Related papers: Supervised Learning for Non-Sequential Data: A Can…

The canonical polyadic decomposition (CPD) is a compact decomposition which expresses a tensor as a sum of its rank-1 components. A common step in the computation of a CPD is computing a generalized eigenvalue decomposition (GEVD) of the…

Recent findings indicate that over-parametrization, while crucial for successfully training deep neural networks, also introduces large amounts of redundancy. Tensor methods have the potential to efficiently parametrize over-complete…

The CANDECOMP/PARAFAC (CP) decomposition is a leading method for the analysis of multiway data. The standard alternating least squares algorithm for the CP decomposition (CP-ALS) involves a series of highly overdetermined linear least…

As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit…

Black-box model structures are dominated by large multivariate functions. Usually a generic basis function expansion is used, e.g. a polynomial basis, and the parameters of the function are tuned given the data. This is a pragmatic and…

In this work we present recent results on application of low-rank tensor decompositions to modelling of aggregation kinetics taking into account multi-particle collisions (for three and more particles). Such kinetics can be described by…

We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking at a fraction of their entries only. Our method combines a neural network encoder with a tensor train decomposition to learn a low-rank…

Deep convolutional networks have proven to be very successful in learning task specific features that allow for unprecedented performance on various computer vision tasks. Training of such networks follows mostly the supervised learning…

Texture classification is a pivotal task in computer vision, presenting unique challenges due to high inter-class similarity and the sensitivity of structural patterns to scale and illumination changes. While Convolutional Neural Networks…

In this paper, we proposed Bayesian Tucker decomposition (BTuD) in which residual is supposed to obey Gaussian distribution analogous to linear regression. Although we have proposed an algorithm to perform the proposed BTuD, the…

The decomposition of tensors into simple rank-1 terms is key in a variety of applications in signal processing, data analysis and machine learning. While this canonical polyadic decomposition (CPD) is unique under mild conditions, including…

We present a novel technique for self-supervised video representation learning by: (a) decoupling the learning objective into two contrastive subtasks respectively emphasizing spatial and temporal features, and (b) performing it…

In the present work, a method is proposed in order to compute a Canonical Polyadic (CP) approximation of a given tensor. It is based on a greedy method and an adaptation of the TT-SVD method. The proposed approach can be straightforwardly…

This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models…

In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…

Supervised learning has been widely used for attack categorization, requiring high-quality data and labels. However, the data is often imbalanced and it is difficult to obtain sufficient annotations. Moreover, supervised models are subject…

Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a geometrically consistent way of treating complex domains,…

Tensor network (TN) representation is a powerful technique for computer vision and machine learning. TN structure search (TN-SS) aims to search for a customized structure to achieve a compact representation, which is a challenging NP-hard…

Self-supervised feature learning enables perception systems to benefit from the vast raw data recorded by vehicle fleets worldwide. While video-level self-supervised learning approaches have shown strong generalizability on classification…

Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parameter decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful…