Organizations: School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel · The Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel · School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel · The Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
The performance of large language models (LLMs) on verifiable tasks is usually measured by pass@k, the probability of answering a question correctly at least once in k trials. At a fixed budget, a more suitable metric is coverage@cost, the average number of unique questions answered as a function of the total number of attempts. We connect the two metrics and show that the empirically-observed power-law behavior in pass@k leads to a sublinear growth of the coverage@cost (diminishing returns). To solve this problem, we propose Reset-and-Discard (ReD), a query method of LLMs that increases coverage@cost for a given budget, regardless of the pass@k form. Moreover, given a pass@k, we can quantitatively predict the savings in the total number of attempts using ReD. If pass@k is not available for the model, ReD can infer its power-law exponent. Experiments on three LLMs across coding (HumanEval), math (GSM8K), and reasoning (MMLU-Pro) benchmarks demonstrate that ReD substantially reduces the required attempts, tokens, and USD cost to reach a desired coverage, while also offering an efficient way to measure inference power-laws. ReD's advantage is maintained for imperfect verifiers and outperforms the tested allocation baselines.
Businesses increasingly rely on large language models (LLMs) to automate simple repetitive tasks instead of developing custom machine learning models. LLMs require few, if any, training examples and can be utilized by users without expertise in model development. However, this comes at the cost of substantially higher resource and energy consumption compared to smaller models, which often achieve similar predictive performance for simple tasks. In this paper, we present our vision for just-in-time model replacement (JITR), where, upon identifying a recurring task in calls to an LLM, the model is replaced transparently with a cheaper alternative that performs well for this specific task. JITR retains the ease of use and low development effort of LLMs, while saving significant cost and energy. We discuss the main challenges in realizing our vision regarding the identification of recurring tasks and the creation of a custom model. Specifically, we argue that model search and transfer learning will play a crucial role in JITR to efficiently identify and fine-tune models for a recurring task. Using our JITR prototype Poodle, we reduce inference time by up to 7.5x compared to a self- hosted LLM and save more than $2,200 per 1M requests compared to a flagship hosted LLM, while achieving accuracy competitive with the LLM baseline.
After a weak verifier accepts a large-language-model response, a second call may resample or reroute. Because correctness is hidden, action selection is an identification problem. We order three gates: recoverable stopping debt, two-sided FIT action support, and held-out value from an outcome-blind selector. In a pinned 152-query MBPP+ experiment, a Qwen2.5-14B Base-only false-positive stop leaves +2.592 percentage points of Qwen2.5-7B recovery (query-cluster 95% interval [+1.618, +3.664]). Separately, after 7B Base-test rejection, fixed escalation to 14B exceeds leave-one-out 7B resampling by +2.882 points [+0.931, +5.201]; this is fixed-action ranking, not conditional selection. An all-episode audit produces a +2.697-point realized-maximum gap, but for two actions this statistic equals (1/2)E|Delta| - (1/2)|E Delta| and contains no observable-history term. It lies inside an exact-fold exchangeable reference (mean +3.158; 95% interval [+2.434, +3.947]). The audit unconditionally acts on 1,520 episodes: 1,240 observable stops and 280 verifier rejections; 198 stops are evaluator-only false positives. Neither tested outcome-blind controller improves on fixed rerouting. A separate LiveCodeBench ladder has all-zero FIT action advantages despite exclusive TEST rescues. A preregistered BigCodeBench support gate then finds only 23/19 and 22/19 signed episodes/queries against minima of 25/20, so L1-L4, DEV, and TEST stay unopened. Stopping debt exists, but current evidence does not identify when to resample rather than reroute.
Standard evaluation of large language models assumes stable model rankings across inference conditions. We challenge this assumption by varying the token generation budget, i.e., the maximum tokens a model may produce, across seven levels (64--4,096), evaluating four models on three reasoning benchmarks (56,476 inferences). We report four findings: (i) 3--19% of items exhibit non-monotone behavior (accuracy decreasing with more budget), even after controlling for truncation, and this phenomenon is model-specific (cross-model overlap: 6--14%). (ii) Model rankings reverse across budgets on all benchmarks (p<0.01, McNemar). (iii) Oracle analysis reveals model complementarity up to +27.8pp, most pronounced at constrained budgets. (iv) A budget-aware router captures 14.1% of the oracle gap cross-domain; budget features help within-domain (+1.6 to +5.7pp) but are domain-specific and hurt transfer (−1.2pp). These results argue for budget-conditioned evaluation protocols.