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We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a…
Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable…
Predicting materials properties from composition or structure is of great interest to the materials science community. Deep learning has recently garnered considerable interest in materials predictive tasks with low model errors when…
Density functional theory and its optimization algorithm are the main methods to calculate the properties in the field of materials. Although the calculation results are accurate, it costs a lot of time and money. In order to alleviate this…
Machine learning has emerged as a powerful approach in materials discovery. Its major challenge is selecting features that create interpretable representations of materials, useful across multiple prediction tasks. We introduce an…
Nuclear magnetic resonance (NMR) is a powerful spectroscopic technique that is sensitive to the local atomic structure of matter. Computational predictions of NMR parameters can help to interpret experimental data and validate structural…
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…
When designing materials to optimize certain properties, there are often many possible configurations of designs that need to be explored. For example, the materials' composition of elements will affect properties such as strength or…
The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way…
Deep neural networks have demonstrated remarkable efficacy in extracting meaningful representations from complex datasets. This has propelled representation learning as a compelling area of research across diverse fields. One interesting…
Materials characterization remains a significant, time-consuming undertaking. Generally speaking, spectroscopic techniques are used in conjunction with empirical and ab-initio calculations in order to elucidate structure. These experimental…
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…
The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…
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 network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
Machine learning models can be used to predict physical quantities like homogenized elasticity stiffness tensors, which must always be symmetric positive definite (SPD) based on conservation arguments. Two datasets of homogenized elasticity…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…
Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory…
Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…