# ROUTEAUDIT: Interaction-Aware Identification for Budgeted Multi-Verifier Routing

arXiv: https://arxiv.org/abs/2610.02808 · HTML: https://mlsanity.com/paper/2610.02808/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 33 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 30 of 32)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [ToolSandbox: A Stateful, Conversational, Interactive Evaluation Benchmark for LLM Tool Use Capabilities](https://mlsanity.com/paper/2408.04682/) (2024)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Defining and Characterizing Reward Hacking](https://mlsanity.com/paper/2209.13085/) (2022)
- [AgentV-RL: Scaling Reward Modeling with Agentic Verifier](https://mlsanity.com/paper/2604.16004/) (2026)
- [Process-Verified Reinforcement Learning for Theorem Proving via Lean](https://mlsanity.com/paper/2606.20068/) (2026)
- [Zero-Overhead Introspection for Adaptive Test-Time Compute](https://mlsanity.com/paper/2512.01457/) (2025)
- [Reward Model Routing in Alignment](https://mlsanity.com/paper/2510.02850/) (2025)
- [Cost-Optimal LLM Routing with Limited User Feedback under User Satisfaction Guarantees](https://mlsanity.com/paper/2606.19376/) (2026)
- [CAPS: Cascaded Adaptive Pairwise Selection for Efficient Parallel Reasoning](https://mlsanity.com/paper/2605.15513/) (2026)
- [Adaptive Generate-Rank-Verify: Inference-Time Search with Costly Verification](https://mlsanity.com/paper/2605.17609/) (2026)

## Abstract (arXiv)

Adaptive multi-verifier systems are commonly compared through endpoint quality-cost gaps, even when the verifier catalog, availability, accounting, information filtration, or scorer changes with the policy. We formulate verifier routing as a contract-conditioned identification problem. The contract records request support, verifier catalog, realized availability, resource accounting, online filtration, and post-trace scoring; a matched route contrast changes only the policy coordinate. ROUTEAUDIT adds three measurable objects to this contract. A contract lattice averages coordinate increments over every admissible bridge order and reports the resulting attribution together with its path sensitivity. A policy-independent response tape identifies paired sequential contrasts when adaptive policies reveal different observations. For incomplete matching, request-level bounds use whichever potential outcome remains observed and give a sharp finite-population interval. The protocol commits paid observations and ledger events before the oracle join and returns an attribution certificate for each comparison. On two held-out raw-tail caches, matched static SF+SA equals the cascade, assigning the apparent gains of 0.1797 and 0.1250 over full static to the verifier-set edge. On 1,319 held-out task requests, the learned and RLVR studies report quality 0.9522 and 0.9553 versus 0.9484 for matched static; the RLVR-static paired difference is +0.0068 with a request-paired interval [0.0015,0.0122] and a training-seed-by-request hierarchical interval [0.0006,0.0131]. Controlled attribution recovery yields route mean absolute error 0.0011 and endpoint reconstruction error 0.0004. Factorial, bridge-order, and stochastic-provider studies evaluate the certificate interface; RLVR supplies a learned-policy stress test under the same identification contract.