# Oracle Gaps in Reliability Coverage: Sampling Noise or Policy Specialization?

arXiv: https://arxiv.org/abs/2609.32996 · HTML: https://mlsanity.com/paper/2609.32996/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 35 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping](https://mlsanity.com/paper/2002.06305/) (2020)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [Adding Error Bars to Evals: A Statistical Approach to Language Model Evaluations](https://mlsanity.com/paper/2411.00640/) (2024)
- [A Unified Theory of Diversity in Ensemble Learning](https://mlsanity.com/paper/2301.03962/) (2023)
- [The Path Not Taken: RLVR Provably Learns Off the Principals](https://mlsanity.com/paper/2511.08567/) (2025)
- [Rethinking Mixture-of-Agents: Is Mixing Different Large Language Models Beneficial?](https://mlsanity.com/paper/2502.00674/) (2025)
- [LLMRouterBench: A Massive Benchmark and Unified Framework for LLM Routing](https://mlsanity.com/paper/2601.07206/) (2026)
- [When Does Combining Language Models Help? A Co-Failure Ceiling on Routing, Voting, and Mixture-of-Agents Across 67 Frontier Models](https://mlsanity.com/paper/2606.27288/) (2026)
- [Beyond Pass@k: Breadth-Depth Metrics for Reasoning Boundaries](https://mlsanity.com/paper/2510.08325/) (2025)
- [Are Diversity Metrics Measuring Diversity? A Capability-Controlled Audit of Majority-Vote Gain in LLM Ensembles](https://mlsanity.com/paper/2607.20768/) (2026)
- [Quantifying Diversity of Thought: A Predictive Law of Weighted LLM Ensemble Lift](https://mlsanity.com/paper/2607.17384/) (2026)
- [Sparsity Curse: Understanding RLVR Model Parameter Space from Model Merging](https://mlsanity.com/paper/2606.18521/) (2026)

## Abstract (arXiv)

Policies trained from the same base model can appear to solve different problems. An oracle that chooses the best policy for each problem may therefore appear much stronger than any single policy. Selecting the largest estimated success rate also selects favorable sampling errors. We study this effect through reliability coverage, the fraction of problems whose success probability reaches a chosen threshold. Our first test redistributes stored correctness outcomes across policies within each problem. A second also preserves each policy's total successes, accounting for overall quality differences under a specified statistical model. For five training seeds of a seven-billion-parameter vision-language model, redistribution reproduces 0.096 of an estimated 0.113 oracle gap at threshold 0.10. Neither test finds significant evidence at this threshold. Small advantages remain unresolved. Mixtures, routers, voting, and weight averaging show no detectable improvement over their corresponding single-policy baselines. Training policies on different datasets shows little detectable specialization under light post-training, and no router gain. A stronger recipe does create it, both tests detect it, and a router gain appears only at the high thresholds where the specialists separate. In a control with predictable specialization, a router recovers about half the oracle gap. Coverage bounds explain why even a genuine oracle advantage need not yield a deployment gain. The tests assess apparent specialization from stored responses before investment in routing. Code: https://github.com/KurbanIntelligenceLab/oracle-gaps