# Semantic Early-Stopping for Iterative LLM Agent Loops Source: [Semantic Early-Stopping for Iterative LLM Agent Loops]() Collection index: [llms.txt]() Data updated: 2026-06-27T05:00:11.922Z Authors: Sahil Shrivastava Published: 2026-06-25T13:24:21.000Z ## Abstract Multi-agent large language model (LLM) loops, for example a Writer that drafts and a Critic that revises, are almost always terminated by a fixed iteration cap (max\_iterations). This is a syntactic kill-switch: it is blind to whether the answer is still improving, so it over-spends tokens on easy inputs and truncates hard ones. We study semantic early-stopping: the loop halts when consecutive draft embeddings stop changing in meaning (cosine distance with a patience window) and the answer's measured quality stops improving. Our work makes three contributions. First, an honest theoretical footing: we prove deterministic termination and well-definedness and machine-check these claims, while treating the convergence of the distance sequence as an empirically tested conjecture rather than a (previously over-claimed) Banach contraction. Second, a judge-efficient evaluation protocol: we generate each question's full trajectory once, replay every stopping policy over the identical drafts, and cache every LLM-judge call, yielding a strictly paired efficiency-versus-quality comparison at low cost; we further separate operational tokens (charged to a policy) from evaluation tokens (a measurement instrument). Third, an empirical study on multi-hop retrieval-augmented question answering (HotpotQA). On the 60-question test split, a judge-free semantic stopper reduces operational tokens by 38% relative to max\_iterations at parity quality (Delta-IS = -0.004, p = 0.81), whereas the full quality-gated variant is counter-productive because its per-round judging dominates cost. An oracle that selects the best round attains +0.115 Information Score over every practical policy (p ~ 4e-11), reframing the problem from "when to stop" (easy) to "which round is best" (open). ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Multi-hop Question Answering on HotpotQA N=60 (test)](): Multi-hop Question Answering; HotpotQA N=60 (test); Average Rounds: 2.4. ## Original sources and implementation [Original paper]() [PDF]()