Related papers: Compiling Structured Tensor Algebra
Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…
Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…
The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This…
While loop reordering and fusion can make big impacts on the constant-factor performance of dense tensor programs, the effects on sparse tensor programs are asymptotic, often leading to orders of magnitude performance differences in…
Abstractive summarization, the task of generating a concise summary of input documents, requires: (1) reasoning over the source document to determine the salient pieces of information scattered across the long document, and (2) composing a…
Automatic optimization for tensor programs becomes increasingly important as we deploy deep learning in various environments, and efficient optimization relies on a rich search space and effective search. Most existing efforts adopt a…
In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…
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…
Representing meaning in the form of high dimensional vectors is a common and powerful tool in biologically inspired architectures. While the meaning of a set of concepts can be summarized by taking a (possibly weighted) sum of their…
Efficient execution of deep learning workloads on dataflow architectures is crucial for overcoming memory bottlenecks and maximizing performance. While streaming intermediate results between computation kernels can significantly improve…
Structured prediction problems are one of the fundamental tools in machine learning. In order to facilitate algorithm development for their numerical solution, we collect in one place a large number of datasets in easy to read formats for a…
Structured sparse coding and the related structured dictionary learning problems are novel research areas in machine learning. In this paper we present a new application of structured dictionary learning for collaborative filtering based…
High-dimensional sparse data emerge in many critical application domains such as healthcare and cybersecurity. To extract meaningful insights from massive volumes of these multi-dimensional data, scientists employ unsupervised analysis…
In CS literature, the efforts can be divided into two groups: finding a measurement matrix that preserves the compressed information at the maximum level, and finding a reconstruction algorithm for the compressed information. In the…
The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network…
Abstractive text summarization aims at compressing the information of a long source document into a rephrased, condensed summary. Despite advances in modeling techniques, abstractive summarization models still suffer from several key…
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.
We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model…
A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…