640 citations · 3.8k across the 44 of their papers we have counts for
45 papers
First Proof
Mohammed Abouzaid, Andrew J. Blumberg, Martin Hairer +8
To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the resear…
The Fascinating World of 2 2 2 Tensors: Its Geometry and Optimization Challenges
Gabriel H. Brown, Joe Kileel, Tamara G. Kolda
This educational article highlights the geometric and algebraic complexities that distinguish tensors from matrices, to supplement coverage in advanced courses on linear algebra, m…
Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data
Brett W. Larsen, Tamara G. Kolda, Anru R. Zhang +1
The canonical polyadic (CP) tensor decomposition decomposes a multidimensional data array into a sum of outer products of finite-dimensional vectors. Instead, we can replace some o…
Convergence of Alternating Gradient Descent for Matrix Factorization
Rachel Ward, Tamara G. Kolda
We consider alternating gradient descent (AGD) with fixed step size applied to the asymmetric matrix factorization objective. We show that, for a rank- matrix $\mathbf{A} \in \m…
Scalable symmetric Tucker tensor decomposition
Ruhui Jin, Joe Kileel, Tamara G. Kolda +1
We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special struc…
Tensor Moments of Gaussian Mixture Models: Theory and Applications
João M. Pereira, Joe Kileel, Tamara G. Kolda
Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The -th moment of an -dimensio…