🤖 AI Summary
This study addresses the absence of predictive theory and the failure of validation mechanisms in the self-evolution of LLM agents. Building upon a DSH plugin architecture, we model agent instances as hard spheres to establish a kinetic theory framework for gated self-evolution. Methodologically, we propose a separation theorem ensuring evaluator independence and construct a master equation with a moment hierarchy, achieving a rigorous mapping from discrete collisions to fluid statistics. By deriving an improved time certificate and resolution law, validated through minimal faithful instances in the WebShop environment, our experiments confirm that population fluctuation scaling adheres to density-gated laws. Ultimately, this work provides a predictable theoretical framework for understanding and guiding agent evolution.
📝 Abstract
We find traces of fluid dynamics in the self-evolution of an LLM agent, and give the kinetic theory that predicts them. Gated self-evolution is the loop in which an agent rewrites its own skills under a validation gate. Self-evolution research has treated the agent as the unit; we study instead the individual instances inside it. Here the agent is DSH-plugin-based: it runs in production on DeepSeek Harness (DSH), and its plugins satisfy four architectural properties (permutation symmetry, reversibility, acyclicity, typed contracts), which license treating these instances as identical hard spheres; the theory is accordingly scoped to DSH-class plugin populations. On this scope the paper builds three theory layers. The rigorous layer, independent of any analogy, comprises an any-time hitting-time certificate bounding the expected rounds to any prescribed improvement, a resolution law that prices held-out validation budgets, and a separation theorem: the daemon must stay outside the population, because merging evaluator with evaluated voids the certificate. The kinetic layer is a master equation over the plugin x version x task grid with four operators (collision, reaction, external field, gate), where collision is co-activation. Its moment hierarchy, the step that turns a gas into fluid equations, generates the falsifiable statistical signatures. Throughout, the fluid reading is a bounded analogy: momentum is not conserved, so no Navier-Stokes limit exists. The measured layer runs on a faithful minimal instance, a large library of four-parameter skill plugins retrieved one per episode with a co-activation probe, in a one-model, one-task-family WebShop environment; every element maps to the DSH loop by architectural role. Population fluctuation scaling is density-gated: invisible at sparse edit density, it emerges at the predicted rate under tripled density, as directional evidence.