Related papers: Seq2Tens: An Efficient Representation of Sequences…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

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…

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…

Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…

In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…

Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…

Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Analyzing sequential data is crucial in many domains, particularly due to the abundance of data collected from the Internet of Things paradigm. Time series classification, the task of categorizing sequential data, has gained prominence,…

We introduce complex-valued tensor network models for sequence processing motivated by correspondence to probabilistic graphical models, interpretability and resource compression. Inductive bias is introduced to our models via network…

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…

Recently, deep architectures, such as recurrent and recursive neural networks have been successfully applied to various natural language processing tasks. Inspired by bidirectional recurrent neural networks which use representations that…

The prevalent approach to sequence to sequence learning maps an input sequence to a variable length output sequence via recurrent neural networks. We introduce an architecture based entirely on convolutional neural networks. Compared to…

This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…

Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring…

Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems…