Related papers: Correct Compilation of Semiring Contractions
We provide a comparative study between neural word representations and traditional vector spaces based on co-occurrence counts, in a number of compositional tasks. We use three different semantic spaces and implement seven tensor-based…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
We prove that the category of algebras over a cofibrant operad admits a closed model category structure. This leads to the notion of "virtual operad algebra" - the algebra over a cofibrant resolution of the given operad. In particular,…
In many instances one has to deal with parametric models. Such models in vector spaces are connected to a linear map. The reproducing kernel Hilbert space and affine- / linear- representations in terms of tensor products are directly…
A notion of meromorphic open-string vertex algebra is introduced. A meromorphic open-string vertex algebra is an open-string vertex algebra in the sense of Kong and the author satisfying additional rationality (or meromorphicity) conditions…
The minimum k-partition problem is a challenging combinatorial problem with a diverse set of applications ranging from telecommunications to sports scheduling. It generalizes the max-cut problem and has been extensively studied since the…
Given a semidirect product $\frak{g}=\frak{s}\uplus\frak{r}$ of semisimple Lie algebras $\frak{s}$ and solvable algebras $\frak{r}$, we construct polynomial operators in the enveloping algebra $\mathcal{U}(\frak{g})$ of $\frak{g}$ that…
The tensor train decomposition decomposes a tensor into a "train" of 3-way tensors that are interconnected through the summation of auxiliary indices. The decomposition is stable, has a well-defined notion of rank and enables the user to…
Tensor algebra is a crucial component for data-intensive workloads such as machine learning and scientific computing. As the complexity of data grows, scientists often encounter a dilemma between the highly specialized dense tensor algebra…
The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…
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…
We develop and implement in this paper a fast sparse assembly algorithm, the fundamental operation which creates a compressed matrix from raw index data. Since it is often a quite demanding and sometimes critical operation, it is of…
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
Abstract Meaning Representations (AMR) are a broad-coverage semantic formalism which represents sentence meaning as a directed acyclic graph. To train most AMR parsers, one needs to segment the graph into subgraphs and align each such…
In our paper Semi-symmetric Algebras: General Constructions, J. Algebra, 148 (1992), pp. 479-496, we present the construction of the semi-symmetric algebra of a module over a commutative ring with unit, which generalizes the tensor algebra,…
The Computation of discrete Contractive semigroups becomes necessary when we deal with several types of evolution equations in Discretizable Hilbert spaces, in this work we study some properties of the discrete forms of the contractive…
We exhibit a singly generated, semisimple commutative operator algebra with a contractive approximate identity, such that the spectrum of the generator is a null sequence and zero, but the algebra is not the closed linear span of the…
Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In…
We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means…