Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these suboptimal, some cases completely failing detect communities even when other such as belief propagation can do so. Here we introduce a new class spectral based on non-backtracking walk directed edges graph. The spectrum this operator is much better-behaved than that adjacency matrix or commonly used matrices, maintaining strong separation...

We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and exact calculation normalized probability configurations. It computes free energy, estimates physical quantities such as entropy, magnetizations correlations, generates uncorrelated samples all at once. Training network employs policy gradient in reinforcement...

We propose a tensor network approach to compute amplitudes and probabilities for large number of correlated bitstrings in the final state quantum circuit. As an application, we study Google's Sycamore circuits, which are believed be beyond reach classical supercomputers have been used demonstrate supremacy. By employing small computational cluster containing 60 graphical processing units (GPUs), exact 2×10^{6} with some entries fixed (which span subspace output probability distribution)...

We study the problem of generating independent samples from output distribution Google's Sycamore quantum circuits with a target fidelity, which is believed to be beyond reach classical supercomputers and has been used demonstrate supremacy. propose method classically solve this by contracting corresponding tensor network just once, massively more efficient than existing methods in large number uncorrelated fidelity. For supremacy circuit 53 qubits 20 cycles, we have generated 1×10^{6}...

Estimating free energy is a fundamental problem in statistical mechanics. Recently, machine-learning-based methods, particularly the variational autoregressive networks (VANs) have been proposed to minimize and approximate Boltzmann distribution. VAN enjoys notable advantages, including exact computation of normalized joint distribution fast sampling, which are critical features often missing Markov chain Monte Carlo algorithms. However, also faces significant computational challenges. These...

Significance Most work on community detection does not address the issue of statistical significance, and many algorithms are prone to overfitting. We this using tools from physics. Rather than trying find partition a network that maximizes modularity, our approach seeks consensus high-modularity partitions. do with scalable message-passing algorithm, derived by treating modularity as Hamiltonian applying cavity method. show analytically algorithm succeeds all way down detectability...

Modeling the probability distribution of complex data using insights from quantum physics is a fresh approach to generative modeling in machine learning, and shows great potential compared conventional neural network approaches.

Decycling and dismantling of complex networks are underlying many important applications in network science. Recently these two closely related problems were tackled by several heuristic algorithms, simple considerably sub-optimal, on the one hand, involved accurate message-passing ones that evaluate single-node marginal probabilities, other hand. In this paper we propose a extremely fast algorithm, CoreHD, which recursively removes nodes highest degree from 2-core network. CoreHD performs...

We introduce Yao, an extensible, efficient open-source framework for quantum algorithm design. Yao features generic and differentiable programming of circuits. It achieves state-of-the-art performance in simulating small to intermediate-sized circuits that are relevant near-term applications. the design principles critical techniques behind Yao. These include block intermediate representation circuits, a builtin automatic differentiation engine optimized reversible computing, batched...

We present the full-resolution correspondence learning for cross-domain images, which aids image translation. adopt a hierarchical strategy that uses from coarse level to guide fine levels. At each hierarchy, can be efficiently computed via PatchMatch iteratively leverages matchings neighborhood. Within iteration, ConvGRU module is employed refine current considering not only of larger context but also historic estimates. The proposed Co-CosNet v2, GRU-assisted approach, fully differentiable...

In this paper, we discuss an unsupervised deep learning (DL) method for solving time domain electromagnetic simulations. Compared to the conventional approach, our encodes initial conditions, boundary conditions as well Maxwell's equations constraints when training network, turning simulation problem into optimization process. High prediction accuracy of fields, without discretization or interpolation in space time, can be achieved with limited number layers and neurons each layer neural...

Abstract Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges equilibrium, including accurately describing the joint distribution large number configurations, and also poses new as evolves over time. Characterizing dynamical phase transitions an emergent behavior further requires tracking nonequilibrium systems under control parameter. While methods have been proposed, such tensor networks for one-dimensional lattices, we...

The proliferation of models for networks raises challenging problems model selection: the data are sparse and globally dependent, typically high-dimensional have large numbers latent variables. Together, these issues mean that usual model-selection criteria do not work properly networks. We illustrate challenges, show one way to resolve them, by considering key network-analysis problem dividing a graph into communities or blocks nodes with homogeneous patterns links rest network. standard...

We study the fundamental limits on learning latent community structure in dynamic networks. Specifically, we stochastic block models where nodes change their membership over time, but edges are generated independently at each time step. In this setting (which is a special case of several existing models), able to derive detectability threshold exactly, as function rate and strength communities. Below threshold, claim that no algorithm can identify communities better than chance. then give...

We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of wide use in inference and learning problems defined on graphs. show applications our algorithm graphical models, specifically estimating free energy spin glasses various graphs, where largely outperforms existing algorithms, including mean-field methods recently proposed neural-network-based methods. further apply simulation random...

Abstract We extend the ability of an unitary quantum circuit by interfacing it with a classical autoregressive neural network. The combined model parametrizes variational density matrix as mixture pure states, where network generates bitstring samples input states to circuit. devise efficient algorithm jointly optimize and solve statistical mechanics problems. One can obtain thermal observables such free energy, entropy, specific heat. As byproduct, also gives access low energy excitation...

Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning recent years. However, order to achieve exact contraction, only treelike tensor networks such the matrix product states and tree have considered, even for modeling two-dimensional data images. In this work, we construct supervised images using projected entangled pair (PEPS), network having similar structure prior natural Our approach first performs feature...

We propose a general tensor network method for simulating quantum circuits. The is massively more efficient in computing large number of correlated bitstring amplitudes and probabilities than existing methods. As an application, we study the sampling problem Google's Sycamore circuits, which are believed to be beyond reach classical supercomputers have been used demonstrate supremacy. Using our method, employing small computational cluster containing 60 graphical processing units (GPUs),...

Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which advantages principle understanding expressive power using entanglement properties, and as bridge connecting classical computation quantum computation. Despite great potential, however, existing network for only work proof principle, their performance much worse than...

In this work, we propose an ID-preserving talking head generation framework, which advances previous methods in two aspects. First, as opposed to interpolating from sparse flow, claim that dense landmarks are crucial achieving accurate geometry-aware flow fields. Second, inspired by face-swapping methods, adaptively fuse the source identity during synthesis, so network better preserves key characteristics of image portrait. Although proposed model surpasses prior fidelity on established...

Predicting labels of nodes in a network, such as community memberships or demographic variables, is an important problem with applications social and biological networks. A recently discovered phase transition puts fundamental limits on the accuracy these predictions if we have access only to network topology. However, know correct some fraction $\ensuremath{\alpha}$ nodes, can do better. We study diagram this semisupervised learning for networks generated by stochastic block model. use...

We present a unified exact tensor network approach to compute the ground state energy, identify optimal configuration, and count number of solutions for spin glasses. The method is based on networks with tropical algebra defined semiring $(\mathbb{R}\ensuremath{\cup}{\ensuremath{-}\ensuremath{\infty}},\ensuremath{\bigoplus},\ensuremath{\bigodot})$. Contracting gives energy; differentiating through contraction configuration; mixing ordinary counts degeneracy. brings together concepts from...