Related papers: Tucker Tensor Decomposition on FPGA
Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach,…
Transformers have attained superior performance in natural language processing and computer vision. Their self-attention and feedforward layers are overparameterized, limiting inference speed and energy efficiency. Tensor decomposition is a…
In the last decades, tensors have emerged as the right tool to represent multidimensional data in a compact yet informative manner. Moreover, it is well-known that by performing low-rank factorizations of such tensors one is often able to…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during training and inference phases. Given its easy implementation and flexibility, one promising…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using…
We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated…
With an ongoing trend in computing hardware towards increased heterogeneity, domain-specific co-processors are emerging as alternatives to centralized paradigms. The tensor core unit (TPU) has shown to outperform graphic process units by…
The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…
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,…
Two essential problems in Computer Algebra, namely polynomial factorization and polynomial greatest common divisor computation, can be efficiently solved thanks to multiple polynomial evaluations in two variables using modular arithmetic.…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
This work presents a GPU thread mapping approach that allows doing fast parallel stencil-like computations on discrete fractals using their compact representation. The intuition behind is to employ two GPU tensor-core accelerated thread…
Although code generation for Convolution Neural Network (CNN) models has been extensively studied, performing efficient data slicing and parallelization for highly-constrai\-ned Multicore Neural Processor Units (NPUs) is still a challenging…
We propose an efficient, distributed, out-of-memory implementation of the truncated singular value decomposition (t-SVD) for heterogeneous (CPU+GPU) high performance computing (HPC) systems. Various implementations of SVD have been…
In 2011, Kilmer and Martin proposed tensor singular value decomposition (T-SVD) for third order tensors. Since then, T-SVD has applications in low rank tensor approximation, tensor recovery, multi-view clustering, multi-view feature…
The paper introduces a hybrid approach to the CUR-type decomposition of tensors in the Tucker format. The idea of the hybrid algorithm is to write a tensor $\mathcal{X}$ as a product of a core tensor $\mathcal{S}$, a matrix $C$ obtained by…
Tensor decomposition has become an essential tool in many applications in various domains, including machine learning. Sparse Matricized Tensor Times Khatri-Rao Product (MTTKRP) is one of the most computationally expensive kernels in tensor…
Specialized accelerators for tensor-operations, such as blocked-matrix operations and multi-dimensional convolutions, have been emerged as powerful architecture choices for high-performance Deep-Learning computing. The rapid development of…