TASR: Training-Free Adaptive Stopping for Iterative Retrieval
Iterative retrieval-augmented generation agents commonly overspend by continuing to retrieve after the model has converged on an answer, incurring calls that change neither the prediction nor the supporting evidence. Existing remedies learn a stopping policy from labeled trajectories, tying the decision to a trained component that requires retraining for each new model or task. We propose TASR (Training-Free Adaptive Stopping Rule), a one-line predicate that fires when the model repeats its previous-round normalized answer and the isotonically calibrated logit margin exceeds 0.25. No classifier or value head is learned; the threshold is fixed across all thirty-two (model, retriever, corpus) configurations we evaluate. On a 3-model x 2-dataset distractor grid, TASR retains 94.8% of fixed-k=5's macro F1 at 62.6% of its calls and exceeds fixed-k=3 by +3.42 F1. The pattern holds on nine open-domain BM25 cells (55.01 F1 at 2.98 calls vs. 54.33 at 3.00 for fixed-k=3) and, with calibration locked from the distractor split, on nine dense-retrieval cells across two retriever families, and on eight cells of a Nemotron-3-Ultra-550B production model, with zero significant regressions in any extension. The rule was selected from an exhaustive enumeration of 381 candidate stopping rules on the canonical selection cell, where no alternative Pareto-dominates it. A signal-quality analysis shows that verbalized 1-5 confidence collapses on RLHF-tuned models (96.5% of values equal 5, entropy 0.182 nats), while the logit margin achieves 40x better class-conditional separation, grounding the design in a measurable model pathology. TASR is an auditable, training-free Pareto baseline for adaptive stopping in iterative retrieval. Code is publicly available at https://github.com/JSBAICenter/TASR