Related papers: Optimizing Tensor Programs on Flexible Storage
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…
Several Krylov-type procedures are introduced that generalize matrix Krylov methods for tensor computations. They are denoted minimal Krylov recursion, maximal Krylov recursion, contracted tensor product Krylov recursion. It is proved that…
Auto-scheduling for tensor programs is a process where a search algorithm automatically explores candidate schedules (program transformations) for a given program on a target hardware platform to improve its performance. However this can be…
Neural networks have proven to be extremely powerful tools for modern artificial intelligence applications, but computational and storage complexity remain limiting factors. This paper presents two compatible contributions towards reducing…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…
High-performance deep learning depends on efficient tensor programs. In recent years, automatic tensor program optimization, also known as tensor compilation, has emerged as the primary approach to generating efficient tensor programs.…
Tensor decomposition has become an essential tool in many data science applications. Sparse Matricized Tensor Times Khatri-Rao Product (MTTKRP) is the pivotal kernel in tensor decomposition algorithms that decompose higher-order real-world…
We provide a new hierarchy of semidefinite programming relaxations, called NCTSSOS, to solve large-scale sparse noncommutative polynomial optimization problems. This hierarchy features the exploitation of term sparsity hidden in the input…
Reservoir computing is a machine learning paradigm that uses a high-dimensional dynamical system, or \emph{reservoir}, to approximate and predict time series data. The scale, speed and power usage of reservoir computers could be enhanced by…
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…
Tensor processing infrastructures such as deep learning frameworks and specialized hardware accelerators have revolutionized how computationally intensive code from domains such as deep learning and image processing is executed and…
Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and…
Many problems in operations research require that constraints be specified in the model. Determining the right constraints is a hard and laborsome task. We propose an approach to automate this process using artificial intelligence and…
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…
This paper presents a code generator for sparse tensor contraction computations. It leverages a mathematical representation of loop nest computations in the sparse polyhedral framework (SPF), which extends the polyhedral model to support…
The conventional definition of a depth function is vector-based. In this paper, a novel projection depth (PD) technique directly based on tensors, such as matrices, is instead proposed. Tensor projection depth (TPD) is still an ideal depth…
With the prevalence of in-database AI-powered analytics, there is an increasing demand for database systems to efficiently manage the ever-expanding number and size of deep learning models. However, existing database systems typically store…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…
Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by…