Fleming-Viot Selection of the Yaglom Limit for Age-Structured Bellman-Harris Processes, with Application to Livestock Epidemic Surveillance

arXiv:2607.29251 2026 Dynamics 1 ideas extracted · analyzed Aug 31, 2026

What the math gives to ML

The paper develops a Fleming–Viot particle system that approximates the Yaglom or quasi-stationary distribution of an absorbing, age-structured branching process. Its transferable mechanism is to maintain an ensemble of stochastic trajectories, kill members that enter an absorbing failure state, and replace each killed member by a copy of a surviving member. A neural implementation can use this mechanism to maintain robust optimizer or inference trajectories conditioned on avoiding divergence, NaNs, excessive loss, or constraint violations. The quantitative signatures are exponential convergence of the conditional survivor law and polynomial reduction of finite-ensemble error with particle count.

Ideas from this paper

Unverified 2026

Fleming-Viot Stable-Trajectory Optimizer

Run multiple neural-network parameter trajectories in parallel and define divergence, NaNs, loss explosions, or trust-region violations as absorbing failure events. Whenever one replica fails, replace it with a copy of a uniformly selected survivor while tracking the time since its last replacement. This creates an empirical quasi-stationary distribution of robust training states instead of relying on one potentially unstable trajectory.

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Paper: Fleming-Viot Selection of the Yaglom Limit for Age-Structured Bellman-Harris Processes, with Application to Livestock Epidemic Surveillance arXiv:2607.29251