# Cross-View Correspondence Is a Measurement Intervention: Two-Sided Validation for Agent Evaluation and Credit Assignment

arXiv: https://arxiv.org/abs/2608.17713 · HTML: https://mlsanity.com/paper/2608.17713/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 39 references that are in the map.
- First posted on arXiv 18 Aug 2026.

## Builds on (most cited first, 22 of 22)

- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (2023)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [A Generic First-Order Algorithmic Framework for Bi-Level Programming Beyond Lower-Level Singleton](https://mlsanity.com/paper/2006.04045/) (2020)
- [RoTBench: A Multi-Level Benchmark for Evaluating the Robustness of Large Language Models in Tool Learning](https://mlsanity.com/paper/2401.08326/) (2024)
- [Earth-Agent: Unlocking the Full Landscape of Earth Observation with Agents](https://mlsanity.com/paper/2509.23141/) (2025)
- [On Finding Small Hyper-Gradients in Bilevel Optimization: Hardness Results and Improved Analysis](https://mlsanity.com/paper/2301.00712/) (2023)
- [MCPEval: Automatic MCP-based Deep Evaluation for AI Agent Models](https://mlsanity.com/paper/2507.12806/) (2025)
- [Demystifying Group Relative Policy Optimization: Its Policy Gradient is a U-Statistic](https://mlsanity.com/paper/2603.01162/) (2026)
- [GUI-Robust: A Comprehensive Dataset for Testing GUI Agent Robustness in Real-World Anomalies](https://mlsanity.com/paper/2506.14477/) (2025)
- [Probabilistic Permutation Invariant Training for Speech Separation](https://mlsanity.com/paper/1908.01768/) (2019)
- [M^3-Bench: Multi-Modal, Multi-Hop, Multi-Threaded Tool-Using MLLM Agent Benchmark](https://mlsanity.com/paper/2511.17729/) (2025)
- [LeTS: Learning to Think-and-Search via Process-and-Outcome Reward Hybridization](https://mlsanity.com/paper/2505.17447/) (2025)
- [MatchTIR: Fine-Grained Supervision for Tool-Integrated Reasoning via Bipartite Matching](https://mlsanity.com/paper/2601.10712/) (2026)
- [Robust Perception through Equivariance](https://mlsanity.com/paper/2212.06079/) (2022)
- [Quantifying perturbation impacts for large language models](https://mlsanity.com/paper/2412.00868/) (2024)
- [On the Hidden Objective Biases of Group-based Reinforcement Learning](https://mlsanity.com/paper/2601.05002/) (2026)
- [Consistency as a Testable Property: Statistical Methods to Evaluate AI Agent Reliability](https://mlsanity.com/paper/2605.10516/) (2026)
- [RepoMirage: Probing Repository Context Reasoning in Code Agents with Perturbations](https://mlsanity.com/paper/2605.26177/) (2026)
- [A robust approach to quantifying uncertainty in matching problems of causal inference](https://mlsanity.com/paper/1812.02227/) (2018)
- [Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets](https://mlsanity.com/paper/2605.09209/) (2026)
- [An Axiomatic Theory of Tie-Breaking: Impossibility, Characterization, and Decomposition](https://mlsanity.com/paper/2605.22846/) (2026)

## Abstract (arXiv)

Agent evaluations and trace-based learning often compare outputs across transformed views through a post-response correspondence treated as neutral preprocessing. We show that this correspondence is a measurement intervention: omitting it can manufacture sensitivity, an over-aggressive map can manufacture invariance, and multiple optimal correspondences can leave mechanism labels and signed learning credit unidentified. We develop a validity theory and audit with three components: two-sided validation of nuisance removal and response preservation, all-optima identification of downstream conclusions, and uncertainty propagation after validity is established. We characterize the linear feasibility boundary for response-preserving nuisance removal, compute sharp ranges over exact-optimum correspondence sets, and give a distribution-free certificate that retains a credit coordinate only when all exact optima agree on its nonzero sign. Across public code and SQL pipelines, two deterministic optimal tracebacks disagree on temporal localization for 55.9% of 1,586 nonzero trajectory pairs; two frozen 800-rollout tool-use audits, including a task-and-seed-disjoint replication, expose exact-optimum reversals of intended turn-level credit, although a clean public quick-start subset shows none. A pre-registered transport gate failed on natural responses; frozen corrected and held-out controls then show that a map calibrated only on benign examples erases every retained harmful response, while two-sided validation selects response-preserving alternatives. Cross-view correspondence must therefore be declared, validated, and propagated into uncertainty before agent evaluation or credit assignment supports a point conclusion.