1 citations · 1 across the 6 of their papers we have counts for
7 papers
Optimal Monte Carlo integration on matrix manifolds
Aleksei G. Sorokin, Yihan Guo, Lek-Heng Lim
This article develops optimal order (up to logarithmic factors) weighted cubature rules for Monte Carlo numerical integration in Sobolev reproducing kernel Hilbert spaces over comm…
Low-dimensional topology of deep neural networks
Junyu Ren, Lek-Heng Lim
We study layered models, including feedforward networks, ResNets, and transformers, by limiting each layer to a width of , i.e., as representation space. This…
Eigen, singular, cosine-sine, and Autonne--Takagi vectors distributions of random matrix ensembles
Yihan Guo, Lek-Heng Lim
We show that some of the best-known matrix decompositions of some of the best-known random matrix ensembles give us the unique -invariant uniform distributions on some of the be…
Pierce-Birkhoff conjecture is true for splines
Zehua Lai, Lek-Heng Lim
We prove the Pierce--Birkhoff conjecture for splines, i.e., continuous piecewise polynomials of degree in variables on a hyperplane partition of , can be writ…
Stiefel optimization is NP-hard
Zehua Lai, Lek-Heng Lim, Tianyun Tang
We show that linearly constrained linear optimization over a Stiefel or Grassmann manifold is NP-hard in general. We show that the same is true for unconstrained quadratic optimiza…
Euclidean distance degree in manifold optimization
Zehua Lai, Lek-Heng Lim, Ke Ye
We determine the Euclidean distance degrees of the three most common manifolds arising in manifold optimization: flag, Grassmann, and Stiefel manifolds. For the Grassmannian, we wi…
Attention is a smoothed cubic spline
Zehua Lai, Lek-Heng Lim, Yucong Liu
We highlight a perhaps important but hitherto unobserved insight: The attention module in a transformer is a smoothed cubic spline. Viewed in this manner, this mysterious but criti…