Related papers: An OpenMath Content Dictionary for Tensor Concepts
Tensor hierarchy algebras constitute a class of non-contragredient Lie superalgebras, whose finite-dimensional members are the "Cartan-type" Lie superalgebras in Kac's classification. They have applications in mathematical physics,…
This is an expository paper on tensor products where the standard approaches for constructing concrete instances of algebraic tensor products of linear spaces, via quotient spaces or via linear maps of bilinear maps, are reviewed by…
The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…
Learning vector calculus techniques is one of the major missions to be accomplished by physics undergraduates. However, beginners report various difficulties dealing with the index notation due to its bulkiness. Meanwhile, there have been…
We present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor…
Current open-domain neural semantics parsers show impressive performance. However, closer inspection of the symbolic meaning representations they produce reveals significant weaknesses: sometimes they tend to merely copy character sequences…
Many problems in high-dimensional statistics appear to have a statistical-computational gap: a range of values of the signal-to-noise ratio where inference is information-theoretically possible, but (conjecturally) computationally…
Progress in AI is hindered by the lack of a programming language with all the requisite features. Libraries like PyTorch and TensorFlow provide automatic differentiation and efficient GPU implementation, but are additions to Python, which…
A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…
Within the field of numerical multilinear algebra, block tensors are increasingly important. Accordingly, it is appropriate to develop an infrastructure that supports reasoning about block tensor computation. In this paper we establish…
Equivariant atomistic machine learning models have brought substantial gains in both extrapolation capability and predictive accuracy. Depending on the basis of the space, two distinct types of irreducible representations are utilized. From…
This paper presents a novel framework for tensor eigenvalue analysis in the context of multi-modal data fusion, leveraging topological invariants such as Betti numbers. Traditional approaches to tensor eigenvalue analysis often extend…
The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and…
Tensor programs often need to process large tensors (vectors, matrices, or higher order tensors) that require a specialized storage format for their memory layout. Several such layouts have been proposed in the literature, such as the…
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…
Tensors or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Tensors have a rich history, stretching over…
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…
We describe a new construction of an incoherent dictionary, referred to as the oscillator dictionary, which is based on considerations in the representation theory of finite groups. The oscillator dictionary consists of order of p^5 unit…
Simplification of expressions in computer algebra systems often involves a step known as "canonicalisation", which reduces equivalent expressions to the same form. However, such forms may not be natural from the perspective of a…
We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…