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cs.LG2026
Muon Under Gradient Noise and the Limits of Orthogonalization Near Optima
Xiaohui Xie
Muon replaces the momentum buffer of each weight matrix by its orthogonal polar factor. We ask what this orthogonalization does near an optimum, where minibatch noise dominates the…
cs.LG2025★ 1 cited
Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptation
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie +1
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while prese…
cs.LG2024★ 4 cited
BiLO: Bilevel Local Operator Learning for PDE Inverse Problems
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie +1
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization…