Related papers: Complex Time Evolution in Tensor Networks
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…
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…
The entangling power and operator entanglement entropy are state independent measures of entanglement. Their growth and saturation is examined in the time-evolution operator of quantum many-body systems that can range from the integrable to…
Modern deep learning has enabled unprecedented achievements in various domains. Nonetheless, employment of machine learning for wave function representations is focused on more traditional architectures such as restricted Boltzmann machines…
The ability to identify and temporally segment fine-grained human actions throughout a video is crucial for robotics, surveillance, education, and beyond. Typical approaches decouple this problem by first extracting local spatiotemporal…
We study the approximation properties of convolutional architectures applied to time series modelling, which can be formulated mathematically as a functional approximation problem. In the recurrent setting, recent results reveal an…
We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…
We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle…
The growing share of renewable energy makes the optimization of power flows in power system models computationally more complicated, due to the widely distributed weather-dependent electricity generation. This article evaluates two methods…
Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…
Classically, the time complexity of a first-order method is estimated by its number of gradient computations. In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed…
Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…
Most methods for time series classification that attain state-of-the-art accuracy have high computational complexity, requiring significant training time even for smaller datasets, and are intractable for larger datasets. Additionally, many…
While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…
Many-body calculations at the two-particle level require a compact representation of two-particle Green's functions. In this paper, we introduce a sparse sampling scheme in the Matsubara frequency domain as well as a tensor network…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
In this paper we examine a number of methods for probing and understanding the large-scale structure of networks that evolve over time. We focus in particular on citation networks, networks of references between documents such as papers,…
In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This…