Related papers: Thesis: Tensor networks for dynamic spacetimes
Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond…
Inspired by the ConvNets with structured hidden representations, we propose a Tensor-based Neural Network, TCNN. Different from ConvNets, TCNNs are composed of structured neurons rather than scalar neurons, and the basic operation is neuron…
We develop a formalism to calculate the effective action of the strongly coupled conformal field theory (CFT) in curved spacetime. The effective action of the CFT is obtained from AdS/CFT correspondence. The anti de-Sitter (AdS) spacetime…
Exponential regularization of orthogonal and Anti-de Sitter (AdS) space is presented based on noncommutative geometry. We show that an adequately adopted noncommutative deformation of geometry makes the holography of higher dimensional…
A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure,…
We describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of…
Among various applications of the AdS/CFT correspondence in condensed matter physics of particular importance is the realization of the phase transition between the normal and superconducting phase in a holographic QFT. After seminal papers…
One of the key applications of AdS/CFT correspondence is the duality it dictates between the entanglement entropy of Anti-de Sitter (AdS) black holes and lower-dimensional conformal field theories (CFTs). Here we employ a square lattice of…
The era of "data deluge" has sparked renewed interest in graph-based learning methods and their widespread applications ranging from sociology and biology to transportation and communications. In this context of graph-aware methods, the…
The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…
We give a systematic procedure to evaluate conformal partial waves involving symmetric tensors for an arbitrary CFT$_d$ using geodesic Witten diagrams in AdS$_{d+1}$. Using this procedure we discuss how to draw a line between the tensor…
The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better…
We use the framework of $\textit{fixed-point BCFT tensor networks}$ to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS$_3$/CFT$_2$, for both…
Understanding the evolutionary patterns of real-world evolving complex systems such as human interactions, transport networks, biological interactions, and computer networks has important implications in our daily lives. Predicting future…
We investigate the AdS/CFT interpretation of the class of algebraically special solutions of Einstein gravity with a negative cosmological constant. Such solutions describe a CFT living in a 2+1 dimensional time-dependent geometry that,…
We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial…
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…
Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a tensor representation whose entries are predicted by models…
The fields of neural computation and artificial neural networks have developed much in the last decades. Most of the works in these fields focus on implementing and/or learning discrete functions or behavior. However, technical, physical,…
The ability to learn compact, high-quality, and easy-to-optimize representations for visual data is paramount to many applications such as novel view synthesis and 3D reconstruction. Recent work has shown substantial success in using tensor…