-dimensional non-convex landscapes. Our aim is to show how approaches developed in physics, mainly…
Non-convex optimization with local search heuristics has been widely used in machine learning, achieving many state-of-art results. It becomes increasingly important to understand why they can work for these NP-hard problems on typical…
The Thouless, Anderson, Palmer (TAP) approach to thermodynamics of mean field spin-glasses is generalised to dynamics. A method to compute the dynamical TAP equations is developed and applied to the p-spin spherical model. In this context…
We use heuristic optimization methods in extensive computations to determine with low systematic error ground state configurations of the mean-field $p$-spin glass model with $p=3$. Here, all possible triplets in a system of $N$ Ising spins…
Given the fundamental importance of combinatorial optimization across many diverse application domains, there has been widespread interest in the development of unconventional physical computing architectures that can deliver better…
Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…
In these notes, we continue our investigation of classical toy models of disordered statistical mechanics through various techniques recently developed and tested mainly on the paradigmatic SK spin glass. Here we consider the p-spin-glass…
Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40^2. A combination of a genetic algorithm and Cluster-Exact Approximation is used. For…
The planted p-spin interaction model is a paradigm of random-graph systems possessing both a ferromagnetic phase and a disordered phase with the latter splitting into many spin glass states at low temperatures. Conventional simulated…
The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial…
We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original…
The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost…
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…
A method is presented, which allows to sample directly low-temperature configurations of glassy systems, like spin glasses. The basic idea is to generate ground states and low lying excited configurations using a heuristic algorithm. Then,…
Computing the ground state of Ising spin-glass models with p-spin interactions is, in general, an NP-hard problem. In this work we show that unlike in the case of the standard Ising spin glass with two-spin interactions, computing ground…
Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and automated reasoning.…
In this work we study numerically a short range p-spin glass model in three dimensions. The behaviour of the model appears to be remarkably different from mean field predictions. In fact it shares some features typical of models with full…