Related papers: Tensor-based algorithms for image classification

The use of recurrent neural networks to represent the dynamics of unstable systems is difficult due to the need to properly initialize their internal states, which in most of the cases do not have any physical meaning, consequent to the…

We propose a novel technique for faster deep neural network training which systematically applies sample-based approximation to the constituent tensor operations, i.e., matrix multiplications and convolutions. We introduce new sampling…

Over the long history of machine learning, which dates back several decades, recurrent neural networks (RNNs) have been used mainly for sequential data and time series and generally with 1D information. Even in some rare studies on 2D…

Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has…

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For…

In Cultural Heritage, hyperspectral images are commonly used since they provide extended information regarding the optical properties of materials. Thus, the processing of such high-dimensional data becomes challenging from the perspective…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Tensor networks, which have been traditionally used to simulate many-body physics, have recently gained significant attention in the field of machine learning due to their powerful representation capabilities. In this work, we propose a…

High-dimensional tensor models are notoriously computationally expensive to train. We present a meta-learning algorithm, MMT, that can significantly speed up the process for spatial tensor models. MMT leverages the property that spatial…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Recently, machine learning has been introduced in the inverse design of physical devices, i.e., the automatic generation of device geometries for a desired physical response. In particular, generative adversarial networks have been proposed…

Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…

We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated…

Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic…

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…

Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…

Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…

In the evolving domains of Machine Learning and Data Analytics, existing dataset characterization methods such as statistical, structural, and model-based analyses often fail to deliver the deep understanding and insights essential for…

Machine learning (ML) and tensor-based methods have been of significant interest for the scientific community for the last few decades. In a previous work we presented a novel tensor-based system identification framework to ease the…