Cross-View Correspondence Is a Measurement Intervention: Two-Sided Validation for Agent Evaluation and Credit Assignment
Organizations: School of Computation, Information and Technology Technical University of Munich, Germany
Abstract
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.
Figures & tables
| Contract / compiler | Solver-invariant object | Exact method | Boundary |
|---|---|---|---|
| Declared selector | one assignment and update | assignment + compiler | polynomial, selector-relative |
| Affine on exact faces | compact polytope | LP support; QP closest point | polynomial, all optima |
| Local nonlinear, width | finite factor graph | min-sum elimination | |
| Shared group standardizer | coupled exact-tie states | support / universal threshold | NP-hard / coNP-hard |
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
| Evidence | Analysis unit | Provenance | Supports | Does not support |
|---|---|---|---|---|
| Temporal localization | nonzero code/SQL pairs | frozen thresholds and exact reanalysis | lack one early/late label across all optima | first discovery of the source paper’s routing hazard; a claim about every trajectory metric |
| Strict trajectory repair | public task-configuration cells | pre-registered source audit | false-perfect; nine model-pair reversals | a new sequence metric; changed end-to-end accuracy; universal benchmark affectedness |
| MatchTIR discovery | materially affected task groups | frozen -rollout sample | groups admit intended-credit sign reversal | branch use in the released training run; final-policy damage |
| MatchTIR quick-start | material groups; clean distinct groups | reconstructed public path | reversals; in the clean subset | use of the intended branch; final-policy effect |
| MatchTIR replication | materially affected task groups | task-and-seed-disjoint frozen sample | groups replicate sign reversal | deployment prevalence outside the sampled frame |
| Natural update bodies | frozen tasks, one parameter tensor | post-hoc certificate audit | common-progress certificates and one abstention | changed training decisions or policy improvement |
| Cell | Nonzero pairs | Sharp source-state mean range | Pairwise unidentified | Published directional claim & audit consequence |
|---|---|---|---|---|
| Spider2-DBT / Codex / header shuffle | 64 | early; reversible over exact optima | ||
| Spider2-DBT / Codex / header translation | 64 | none | ||
| Spider2-DBT / Codex / timestamp | 64 | none | ||
| Spider2-DBT / OpenHands / header shuffle | 64 | late; retained over exact optima | ||
| Spider2-DBT / OpenHands / header translation | 64 | none | ||
| Spider2-DBT / OpenHands / timestamp | 63 | none |
| Conformance check | Audited population | Exact result |
|---|---|---|
| Independent finite construction | 813 no-isolate graphs through five vertices; 25,264 signs; 160 gadgets | zero failures |
| Binary source fibers | 990 binary gadgets | exactly two returned vectors per fiber |
| Anchor source fibers | 360 anchors | exactly one returned vector per fiber |
| Literal call-dictionary compilation | 744 compiled assignments | cut ordering preserved in every assignment |
| Upstream compiler versus independent port | 420 random cases | maximum numerical discrepancy |
| Dyadic promise serialization | graph sizes through | at most 109 denominator bits |
| Audit | Status | Cells | False-perfect (clustered CI) | Ranking effect | |
|---|---|---|---|---|---|
| Earth-Agent RGB | pre-registered GO | 9 pair reversals; top changes | |||
| Earth-Agent common tasks | post-hoc robustness | 18 pair reversals; top changes | |||
| MCPEval held out | pre-registered REDUCE | 1 pair reversal |
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