Related papers: Tensor Networks for Probabilistic Sequence Modelin…

This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the…

The Recurrent Neural Networks and their variants have shown promising performances in sequence modeling tasks such as Natural Language Processing. These models, however, turn out to be impractical and difficult to train when exposed to very…

Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…

Tensor networks such as matrix product states (MPS) and projected entangled pair states (PEPS) are commonly used to approximate quantum systems. These networks are optimized in methods such as DMRG or evolved by local operators. We provide…

Originating from condensed matter physics, tensor networks are compact representations of high-dimensional tensors. In this paper, the prowess of tensor networks is demonstrated on the particular task of one-class anomaly detection. We…

A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well…

Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…

Recurrent neural networks (RNN) such as long-short-term memory (LSTM) networks are essential in a multitude of daily live tasks such as speech, language, video, and multimodal learning. The shift from cloud to edge computation intensifies…

Tensor Network States are ans\"atze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation…

Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack…

Tensor networks are generated by a set of small rank tensors and define many-body quantum states in a succinct form. The corresponding map is not one-to-one: different sets of tensors may generate the very same state. A fundamental question…

We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor…

In recent years, interest in expressing the success of neural networks to the quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated…

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in…

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…

Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…

Matrix models, as quantum mechanical systems without explicit spatial dependence, provide valuable insights into higher-dimensional gauge and gravitational theories, especially within the framework of string theory, where they can describe…

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…

We present a tensorization algorithm for constructing tensor train/matrix product state (MPS) representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function…

Active inference provides a general framework for behavior and learning in autonomous agents. It states that an agent will attempt to minimize its variational free energy, defined in terms of beliefs over observations, internal states and…