The Kronecker product of two Schur functions s λ and s µ , denoted s λ * s µ , is defined as the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group indexed by partitions of n, λ and µ, respectively. The coefficient, g λ,µ,ν , of s ν in s λ * s µ is equal to the multiplicity of the irreducible representation indexed by ν in the tensor product...

We develop efficient data-sparse representations to a class of high order tensors via a block many-fold Kronecker product decomposition. Such a decomposition is based on low separation-rank approximations of the corresponding multivariate generating function. We combine the Sinc interpolation and a quadrature-based approximation with hierarchically organised block tensor-product formats. Differ...

We consider semidefinite optimization problems that include constraints of the form G(x) 0 and H(x) 0, where the components of the symmetric matrices G(·) and H(·) are affine functions of x ∈ Rn. In such a case we obtain a new constraint K(x,X) 0, where the components of K(·, ·) are affine functions of x and X, and X is an n×n matrix that is a relaxation of xxT . The constraint K(x,X) 0 is base...

A Kronecker product model is the set of visible marginal probability distributions of an exponential family whose sufficient statistics matrix factorizes as a Kronecker product of two matrices, one for the visible variables and one for the hidden variables. We estimate the dimension of these models by the maximum rank of the Jacobian in the limit of large parameters. The limit is described by t...

Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. For the mutual incoherence we also discuss results for sums of Kronecker products.

Modern Convolutional Neural Network (CNN) architectures, despite their superiority in solving various problems, are generally too large to be deployed on resource constrained edge devices. In this paper, we reduce memory usage and floating-point operations required by convolutional layers CNNs. We compress these generalizing the Kronecker Product Decomposition apply multidimensional tensors, le...

Researchers developing implementations of distributed graph analytic algorithms require graph generators that yield graphs sharing the challenging characteristics of real-world graphs (small-world, scale-free, heavy-tailed degree distribution) with efficiently calculable ground-truth solutions to the desired output. Reproducibility for current generators [1] used in benchmarking are somewhat la...