Related papers: HaTT: Hadamard avoiding TT recompression
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
Solving the Boltzmann-BGK equation with traditional numerical methods suffers from high computational and memory costs due to the curse of dimensionality. In this paper, we propose a novel accuracy-preserved tensor-train (APTT) method to…
A new transform over finite fields, the finite field Hartley transform (FFHT), was recently introduced and a number of promising applications on the design of efficient multiple access systems and multilevel spread spectrum sequences were…
Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…
Despite their successes, what makes kernel methods difficult to use in many large scale problems is the fact that storing and computing the decision function is typically expensive, especially at prediction time. In this paper, we overcome…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
Randomized iterative algorithms, such as the randomized Kaczmarz method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights…
In this paper the approach to obtaining nonrecurrent formulas for some recursively defined sequences is illustrated. The most interesting result in the paper is the formula for the solution of quadratic map-like recurrence. Also, some…
Coupled tensor decomposition (CTD) can extract joint features from multimodal data in various applications. It can be employed for federated learning networks with data confidentiality. Federated CTD achieves data privacy protection by…
Implicit Neural Representations (INRs) encode discrete signals using Multi-Layer Perceptrons (MLPs) with complex activation functions. While INRs achieve superior performance, they depend on full-precision number representation for accurate…
The Hadamard and SJT product of matrices are two types of special matrix product. The latter was first defined by Chen. In this study, they are applied to the differential quadrature (DQ) solution of geometrically nonlinear bending of…
Modern AI models are growing rapidly in size and redundancy, leading to significant storage and distribution challenges in model hubs. We present TStore, a tensor-centric system for reducing storage overhead through fine-grained…
Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…
Despite their popularity in the field of continuous optimisation, second-order quasi-Newton methods are challenging to apply in machine learning, as the Hessian matrix is intractably large. This computational burden is exacerbated by the…
An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality…
Neural tangent kernel (NTK) is a powerful tool to analyze training dynamics of neural networks and their generalization bounds. The study on NTK has been devoted to typical neural network architectures, but it is incomplete for neural…
Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…
In this work, we firstly apply the Train-Tensor (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor…