Author

Michael Herty

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Preprint Aug 2026

A Mean-Field Theory of Transformers: Well-Posedness of the Coupled Data--Parameter Dynamics and Global Convergence of Training

We develop a rigorous mean-field theory for transformer networks that captures two large-scale limits inherent in the architecture: the number of tokens $N\to\infty$ in the input sequence and the number of attention heads $H\to\infty$ in each layer. It further considers an infinite number of layers leading to a time-co...

Michael Herty, Hailiang Liu · 0 citations

Preprint Aug 2026

Convergence of time-discrete finite particle consensus based optimization in Hilbert spaces

This analysis provides convergence guarantees directly for the computable particle system, complementing recent continuous-time and mean-field results in infinite dimensions and establishing quantitative pairwise contraction, exponential decay of the expected swarm variance, and almost-sure convergence of all particles...

Michael Herty, Hui Huang, Hicham Kouhkouh · 0 citations