Related papers: Tree Tensor Networks Methods for Efficient Calcula…
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…
Vibrational spectroscopy is a key technique to elucidate microscopic structure and dynamics. Without the aid of theoretical approaches, it is however, often difficult to understand such spectra at a microscopic level. Ab initio molecular…
We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space…
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…
We introduce a tree tensor network (TTN) impurity solver that enables highly efficient and accurate real-time simulations of quantum impurity models. By decomposing a noninteracting bath Hamiltonian into a Cayley tree, the method provides a…
We introduce an adaptive-weighted tree tensor network, for the study of disordered and inhomogeneous quantum many-body systems. This ansatz is assembled on the basis of the random couplings of the physical system with a procedure that…
While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…
Given a spatio-temporal network (ST network) where edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of minimum spanning trees of the ST network, where each tree is associated with a time…
Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…
It is widely recognized that the deeper networks or networks with more feature maps have better performance. Existing studies mainly focus on extending the network depth and increasing the feature maps of networks. At the same time,…
Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the…
Tabular datasets play a crucial role in various applications. Thus, developing efficient, effective, and widely compatible prediction algorithms for tabular data is important. Currently, two prominent model types, Gradient Boosted Decision…
The tree-structured stick-breaking process (TS-SBP) mixture model is a non-parametric Bayesian model that can represent tree-like hierarchical structures among the mixture components. For TS-SBP mixture models, only a Markov chain Monte…
Given an undirected graph with costs associated with each edge as well as each pair of edges, the quadratic minimum spanning tree problem (QMSTP) consists of determining a spanning tree of minimum total cost. This problem can be used to…
Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…
In the domain of sequence modelling, Recurrent Neural Networks (RNN) have been capable of achieving impressive results in a variety of application areas including visual question answering, part-of-speech tagging and machine translation.…
Non-invasive brain-computer interfaces help the subjects to control external devices by brain intentions. The multi-class classification of upper limb movements can provide external devices with more control commands. The onsets of the…
Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased…
We apply a series of projection techniques on top of tensor networks to compute energies of ground state wave functions with higher accuracy than tensor networks alone with minimal additional cost. We consider both matrix product states as…
We prove a conjecture of W.~Hackbusch in a bigger generality than in our previous article. Here we consider Tensor Train (TT) model with an arbitrary number of leaves and a corresponding "almost binary tree" for Hierarchical Tucker (HT)…