Related papers: Approximate optimization, sampling and spin-glass …
Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
We give an asymptotic evaluation of the complexity of spherical p-spin spin-glass models via random matrix theory. This study enables us to obtain detailed information about the bottom of the energy landscape, including the absolute minimum…
A spin system is a framework in which the vertices of a graph are assigned spins from a finite set. The interactions between neighbouring spins give rise to weights, so a spin assignment can also be viewed as a weighted graph homomorphism.…
Predicting the quantum dynamics of promising solid-state and molecular quantum technology candidates remains a formidable challenge. Yet, accessing these dynamics is key to understanding and controlling decoherence mechanisms -- a…
Probabilistic constellation shaping enables easy rate adaption and has been proven to reduce the gap to Shannon capacity. Constellation point probabilities are optimized to maximize either the mutual information or the bit-wise mutual…
There are well established reductions between combinatorial sampling and counting problems (Jerrum, Valiant, Vazirani TCS 1986). Building off of a very recent parallel algorithm utilizing this connection (Liu, Yin, Zhang arxiv 2024), we…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
Optimization drives advances in quantum science and machine learning, yet most generative models aim to mimic data rather than to discover optimal answers to challenging problems. Here we present a variational generative optimization…
Global discrete optimization is notoriously difficult due to the lack of gradient information and the curse of dimensionality, making exhaustive search infeasible. Tensor cross approximation is an efficient technique to approximate…
We establish that in the large degree limit, the value of certain optimization problems on sparse random hypergraphs is determined by an appropriate Gaussian optimization problem. This approach was initiated in Dembo et. al.(2016) for…
Best subset of groups selection (BSGS) is the process of selecting a small part of non-overlapping groups to achieve the best interpretability on the response variable. It has attracted increasing attention and has far-reaching applications…
Efficient probabilistic inference by variable elimination in graphical models requires an optimal elimination order. However, finding an optimal order is a challenging combinatorial optimisation problem for models with a large number of…
We present an algorithm for the optimization and thermal equilibration of spin glasses - or more generally, cost functions of the Ising form $H=\sum_{\langle i j\rangle} J_{ij} s_i s_j + \sum_i h_i s_i$, defined on graphs with arbitrary…
This paper studies lower bounds for fundamental optimization problems in the CONGEST model. We show that solving problems exactly in this model can be a hard task, by providing $\tilde{\Omega}(n^2)$ lower bounds for cornerstone problems,…
We introduce a clipping strategy for Stochastic Gradient Descent (SGD) which uses quantiles of the gradient norm as clipping thresholds. We prove that this new strategy provides a robust and efficient optimization algorithm for smooth…
Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…
A new approach to combinatorial optimization based on systematic move-class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy-driven. It is tested on two problems…