Related papers: The Continuous Tensor Abstraction: Where Indices a…
[abridged] Context: Multidimensional arrays are used by many different algorithms. As such, indexing and broadcasting complex operations over multidimensional arrays are ubiquitous tasks and can be performance limiting. Inquiry:…
In this paper, we study inexact high-order Tensor Methods for solving convex optimization problems with composite objective. At every step of such methods, we use approximate solution of the auxiliary problem, defined by the bound for the…
Depthwise convolutions are widely used in lightweight convolutional neural networks (CNNs). The performance of depthwise convolutions is mainly bounded by the memory access rather than the arithmetic operations for classic convolutions so…
Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus the utility of such tensors is low, in terms of the amount of interpretable and…
Tensors (also commonly seen as multi-linear operators or as multi-dimensional arrays) are ubiquitous in scientific computing and in data science, and so are the software efforts for tensor operations. Particularly in recent years, we have…
Training semantic parsers from weak supervision (denotations) rather than strong supervision (programs) complicates training in two ways. First, a large search space of potential programs needs to be explored at training time to find a…
Recent work by Hermanns et al. and Kattenbelt et al. has extended counterexample-guided abstraction refinement (CEGAR) to probabilistic programs. These approaches are limited to predicate abstraction. We present a novel technique, based on…
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…
A tensor in applied mathematics is usually defined as a multidimensional array of numbers. This presumes a choice of basis in $\mathbb{R}^n$ or in some other vector space, and tensorial concepts are defined accordingly. In this article we…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
Sparse tensors are rapidly becoming critical components of modern deep learning workloads. However, developing high-performance sparse operators can be difficult and tedious, and existing vendor libraries cannot satisfy the escalating…
Retrieving graphs from a large corpus, that contain a subgraph isomorphic to a given query graph, is a core operation in many real-world applications. While recent multi-vector graph representations and scores based on set alignment and…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
A lossy compression algorithm for binary redundant memoryless sources is presented. The proposed scheme is based on sparse graph codes. By introducing a nonlinear function, redundant memoryless sequences can be compressed. We propose a…
Text indexing is a classical algorithmic problem that has been studied for over four decades: given a text $T$, pre-process it off-line so that, later, we can quickly count and locate the occurrences of any string (the query pattern) in $T$…
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…
We discuss proper outerness for finite index endomorphisms and finite index bimodules of simple C$^*$-algebras, extending recent similar results by Izumi concerning the purely infinite setting. Our main result is that proper outerness holds…
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We…