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math.AP2026
A Mean-Field Theory of Transformers: Well-Posedness of the Coupled Data--Parameter Dynamics and Global Convergence of Training
Michael Herty, Hailiang Liu
We develop a rigorous mean-field theory for transformer networks that captures two large-scale limits inherent in the architecture: the number of tokens in the input s…
math.NA2026
Inf-Sup Neural Networks for High Dimensional PDEs
Ziren Chen, Hailiang Liu
Solving partial differential equations (PDEs) in high dimensions remains challenging due to the curse of dimensionality. We propose a neural-network-based framework that reformulat…
cs.LG2026
Neural solver for Wasserstein Geodesics and optimal transport dynamics
Hailiang Liu, Yan-Han Chen
In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce…