Auto Researching, not hyperparameter tuning: Convergence Analysis of 10,000 Experiments

When LLM agents autonomously design ML experiments, do they perform genuine architecture search -- or do they default to hyperparameter tuning within a narrow region of the design space? We answer this question by analyzing 10,469 experiments executed by two LLM agents (Claude Opus and Gemini 2.5 Pro) across a combinatorial configuration space of 108,000 discrete cells for dashcam collision detection over 27 days. Through ANOVA decomposition, we find that \textbf{architectural choices explain 94\% of performance variance} ($F = 1324$, $\eta^2 = 0.94$), while hyperparameter variation within a fixed architecture explains only 6\%. Cross-task validation on a second collision dataset confirms this finding (75\% architecture-explained variance) with a \emph{different} winning backbone, confirming genuine architecture discovery. The agents' key contribution is discovering that V-JEPA\,2 video features with Zipformer temporal encoders achieve 0.9245 AP -- a configuration no human proposed -- and concentrating search on productive architectural regions: at $N = 50$, LLM-guided search reaches AP $= 0.985$ versus $0.965$ for from-scratch random search. Post-bugfix convergence follows a power law ($c = 0.11$, $R^2 = 0.93$); the low exponent reflects the cost of broad exploration, not inefficiency, since the LLM discovers qualitatively better regions than random or Bayesian baselines. We characterize multi-agent search dynamics via entropy cycles and Jensen--Shannon specialization, providing the first large-scale empirical framework for LLM-guided combinatorial ML experiment design.