mlsanityData to 7 Oct 2026

A note on conditional PAC-efficient reasoning in large language model routing

arXiv 2512.03057 ↗First posted 25 Nov 2025stat.ML cs.AI cs.LGcited by 3

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

We study distribution-free risk control for model routing, motivated by large language model reasoning. We formalize pointwise conditional efficiency under a probably approximately correct guarantee and show that it forces a nearly impossible router: at almost every input where the fast model exceeds the target loss, the algorithm must route to the expert with probability at least one minus the prescribed error level. We therefore introduce a restricted conditional formulation based on a prespecified family of conditioning sets, together with an explicit router. The proposed router achieves finite-sample conditional validity and, under separation and margin conditions, near-oracle expert usage. The main insight is that the level of conditioning determines whether distribution-free reliability can coexist with computational savings: pointwise control is too strong, whereas structured setwise control remains feasible.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 29 of its 41 references that are in the map. First posted on arXiv 25 Nov 2025.

Builds on

29 of 41 references.

Closest ancestors · 5

Same direction, newest first

  1. 2025On the Provable Performance Guarantee of Efficient Reasoning Models10 Oct
  2. 2025OptimalThinkingBench: Evaluating Over and Underthinking in LLMs18 Aug
  3. 2025CP-Router: An Uncertainty-Aware Router Between LLM and LRM26 May
  4. 2025Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models20 Mar
  5. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug

Other references · 24

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  4. 2022Fast Inference from Transformers via Speculative Decodingcited by 1,615
  5. 2016Distribution-Free Predictive Inference For Regressioncited by 657
  6. 2024RouteLLM: Learning to Route LLMs with Preference Datacited by 633
  7. 2022Conformal prediction beyond exchangeabilitycited by 348
  8. 2016Least Ambiguous Set-Valued Classifiers with Bounded Error Levelscited by 270
  9. 2023Conformal Prediction With Conditional Guaranteescited by 146
  10. 2021Testing for Outliers with Conformal p-valuescited by 133
  11. 2021Localized Conformal Prediction: A Generalized Inference Framework for Conformal Predictioncited by 112
  12. 2024On the Algorithmic Bias of Aligning Large Language Models with RLHF: Preference Collapse and Matching Regularizationcited by 72
12 more
  1. 2024A Unified Approach to Routing and Cascading for LLMscited by 71
  2. 2021Conformalized Survival Analysiscited by 53
  3. 2023Conformal prediction with local weights: randomization enables local guaranteescited by 47
  4. 2021Selection and Aggregation of Conformal Prediction Setscited by 46
  5. 2024LAMBDA: A Large Model Based Data Agentcited by 30
  6. 2017Fast Exact Conformalization of Lasso using Piecewise Linear Homotopycited by 20
  7. 2020A Two-Sample Conditional Distribution Test Using Conformal Prediction and Weighted Rank Sumcited by 18
  8. 2024Debiasing Watermarks for Large Language Models via Maximal Couplingcited by 18
  9. 2022Conformalized survival analysis with adaptive cutoffscited by 17
  10. 2023Conformal Prediction for Network-Assisted Regressioncited by 14
  11. 2024Towards Better Statistical Understanding of Watermarking LLMscited by 14
  12. 2023Selective conformal inference with false coverage-statement rate controlcited by 11

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026RACER: Risk-Aware Calibrated Efficient Routing for Large Language Modelscited by 4
  2. 2026Anytime Safe PAC Efficient Reasoningcited by 1
  3. 2026Conditional Performance Guarantee for Large Reasoning Modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Reasoning Is Not Free: Robust Adaptive Cost-Efficient Routing for LLM-as-a-Judge
  2. 2026Policy-Guided Stepwise Model Routing for Cost-Effective Reasoning
  3. 2025Confidence-Guided Stepwise Model Routing for Cost-Efficient Reasoning
  4. 2026ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inference
  5. 2026Rethinking Stepwise Model Routing: A Cost-Efficient Table Reasoning Perspective
  6. 2025Optimizing Reasoning Efficiency through Prompt Difficulty Prediction
  7. 2026When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models
  8. 2026Signed Rescue Routing: Harm-Aware Cascades for Efficient LLM Inference