Attention in minimal transformers under corruption performs in-context empirical Bayes via a single kernel-weighted posterior mean step followed by depth-driven particle dynamics refinement.
Propagation of Chaos: A Review of Models, Methods and Applications. I. Models and Methods
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Proves uniform-in-time propagation of chaos for second-order CBO at Monte Carlo rate via shifted internal variables, a position-velocity Lyapunov functional, and centered-moment decay.
Two-type interacting particles with non-local order-based switching converge in law to a McKean-Vlasov process whose long-time behavior includes traveling waves identified via phase-plane analysis of a reduced ODE system for exponential jumps.
Characterizes the distributional mean-field limit of co-evolving latent space networks with feedback, including empirical measures and graphon convergence, via a conditional propagation of chaos result.
Presents an optimal transport framework for simulating particle systems with arbitrary cell shapes and volumes that automatically handles exclusion constraints.
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