Related papers: Riemann Tensor Polynomial Canonicalization by Grap…

We use computational algorithms recently developed by us to study completely four index divergence free quadratic in Riemann tensor polynomials in GR. Some results are new and some other reproduce and/or correct known ones. The algorithms…

The arithmetic of N, Z, Q, R can be extended to a graph arithmetic where N is the semiring of finite simple graphs and where Z and Q are integral domains, culminating in a Banach algebra R. A single network completes to the Wiener algebra.…

We prove that the combinatorial Weisfeiler-Leman algorithm of dimension $(3k+4)$ is a complete isomorphism test for the class of all graphs of rank width at most $k$. Rank width is a graph invariant that, similarly to tree width, measures…

Complicated mathematical equations involving products of tensors with permutation symmetries, frequently encountered in fields such as general relativity and quantum chemistry (e.g., equations in high-order coupled cluster theories),…

Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…

We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the existing optimization-based approach, we work from a purely matrix-algebraic…

Ryser's max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with matching number at least $\ell$. In a previous paper by the authors, a generalization was…

Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to…

We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to…

The purpose of this article is to investigate triangularization and simultaneous triangularization of matrices over max algebras using graph theoretic methods. We establish a connection between commutators and commutants with simultaneous…

Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…

Tensor factorizations have become increasingly popular approaches for various learning tasks on structured data. In this work, we extend the RESCAL tensor factorization, which has shown state-of-the-art results for multi-relational…

Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within…

We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.

A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all…

Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…

The state-of-the-art tools for practical graph canonization are all based on the individualization-refinement paradigm, and their difference is primarily in the choice of heuristics they include and in the actual tool implementation. It is…

In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small…

Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…

We propose a universal approach to a range of enumeration problems in graphs. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. In particular, this leads to an algorithm…