Related papers: Tensor networks and efficient descriptions of clas…
Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of tensor…
It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast…
Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for…
We propose and demonstrate a representation learning approach by maximizing the mutual information between local features of images and text. The goal of this approach is to learn useful image representations by taking advantage of the rich…
Scaling up model and data size has been quite successful for the evolution of LLMs. However, the scaling law for the diffusion based text-to-image (T2I) models is not fully explored. It is also unclear how to efficiently scale the model for…
Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and…
This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will…
It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this…
We propose a method to enhance the performance of Large Language Models (LLMs) by integrating quantum computing and quantum-inspired techniques. Specifically, our approach involves replacing the weight matrices in the Self-Attention and…
Several complex systems are characterized by presenting intricate characteristics taking place at several scales of time and space. These multiscale characterizations are used in various applications, including better understanding…
Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of…
Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as…
Complex systems that consist of different kinds of entities that interact in different ways can be modeled by multilayer networks. This paper uses the tensor formalism with the Einstein tensor product to model this type of networks. Several…
We demonstrate the use of tensor networks for image classification with the TensorNetwork open source library. We explain in detail the encoding of image data into a matrix product state form, and describe how to contract the network in a…
The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of…
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated…
Unsupervised text embedding methods, such as Skip-gram and Paragraph Vector, have been attracting increasing attention due to their simplicity, scalability, and effectiveness. However, comparing to sophisticated deep learning architectures…
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…