Related papers: Capturing long-range memory structures with tree-g…

Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…

Because of their superior ability to preserve sequence information over time, Long Short-Term Memory (LSTM) networks, a type of recurrent neural network with a more complex computational unit, have obtained strong results on a variety of…

Modeling the sequential information of image sequences has been a vital step of various vision tasks and convolutional long short-term memory (ConvLSTM) has demonstrated its superb performance in such spatiotemporal problems. Nevertheless,…

Classical simulations of quantum circuits play a vital role in the development of quantum computers and for taking the temperature of the field. Here, we classically simulate various physically-motivated circuits using 2D tensor network…

This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for…

The paper introduces two new aggregation functions to encode structural knowledge from tree-structured data. They leverage the Canonical and Tensor-Train decompositions to yield expressive context aggregation while limiting the number of…

We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…

The duration, strength and structure of memory effects are crucial properties of physical evolution. Due to the invasive nature of quantum measurement, such properties must be defined with respect to the probing instruments employed. Here,…

We propose a time series analysis framework focused on higher-order temporal correlations in the event sequence beyond the interevent time distribution by employing the burst-tree decomposition method. Bursts are clustered events that…

We discuss the enumeration of Feynman diagrams at tree order for processes with external lines of different types. We show how this can be done by iterating algebraic Schwinger-Dyson equations. Asymptotic estimates for very many external…

We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…

Sequential data such as time series, video, or text can be challenging to analyse as the ordered structure gives rise to complex dependencies. At the heart of this is non-commutativity, in the sense that reordering the elements of a…

Tensor network states are an indispensable tool for the simulation of strongly correlated quantum many-body systems. In recent years, tree tensor network states (TTNS) have been successfully used for two-dimensional systems and to benchmark…

Temporal gates play a significant role in modern recurrent-based neural encoders, enabling fine-grained control over recursive compositional operations over time. In recurrent models such as the long short-term memory (LSTM), temporal gates…

Tree-like structures, such as blood vessels, often express complexity at very fine scales, requiring high-resolution grids to adequately describe their shape. Such sparse morphology can alternately be represented by locations of centreline…

We investigate the potential of supervised machine learning to propagate a quantum system in time. While Markovian dynamics can be learned easily, given a sufficient amount of data, non-Markovian systems are non-trivial and their…

Network theory has established itself as an appropriate tool for complex systems analysis and pattern recognition. In the context of spatiotemporal data analysis, correlation networks are used in the vast majority of works. However, the…

Processing sentence constituency trees in binarised form is a common and popular approach in literature. However, constituency trees are non-binary by nature. The binarisation procedure changes deeply the structure, furthering constituents…

Dynamical low-rank approximation by tree tensor networks is studied for the data-sparse approximation to large time-dependent data tensors and unknown solutions of tensor differential equations. A time integration method for tree tensor…

We use neural networks to represent the characteristic function of many-body Gaussian states in the quantum phase space. By a pullback mechanism, we model transformations due to unitary operators as linear layers that can be cascaded to…