Related papers: Active learning of tree tensor networks using opti…

In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…

Tensor network contraction is a fundamental mathematical operation that generalizes the dot product and matrix multiplication. It finds applications in numerous domains, such as database systems, graph theory, machine learning, probability…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

This work presents a novel method for task optimization in industrial plants using quantum-inspired tensor network technology. This method obtains the best possible combination of tasks on a set of machines with directed constraints while…

One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on…

We propose a novel technique for faster deep neural network training which systematically applies sample-based approximation to the constituent tensor operations, i.e., matrix multiplications and convolutions. We introduce new sampling…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and…

As the complexity and computational demands of deep learning models rise, the need for effective optimization methods for neural network designs becomes paramount. This work introduces an innovative search mechanism for automatically…

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…

It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…

We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…

We introduce an optimal strategy to sample quantum outcomes of local measurement strings for isometric tensor network states. Our method generates samples based on an exact cumulative bounding function, without prior knowledge, in the…