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math.NA2026
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…
cs.LG2026
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…