34 citations · 65 across the 16 of their papers we have counts for
4 papers · 1 filter
Efficient Tensor Decomposition via Moment Matrix Extension
Bobby Shi, Julia Lindberg, Joe Kileel
Motivated by a flurry of recent work on efficient tensor decomposition algorithms, we show that the celebrated moment matrix extension algorithm of Brachat, Comon, Mourrain, and Ts…
Norming Sets for Tensor and Polynomial Sketching
Yifan Zhang, Joe Kileel
This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank ten…
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…
Geometry and Optimization of Shallow Polynomial Networks
Yossi Arjevani, Joan Bruna, Joe Kileel +2
We study shallow neural networks with monomial activations and output dimension one. The function space for these models can be identified with a set of symmetric tensors with boun…