Related papers: The Tensor Track VII: From Quantum Gravity to Arti…
We present a series of algorithms in tensor networks for anomaly detection in datasets, by using data compression in a Tensor Train representation. These algorithms consist of preserving the structure of normal data in compression and…
Situated as a language between computer science, quantum physics and mathematics, tensor network theory has steadily grown in popularity and can now be found in applications ranging across the entire field of quantum information processing.…
A probing scheme is considered with an accessible and controllable qubit, used to probe an out-of equilibrium system consisting of a second qubit interacting with an environment. Quantum spontaneous synchronization between the probe and the…
Generic open quantum dynamics can be described by two seemingly very distinct approaches: a top down approach by considering an (unknown) environment coupled to the system and affects the observed dynamics of the system; or a bottom up…
Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation…
The problem of partitioning a large and sparse tensor is considered, where the tensor consists of a sequence of adjacency matrices. Theory is developed that is a generalization of spectral graph partitioning. A best rank-$(2,2,\lambda)$…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
We are interested in the estimation of a rank-one tensor signal when only a portion $\varepsilon$ of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral…
In this paper we show how tensor networks help in developing explainability of machine learning algorithms. Specifically, we develop an unsupervised clustering algorithm based on Matrix Product States (MPS) and apply it in the context of a…
A promising area of applications for quantum computing is in linear algebra problems. In this work, we introduce two new quantum t-SVD (tensor-SVD) algorithms. The first algorithm is largely based on previous work that proposed a quantum…
Noise is conventionally viewed as a severe problem in diverse fields, e.g., engineering, learning systems. However, this paper aims to investigate whether the conventional proposition always holds. It begins with the definition of task…
In this paper, we propose an extension of trace ratio based Manifold learning methods to deal with multidimensional data sets. Based on recent progress on the tensor-tensor product, we present a generalization of the trace ratio criterion…
Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize…
Compressive sensing is a sensing protocol that facilitates reconstruction of large signals from relatively few measurements by exploiting known structures of signals of interest, typically manifested as signal sparsity. Compressive…
This paper addresses the detection of a low rank high-dimensional tensor corrupted by an additive complex Gaussian noise. In the asymptotic regime where all the dimensions of the tensor converge towards $+\infty$ at the same rate, existing…
Collaborative robotic systems will be a key enabling technology for current and future industrial applications. The main aspect of such applications is to guarantee safety for humans. To detect hazardous situations, current commercially…
Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is sampled from a low-dimensional structure.…
There has been increased interest in missing sensor data imputation, which is ubiquitous in the field of structural health monitoring (SHM) due to discontinuous sensing caused by sensor malfunction. To address this fundamental issue, this…
This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to…
Learning relies on coordinated synaptic changes in recurrently connected populations of neurons. Therefore, understanding the collective evolution of synaptic connectivity over learning is a key challenge in neuroscience and machine…