This paper explores the properties of the Kronecker product of tensors and its applications to polynomial complexity theory.

This paper develops scalable methods for time-series analysis using tensor algebra in factorial hidden Markov models, improving computational performance and enabling analysis of large systems.

This paper studies the error degree and degeneration order of tensors, improving upon results from Lehmkuhl Lickteig (1989).

This paper connects a generalized notion of tensor rank with multiplicative complexity, enabling control of arithmetic complexity in any constant degree of multilinearity and applications to fine-grai…

This paper presents a deterministic algorithm for computing nonnegative tensor decompositions and determining their minimality and uniqueness.

This paper proposes an algorithm called Tensor-based Second-order Causal Discovery (TSCD) to uncover causal dependencies among variables.

The paper studies the asymptotic rank of the tensor associated with the complete graph and provides upper and lower bounds.

This paper presents a method for identifying probabilistic structures from empirical probability tensors using algebraic statistics and Kronecker-stack class of configuration matrices.

The paper introduces Automatically Differentiable Nonlinear Tensor Networks (ADNTNs) to achieve massive, structured compression of deep neural networks, demonstrating compression ratios up to 77,000x…

This paper generalizes the connection between graph theory, association schemes, and coding theory to the space of tensors over a finite field, and derives the spectrum of the corresponding graph.

The paper presents a solution to enable multiple double arithmetic on NVIDIA A100 tensor cores, which are unsuited for branching operations caused by renormalization.

The paper studies sampling and recovery for tensor-valued dynamical systems using partial spatial observations over time.

The paper proposes a language called Grassmann that bridges coordinate-independent linear algebra and coordinate-dependent implementations.

The paper proves a lower bound on the bilinear complexity of matrix multiplication and formally verifies the result in Lean 4.

This paper presents a polynomial-time Monte Carlo algorithm to determine the symmetry Lie algebra of a parametrized variety directly from the parametrization.

This paper introduces and studies the block tensor rank of sum-rank metric codes, showing its additive decomposition and deriving lower bounds.