Related papers: Approximate optimization, sampling and spin-glass …
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
This work introduces SpinGlassPEPS$.$jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction…
We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system…
Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…
Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we…
The properties of flat minima in the empirical risk landscape of neural networks have been debated for some time. Increasing evidence suggests they possess better generalization capabilities with respect to sharp ones. First, we discuss…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
We propose and analyze a family of approximately-symmetric neural networks for quantum spin liquid problems. These tailored architectures are parameter-efficient, scalable, and significantly outperform existing symmetry-unaware neural…
Tensor networks, which have been traditionally used to simulate many-body physics, have recently gained significant attention in the field of machine learning due to their powerful representation capabilities. In this work, we propose a…
The task of sampling efficiently the Gibbs-Boltzmann distribution of disordered systems is important both for the theoretical understanding of these models and for the solution of practical optimization problems. Unfortunately, this task is…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
The collection of all the strongly connected components in a directed graph, among each cluster of which any node has a path to another node, is a typical example of the intertwining structure and dynamics in complex networks, as its…
Using mappings to computer-science problems and by applying sophisticated algorithms, one can study numerically many problems much better compared to applying standard approaches like Monte Carlo simulations. Here, using calculations of…
Spin glass theory studies the structure of sublevel sets and minima (or near-minima) of certain classes of random functions in high dimension. Near-minima of random functions also play an important role in high-dimensional statistics and…
Spin-glasses are Gibbs distributions that have been studied in CS for many decades. Recently, they have gained renewed attention as they emerge naturally in learning, inference, optimisation etc. We consider the Edwards-Anderson (EA)…
We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking Ansatz we can solve exactly the saddle-point equations for…
This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…