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Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…

With the advent of noisy intermediate-scale quantum (NISQ) devices, practical quantum computing has seemingly come into reach. However, to go beyond proof-of-principle calculations, the current processing architectures will need to scale up…

Symbolic Regression (SR) is a powerful technique for automatically discovering mathematical expressions from input data. Mainstream SR algorithms search for the optimal symbolic tree in a vast function space, but the increasing complexity…

CP decomposition is a powerful tool for data science, especially gene analysis, deep learning, and quantum computation. However, the application of tensor decomposition is largely hindered by the exponential increment of the computational…

Many real-world data, such as recommendation data and temporal graphs, can be represented as incomplete sparse tensors where most entries are unobserved. For such sparse tensors, identifying the top-k higher-order interactions that are most…

It is challenging to reduce the complexity of neural networks while maintaining their generalization ability and robustness, especially for practical applications. Conventional solutions for this problem incorporate quantum-inspired neural…

The Vision Transformer (ViT) has gained prominence for its superior relational modeling prowess. However, its global attention mechanism's quadratic complexity poses substantial computational burdens. A common remedy spatially groups tokens…

Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further,…

Summary: We develop TaSer (TabAnno and SeqMiner), a toolkit for annotating and querying next generation sequence (NGS) dataset in tab-delimited files. TabAnno is a powerful and efficient command-line tool designed to pre-process sequence…

Graphical tensor notation is a simple way of denoting linear operations on tensors, originating from physics. Modern deep learning consists almost entirely of operations on or between tensors, so easily understanding tensor operations is…

Image tokenizers play a critical role in shaping the performance of subsequent generative models. Since the introduction of VQ-GAN, discrete image tokenization has undergone remarkable advancements. Improvements in architecture,…

We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for…

Unsupervised commonsense question answering is appealing since it does not rely on any labeled task data. Among existing work, a popular solution is to use pre-trained language models to score candidate choices directly conditioned on the…

We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not…

Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

Tensor networks have a gauge degree of freedom on the virtual degrees of freedom that are contracted. A canonical form is a choice of fixing this degree of freedom. For matrix product states, choosing a canonical form is a powerful tool,…

High-performance numerical quantum compilers rely on classical optimization, but are limited by slow numerical evaluations and a design that makes extending them with new instructions a difficult, error-prone task for domain experts. This…

This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…

Although symbol-level precoding (SLP) based on constructive interference (CI) exploitation offers performance gains, its high complexity remains a bottleneck. This paper addresses this challenge with an end-to-end deep learning (DL)…