{"path":"research/proving-pass-reliability/literature-report-2026-09-29.md","content":"<!-- Verbatim final report of the research subagent commissioned 2026-09-29 for\nproving-a-pass-reliable.md. Persisted unchanged from the session record (subagent\nad7e74593ee1cb5c3), per the rule that research findings are kept verbatim. The synthesis that\nuses it is ../proving-a-pass-reliable.md. -->\n\n# Statistical guarantees for narrow LLM/ML microtasks: literature report (2026-09-29)\n\n**Read-depth tags:**\n- **FULL TEXT**: I read the main text.\n- **PARTIAL**: I read the abstract plus the major sections.\n- **SNIPPET**: I saw only the abstract, the metadata or a search excerpt.\n- **[computed]**: my own arithmetic, not taken from any source.\n\n## 1. Trust or Escalate\nJung, Brahman, Choi, \"Trust or Escalate: LLM Judges with Provable Guarantees for Human Agreement,\" ICLR 2025 (oral). https://arxiv.org/abs/2407.18370 [FULL TEXT: arXiv v1 with appendices; one appendix table was truncated]\n\n- **Method (selective evaluation).** The judge outputs a pairwise preference and a confidence score. Below a threshold λ it abstains.\n  - On a human-labelled calibration set, each λ gets an exact binomial upper confidence bound on the disagreement rate among the items the judge answers.\n  - λ is lowered step by step (fixed-sequence testing, Bauer 1991). The procedure keeps the lowest λ at which every larger λ still has a bound ≤ α.\n- **What is guaranteed.** With probability ≥1−δ over the calibration draw, P(judge = majority human label | judge answers) ≥ 1−α.\n  - This is precision on the answered items, conditional on the calibration sample. Coverage is not guaranteed.\n  - It assumes the calibration items are i.i.d. from the test distribution.\n  - **Cascades** (Mistral-7B → GPT-3.5 → GPT-4, escalating on abstention): each judge is calibrated on the items the earlier judges skipped, at level δ/|M|, and the levels are combined by a union bound.\n  - The appendix proof argues pointwise. The fixed-sequence argument (see LTT, §3) is what makes a data-chosen threshold valid.\n- **Confidence measure (\"Simulated Annotators\").** An ensemble of K-shot prompts, each built from one annotator's labels. Agreement across the prompts is the confidence. It roughly halved GPT-4's calibration error compared with the model's own predicted probability.\n- **Setup.** 500 calibration items (392 for Auto-J), δ = 0.1, 1,000 random splits.\n- **Results:**\n\n| Dataset, target agreement | Coverage | Guarantee held | Notes |\n|---|---|---|---|\n| TL;DR, 90% | 55.7% | 90.8% of splits | Thresholds set from point estimates held in only 47.5–79.0% |\n| ChatArena, 85% | 63.2% | 91.0% | GPT-4 used on 17.5% of items; GPT-4 alone averaged 77.8% agreement |\n| ChatArena, 80%, cascade without GPT-4 | 68.3% | — | 12.6% of GPT-4's cost |\n\n- Items the judge abstained on had lower human inter-annotator agreement (0.815 vs 0.902).\n- When calibration and test used disjoint sets of evaluated models, the guarantee held in >90% of splits, with slightly lower coverage.\n\n## 2. Conformal factuality and follow-ups\n- **Mohri & Hashimoto**, \"Language Models with Conformal Factuality Guarantees,\" ICML 2024. https://arxiv.org/abs/2402.10978 [FULL TEXT]\n  - **Method.** GPT-4 prompts split the output into sub-claims, and each sub-claim is scored. The best score was frequency across five resamples. Claims below a conformally calibrated threshold are dropped.\n  - **Guarantee.** The probability that the remaining output is entailed by the reference is ≥1−α. This is marginal over the calibration and test draw and assumes exchangeability. The entailment oracle may be a human.\n  - **Data.** The authors annotated 50 inputs per dataset; each split calibrated on 25.\n  - **Results.** Correctness rose from ~30% to 80% (FActScore biographies), 78% to 93% (NQ) and 75% to 95% (MATH). On biographies at α = 0.2, about half the claims were removed.\n  - **Limits the authors state:** the guarantee is marginal, not per domain; realized factuality varied across calibration draws (sd ≈ 0.09); the guarantee is lost under distribution change.\n- **Cherian, Gibbs, Candès**, \"Large language model validity via enhanced conformal prediction methods,\" NeurIPS 2024. https://arxiv.org/abs/2406.09714 [SNIPPET]\n  - Validity conditional on topic.\n  - Level-adaptive guarantees that weaken to keep outputs useful.\n  - Better scoring, learned by differentiating through the conditional procedure.\n- **Rubin-Toles, Gambhir, Ramji, Roth, Goel**, \"Conformal Language Model Reasoning with Coherent Factuality,\" ICLR 2025. https://arxiv.org/abs/2505.17126 [PARTIAL]\n  - Filtering claims independently fails for reasoning, where a step can only be judged relative to its premises. They calibrate over subgraphs of a deducibility graph instead.\n  - On MATH and FELM: about 90% coherent factuality while keeping ≥80% of claims.\n  - Calibration that ignored the graph structure often missed the guarantee.\n\n## 3. Learn Then Test; conformal risk control\n- **Angelopoulos, Bates, Candès, Jordan, Lei**, \"Learn then Test: Calibrating predictive algorithms to achieve risk control,\" Annals of Applied Statistics 19(2):1641–1662, 2025. https://arxiv.org/abs/2110.01052 [PARTIAL, §1–3.2]\n  - **Recipe:**\n    1. Choose a grid of thresholds.\n    2. For each threshold, set up the null hypothesis \"risk(λ) > α\".\n    3. Compute finite-sample p-values (Hoeffding–Bentkus for bounded losses).\n    4. Apply any procedure that controls family-wise error: Bonferroni, fixed-sequence (with the order fixed before seeing the data), or graph-based.\n  - **Guarantee.** Every returned λ satisfies P(risk ≤ α) ≥ 1−δ over the calibration draw.\n  - **Conditions.** Requires i.i.d. calibration data. Does not require monotone risk. Allows several risks at once. May return no threshold at all.\n  - One worked example is selective classification with error-when-answering ≤ α. That is exactly an automation threshold.\n- **Predecessor:** Bates et al., \"Distribution-free, risk-controlling prediction sets,\" J. ACM 2021 [SNIPPET].\n- **Angelopoulos, Bates, Fisch, Lei, Schuster**, \"Conformal Risk Control,\" ICLR 2024. https://arxiv.org/abs/2208.02814 [PARTIAL, §1]\n  - Bounds the expected value of a bounded loss that is monotone in λ, tight to O(1/n).\n  - The bound holds in expectation, not with high probability.\n  - Losses that are not monotone are not covered.\n  - Extensions include distribution shift.\n\n## 4. Prediction-powered inference\n- **Angelopoulos, Bates, Fannjiang, Jordan, Zrnic**, \"Prediction-powered inference,\" Science 382:669–674, 2023. https://arxiv.org/abs/2301.09633 [PARTIAL]\n  - A few gold labels plus many model predictions give valid confidence intervals for means, quantiles and regression coefficients.\n  - No assumptions about the model are needed. Better predictions give narrower intervals.\n- **Boyeau, Angelopoulos, Li, Yosef, Malik, Jordan**, \"AutoEval Done Right,\" ICML 2025. https://arxiv.org/abs/2403.07008 [PARTIAL, §1–2]\n  - The metric estimate is a synthetic-label estimate on the unlabelled pool plus a bias correction from the human-labelled set, with a tuned weight (PPI++).\n  - The estimate is unbiased, with asymptotic intervals. Both sets are assumed i.i.d.\n  - About 50% gain in effective sample size on ImageNet and on protein fitness. With a useless annotator it falls back to the classical estimate.\n- **Dorner, Nastl, Hardt**, \"Limits to scalable evaluation at the frontier: LLM as Judge won't beat twice the data,\" ICLR 2025. https://arxiv.org/abs/2410.13341 [PARTIAL]\n  - The possible label savings are set by how well the judge's scores correlate with the truth.\n  - If the judge is no more accurate than the model it evaluates, no debiasing method can more than halve the number of ground-truth labels needed.\n  - The savings they observed in practice were smaller than this limit.\n- **Zrnic & Candès**, \"Active Statistical Inference,\" ICML 2024 [SNIPPET]: human labels are sent where the model is uncertain; the paper reports >80% sample savings.\n- **Gligorić, Zrnic, Lee, Candès, Jurafsky**, \"Can Unconfident LLM Annotations Be Used for Confident Conclusions?,\" NAACL 2025. https://arxiv.org/abs/2408.15204 [SNIPPET]: >25% fewer human labels on three annotation tasks.\n- **Candès, Ilyas, Zrnic**, \"Probably Approximately Correct Labels,\" ICML 2026. https://arxiv.org/abs/2506.10908 [PARTIAL]\n  - Experts label every item above an uncertainty cutoff. The cutoff is set from a small expert-labelled sample so that, with probability ≥1−α, the error over the whole dataset is ≤ ε.\n  - The guarantee is non-asymptotic and holds for any uncertainty score.\n  - GPT-4o text labelling at ε = 5%: 14–28% of expert labels saved. Using AI labels alone gave 19–38% error.\n  - ImageNet: about 60% of expert labels saved.\n- **Mozer**, arXiv 2603.19160, 2026 [SNIPPET]: PPI's mean estimator equals the survey-sampling difference estimator (Cassel et al. 1976).\n\n## 5. Zero-failure bounds and sequential monitoring\n- **Hanley & Lippman-Hand**, \"If nothing goes wrong, is everything all right? Interpreting zero numerators,\" JAMA 249(13):1743–1745, 1983. https://jhanley.biostat.mcgill.ca/Reprints/If_Nothing_Goes_1983.pdf [FULL TEXT]\n  - Solving (1−p)^n = 0.05 gives p ≈ 3/n. For n > 30 this matches the exact value to the nearest percentage point.\n  - The corresponding rules are 4.6/n at 99% and 6.9/n at 99.9%.\n  - They stress that \"a zero numerator does not necessarily mean 'no risk'\", and they limit inference to the sampled population.\n  - Because 0.05 is a single tail, 3/n is a one-sided 95% limit, which is a two-sided 90% limit [computed].\n- **Clopper & Pearson**, Biometrika 26(4):404–413, 1934 [SNIPPET]: exact binomial confidence limits.\n- **Sample sizes** [computed: exact binomial; the smallest n with P(errors ≤ k | n, p) ≤ tail]:\n\n| To show error rate below | 95% one-sided, 0 errors | 95% one-sided, 1 error | 95% two-sided, 0 errors | 95% two-sided, 1 error |\n|---|---|---|---|---|\n| 1% | 299 | 473 | 368 | 555 |\n| 2% | 149 | 236 | 183 | 277 |\n| 5% | 59 | 93 | 72 | 110 |\n| 10% | 29 | 46 | 36 | 54 |\n\n  - With two errors (one-sided): 628 / 313 / 124 / 61.\n  - The binomial model assumes randomly drawn, independent items and a reviewer who makes no mistakes.\n- **Wald**, \"Sequential Tests of Statistical Hypotheses,\" Ann. Math. Stat. 16(2):117–186, 1945 [SNIPPET]\n  - The sequential probability ratio test (SPRT) updates the log-likelihood ratio after each audited item, and stops at ln((1−β)/α) or ln(β/(1−α)).\n  - Worked example [computed]: H0 = 1% error vs H1 = 3%, α = β = 5%.\n    - Accept H0 after 145 consecutive correct items.\n    - Each observed error adds about 54 more required correct items.\n    - Expected number of items: about 287 under H0 and about 201 under H1.\n  - The test needs an indifference zone between p0 and p1.\n- **Anytime-valid alternative for an unknown rate:** Howard, Ramdas, McAuliffe, Sekhon, \"Time-uniform, nonparametric, nonasymptotic confidence sequences,\" Ann. Stat. 49(2):1055–1080, 2021 [SNIPPET].\n\n## 6. Model collapse\n- **Shumailov et al.**, \"AI models collapse when trained on recursively generated data,\" Nature 631:755–759, 2024. https://www.nature.com/articles/s41586-024-07566-y [FULL TEXT, main article]\n  - Training indiscriminately on earlier models' outputs loses the tails of the distribution first, then drifts toward low variance.\n  - Three drivers: finite-sample error, limited expressivity and learning bias.\n  - The theory analyzes pure replacement of the data.\n  - OPT-125m fine-tuned over successive generations degraded. Keeping a random 10% of the original data limited this to minor degradation.\n- **Gerstgrasser et al.**, \"Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data,\" arXiv 2404.01413, 2024 [PARTIAL]\n  - Replacing the data each generation raised test loss for small language models on TinyStories, VAEs and diffusion models.\n  - Accumulating each generation's synthetic data alongside the original real data avoided collapse.\n  - A proof on linear models gives an error bound that does not depend on the number of generations. Under replacement, error grows linearly.\n  - A growing set of purely synthetic data still diverges, at O(log n).\n- **Qualifier:** Dohmatob, Feng, Subramonyam, Kempe, \"Strong Model Collapse,\" ICLR 2025 [SNIPPET]: in a scaling-law regression setting, even about 0.1% synthetic data can stop larger datasets from helping.\n\n## 7. Measured LLM accuracy\n\n**(a) Entity matching**\n- **Peeters, Steiner, Bizer**, \"Entity Matching using Large Language Models,\" EDBT 2025. https://arxiv.org/abs/2310.11244 [PARTIAL]\n  - Zero-shot GPT-4 F1 reached 89.6 on WDC Products (80% hard cases), 95.8 on Abt-Buy and 89.7 on Walmart-Amazon.\n  - It beat fine-tuned pre-trained language models on 3 of 4 e-commerce sets.\n  - Results depended heavily on the prompt: GPT-4o-mini on WDC ranged from 16.9 to 81.2 F1 across prompts.\n- **Peeters, Der, Bizer**, \"WDC Products,\" EDBT 2024 [SNIPPET]: two experts re-checked 600 test pairs and estimated label noise at 4.00% and 4.17%; Cohen's κ 0.91.\n- **Steiner & Bizer**, \"Labeling Training Data for Entity Matching Using Large Language Models,\" arXiv 2606.28823, 2026 [PARTIAL]\n  - One author audited 1,028 test pairs blind, reweighted to the full population.\n  - The published gold labels were wrong on 0.53–2.52% of pairs.\n  - GPT-5.2, Qwen 3.6 Plus and Kimi K2.6 were wrong on 0.65–4.49%, on average 0.5 points from the gold labels.\n  - Zero-shot F1 reached 93.8 (Abt-Buy), 90.5 (Walmart-Amazon) and 87.2 (WDC).\n  - The models may have seen these benchmarks in pretraining.\n\n**(b) Paraphrase, semantic equivalence, claim matching**\n- **Nangia & Bowman**, \"Human vs. Muppet,\" ACL 2019. https://arxiv.org/abs/1905.10425 [PARTIAL]\n  - Human baseline: the majority vote of five crowdworkers, each given 20 practice items.\n  - MRPC: 80.8 accuracy / 86.3 F1. QQP: 80.4 / 59.5.\n  - Fine-tuned BERT beat the humans on both. The QQP labels proved hard to capture in written instructions.\n- **Zhong et al.**, \"Can ChatGPT Understand Too?,\" arXiv 2302.10198, 2023 [PARTIAL]: ChatGPT on 50 MRPC items scored 66% accuracy: 44% on non-paraphrases vs 88% on paraphrases.\n- **Pisarevskaya & Zubiaga**, \"Zero-shot and Few-shot Learning with Instruction-following LLMs for Claim Matching in Automated Fact-checking,\" COLING 2025. https://arxiv.org/abs/2501.10860 [PARTIAL]: on a set with constructed negatives, few-shot Gemini reached F1 97.2 and Mistral 95.0, against 96.2 for fine-tuned XLM-R.\n- **Vykopal et al.**, \"Large Language Models for Multilingual Previously Fact-Checked Claim Detection,\" EMNLP 2025 Findings. https://arxiv.org/abs/2503.02737 [PARTIAL]: human agreement Fleiss' κ 0.60–0.62; the LLMs were weaker in low-resource languages.\n\n**(c) Claim decomposition**\n- **Min et al.**, \"FActScore,\" EMNLP 2023. https://arxiv.org/abs/2305.14251 [PARTIAL]\n  - When experts revised InstructGPT's atomic facts, they split 18% of cases and merged 34%.\n  - Agreement between annotators on support labels was 96%, 90% and 88%.\n  - About 70% of disagreements came from facts that are genuinely debatable.\n- **Wanner, Ebner, Jiang, Dredze, Van Durme**, \"A Closer Look at Claim Decomposition,\" *SEM 2024. https://arxiv.org/abs/2403.11903 [PARTIAL]\n  - The FActScore result changes depending on which decomposer is used.\n  - Their DecompScore is an LLM-judged count of supported subclaims, with no reference decompositions. It ranks a Russellian/neo-Davidsonian prompt highest (42.3, against ~32 and 20.0 for others).\n  - I found no human agreement figures.\n- **Wanner, Van Durme, Dredze**, \"DnDScore,\" EMNLP 2025. https://arxiv.org/abs/2412.13175 [SNIPPET]: the choices of decomposition, decontextualization and verification method change the scores.\n- **Wei et al.**, \"Long-form factuality in large language models,\" NeurIPS 2024. https://arxiv.org/abs/2403.18802 [SNIPPET]: the LLM's fact ratings matched crowd labels on 72% of about 16k facts; in 100 sampled disagreements, SAFE was judged right in 76.\n\n## 8. Known limits\n\n**Distribution shift**\n- Mohri & Hashimoto [FULL TEXT] state that the guarantee can be lost under shift. Jung et al. [FULL TEXT] found theirs held under one shift between disjoint sets of evaluated models.\n- **Anonymous**, \"Understanding Conformal Factuality for RAG-based LLMs,\" ICLR 2026 submission. https://openreview.net/forum?id=OKnM5rEUbg [PARTIAL]\n  - Calibrating on another LLM's claims missed the target.\n  - Plausible distractor claims in test outputs broke the guarantee unless the calibration set contained enough of them. Including them produced more empty outputs.\n- **Hu, Zhang, Wang, Rutkowski, Tao**, \"CoFact,\" ICLR 2026. https://openreview.net/forum?id=eiBp7rsc3K [SNIPPET plus a secondary summary]\n  - Under real topic drift, static conformal filters missed the target at most time steps.\n  - Their online density-ratio reweighting controls only the long-run average, and assumes no concept shift.\n- **Barber, Candès, Ramdas, Tibshirani**, \"Conformal prediction beyond exchangeability,\" Ann. Stat. 51(2):816–845, 2023 [SNIPPET]: weighted quantiles reduce the loss of coverage under drift.\n\n**Correlated errors between generator and judge**\n- **Kim, Garg, Peng, Garg**, \"Correlated Errors in Large Language Models,\" ICML 2025. https://arxiv.org/abs/2506.07962 [PARTIAL]\n  - On HELM, when two models both err, they pick the same wrong answer about 60% of the time (chance is 1/3).\n  - More accurate models have more correlated errors.\n  - A judge inflates the accuracy of weaker models, most for models from its own provider or architecture, and deflates stronger ones.\n- **Goel et al.**, \"Great Models Think Alike and this Undermines AI Oversight,\" ICML 2025 [SNIPPET]: judges favour models similar to themselves; error similarity rises with capability.\n- **Panickssery, Bowman, Feng**, \"LLM Evaluators Recognize and Favor Their Own Generations,\" NeurIPS 2024 [SNIPPET]: self-preference rises linearly with self-recognition.\n\n**Audits of produced items measure precision and miss recall**\n- FActScore [PARTIAL] measures precision only. It does not penalize a model for abstaining or producing fewer facts.\n- Conformal factuality guarantees only the claims it keeps. What it removes is tracked separately [FULL TEXT].\n- SAFE adds a recall term, F1@K [SNIPPET].\n- **Anthony & Nobari**, \"Finite-Sample Coverage Audits for High-Recall Candidate Generation,\" arXiv 2607.21480, 2026 [SNIPPET]\n  - Labels drawn only from inside the candidate set cannot certify any non-trivial bound on missed items.\n  - The excluded pool must be sampled: on the order of N0/m labels to certify fewer than m misses.\n- **Marchant & Rubinstein**, \"In Search of an Entity Resolution OASIS,\" PVLDB 10(11), 2017 [SNIPPET]: importance sampling to estimate precision and recall under extreme class imbalance, with up to 83% fewer labels.\n- **Lewis, Yang, Frieder**, \"Certifying One-Phase Technology-Assisted Reviews,\" CIKM 2021 [SNIPPET]: stopping rules based on sampling, with valid recall guarantees.\n\n## Could not verify\n1. **Gerstgrasser et al.'s venue.** One listing says COLM 2024, another an ICML 2024 workshop; the author's page says arXiv.\n2. **Trust or Escalate figures.** I could not check whether the camera-ready figures match arXiv v1, or read the values in its distribution-shift table.\n3. **AutoEval §3** (pairwise comparison, Chatbot Arena): not read.\n4. **Abstract or metadata only:** Cherian et al., Dohmatob et al., CoFact, Zrnic & Candès, Gligorić et al., Goel et al., Panickssery et al., Bates et al., Clopper–Pearson, Wald, Howard et al.\n5. **Anonymous ICLR 2026 submission:** acceptance status unknown.\n6. **Steiner & Bizer 2026:** a preprint that has not been peer reviewed, and its audit has a single annotator.\n7. **PAC-labels venue (ICML 2026):** taken from the author's page, not from the proceedings.\n8. **Original MRPC inter-annotator agreement** (Dolan & Brockett 2005): not retrieved.\n9. **Missing measurements.** I found no human agreement figures for decomposition itself beyond FActScore's split and merge rates, and no paraphrase-benchmark numbers for current frontier models.\n10. **My computations.** All sample sizes and SPRT figures are my own, not taken from a source.\n"}