Related papers: TensorLy: Tensor Learning in Python

In this paper, we introduce MCTensor, a library based on PyTorch for providing general-purpose and high-precision arithmetic for DL training. MCTensor is used in the same way as PyTorch Tensor: we implement multiple basic, matrix-level…

With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor…

Tensor networks (TNs) are a central computational tool in quantum science and artificial intelligence. However, the lack of unified software interface across tensor-computing frameworks severely limits the portability of TN applications,…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications…

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…

Advance in deep learning algorithms overshadows their security risk in software implementations. This paper discloses a set of vulnerabilities in popular deep learning frameworks including Caffe, TensorFlow, and Torch. Contrast to the small…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…

Tensor computations are increasingly prevalent numerical techniques in data science, but pose unique challenges for high-performance implementation. We provide novel algorithms and systems infrastructure which enable efficient parallel…

Although Answer Set Programming (ASP) allows constraining neural-symbolic (NeSy) systems, its employment is hindered by the prohibitive costs of computing stable models and the CPU-bound nature of state-of-the-art solvers. To this end, we…

Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…

Deep Learning methods employ multiple processing layers to learn hierarchial representations of data. They have already been deployed in a humongous number of applications and have produced state-of-the-art results. Recently with the growth…

Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…

A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…

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…

Deep learning is finding its way into the embedded world with applications such as autonomous driving, smart sensors and aug- mented reality. However, the computation of deep neural networks is demanding in energy, compute power and memory.…

Although recent scaling up approaches to training deep neural networks have proven to be effective, the computational intensity of large and complex models, as well as the availability of large-scale datasets, require deep learning…

The SageManifolds project aims at extending the mathematics software system Sage towards differential geometry and tensor calculus. Like Sage, SageManifolds is free, open-source and is based on the Python programming language. We discuss…

Modern machine learning frameworks are complex: they are typically organised in multiple layers each of which is written in a different language and they depend on a number of external libraries, but at their core they mainly consist of…

Machine learning has changed the computing paradigm. Products today are built with machine intelligence as a central attribute, and consumers are beginning to expect near-human interaction with the appliances they use. However, much of the…