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Expressive Power of Deep Networks on Manifolds: Simultaneous Approximation

arXiv:2509.09362v3 Announce Type: replace-cross Abstract: A key challenge in scientific machine learning is solving partial differential equations (PDEs) on complex domains, where the curved geometry complicates the approximation of functions and their derivatives required by differential operators. This paper establishes…

Scaling Laws for Optimal Data Mixtures

Large foundation models are typically trained on data from multiple domains, with the data mixture—the proportion of each domain used—playing a critical role in model performance. The standard approach to selecting this mixture relies on trial and error, which becomes…

Hell yeah, I want a Gundam keyboard with topre switches

Japanese keyboard maker Realforce is teaming up with the Mobile Suit Gundam franchise and releasing four limited edition mechanical keyboards inspired by popular Gundam designs. The four keyboards are based on the Z Gundam and Hyaku Shiki from Zeta Gundam…