Related papers: Efficient optimization of variational tensor-netwo…

Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic…

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…

Novel randomness-induced disordered ground states in two-dimensional (2D) quantum spin systems have been attracting much interest. For quantitative analysis of such random quantum spin systems, one of the most promising numerical approaches…

Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…

We present a global optimization routine for the variational quantum algorithms, which utilizes the dynamic tunneling flow. Originally designed to leverage information gathered by a gradient-based optimizer around local minima, we adapt the…

Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient…

Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…

Quantum computing offers the potential for computational abilities that can go beyond classical machines. However, they are still limited by several challenges such as noise, decoherence, and gate errors. As a result, efficient classical…

3D medical image processing with deep learning greatly suffers from a lack of data. Thus, studies carried out in this field are limited compared to works related to 2D natural image analysis, where very large datasets exist. As a result,…

We present a surprisingly simple approach to high-accuracy calculations of critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in…

Quantum processing units boost entanglement at the level of hardware and enable physical simulations of highly correlated electron states in molecules and intermolecular chemical bonds. The variational quantum eigensolver provides a…

Autoregressive Neural Networks based on dense or convolutional layers have recently been shown to be a viable strategy for generating classical spin systems. Unlike these methods, sampling with transformers is commonly considered to be…

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…

Tensor network methods strike a middle ground between fully-fledged quantum computing and classical computing, as they take inspiration from quantum systems to significantly speed up certain classical operations. Their strength lies in…

Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete…

Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we…

We study the tensor renormalization group (TRG) in the dimension larger than two as the Higher-order TRG (HOTRG) with the randomized SVD method. The randomized SVD and the detailed discussion on the low order tensor representation, we can…

We introduce a general method for optimizing real-space renormalization-group transformations to study the critical properties of a classical system. The scheme is based on minimizing the Kullback-Leibler divergence between the distribution…

We consider the problem of multiway clustering in the presence of unknown degree heterogeneity. Such data problems arise commonly in applications such as recommendation system, neuroimaging, community detection, and hypergraph partitions in…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…