Related papers: Local Interpolation via Low-Rank Tensor Trains

Folding grid value vectors of size $2^L$ into $L$th order tensors of mode sizes $2\times \cdots\times 2$, combined with low-rank representation in the tensor train format, has been shown to lead to highly efficient approximations for…

Implicit Neural Representations (INRs) model signals as continuous, differentiable functions. However, monolithic INRs scale poorly with data dimensionality, leading to excessive training costs. We propose F-INR, a framework that addresses…

This paper introduces a novel approach to approximating continuous functions over high-dimensional hypercubes by integrating matrix CUR decomposition with hyperinterpolation techniques. Traditional Fourier-based hyperinterpolation methods…

This paper addresses the challenge of reconstructing a 3D power spectrum map from sparse, scattered, and incomplete spectrum measurements. It proposes an integrated approach combining interpolation and block-term tensor decomposition (BTD).…

Recent studies have demonstrated the great potential of reduced order modeling for parametric dynamical systems using low-rank tensor decompositions (LRTD). In particular, within the framework of interpolatory tensorial reduced order models…

Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…

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…

The hierarchical SVD provides a quasi-best low rank approximation of high dimensional data in the hierarchical Tucker framework. Similar to the SVD for matrices, it provides a fundamental but expensive tool for tensor computations. In the…

Performance tuning, software/hardware co-design, and job scheduling are among the many tasks that rely on models to predict application performance. We propose and evaluate low-rank tensor decomposition for modeling application performance.…

Tensor decomposition methodologies are proposed to reduce the memory requirement of translation operator tensors arising in the fast multipole method-fast Fourier transform (FMM-FFT)-accelerated surface integral equation (SIE) simulators.…

A rising problem in the compression of Deep Neural Networks is how to reduce the number of parameters in convolutional kernels and the complexity of these layers by low-rank tensor approximation. Canonical polyadic tensor decomposition…

Compressive imaging (CI) reconstruction, such as snapshot compressive imaging (SCI) and compressive sensing magnetic resonance imaging (MRI), aims to recover high-dimensional images from low-dimensional compressed measurements. This process…

Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…

In this article we consider the iterative schemes to compute the canonical (CP) approximation of quantized data generated by a function discretized on a large uniform grid in an interval on the real line. This paper continues the research…

The state-of-the-art deep neural networks (DNNs) have been widely applied for various real-world applications, and achieved significant performance for cognitive problems. However, the increment of DNNs' width and depth in architecture…

Low Rank Decomposition (LRD) is a model compression technique applied to the weight tensors of deep learning models in order to reduce the number of trainable parameters and computational complexity. However, due to high number of new…

A novel tensor decomposition framework, termed Tensor Star (TS) decomposition, is proposed which represents a new type of tensor network decomposition based on tensor contractions. This is achieved by connecting the core tensors in a ring…

Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…

Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low-rank patterns in multidimensional data. A well-known method for TR decomposition is the alternating…

Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…