Cross-View Correspondence Is a Measurement Intervention: Two-Sided Validation for Agent Evaluation and Credit Assignment
Zhen ZhangAhmad HafezAmr Alanwar
Aug 2026
Machine Learning
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.
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It is shown that the maximum hypergraph density of any multiclass hypothesis class is upper-bounded by its DS dimension, which proves a longstanding conjecture of Daniely and Shalev-Shwartz (2014) and determines the optimal dependence of the sample complexity on the DS dimension for multiclass as well as list learning.
Quantum measurements are the means by which we recover messages encoded into quantum states. They are at the forefront of quantum hypothesis testing, wherein the goal is to perform an optimal measurement for arriving at a correct conclusion. Mathematically, a measurement operator is Hermitian with eigenvalues in [0,1]. By noticing that this constraint on each eigenvalue is the same as that imposed on fermions by the Pauli exclusion principle, we interpret every eigenmode of a measurement operator as an independent effective fermionic mode. Under this perspective, various objective functions in quantum hypothesis testing can be viewed as the total expected energy associated with these fermionic occupation numbers. By instead fixing a temperature and minimizing the total expected fermionic free energy, we find that optimal measurements for these modified objective functions are Fermi-Dirac thermal measurements, wherein their eigenvalues are specified by Fermi-Dirac distributions. In the low-temperature limit, their performance closely approximates that of optimal measurements for quantum hypothesis testing, and we show that their parameters can be learned by classical or hybrid quantum-classical optimization algorithms. This leads to a new quantum machine-learning model, termed Fermi-Dirac machines, consisting of parameterized Fermi-Dirac thermal measurements-an alternative to quantum Boltzmann machines based on thermal states. Beyond hypothesis testing, we show how general semidefinite optimization problems can be solved using this approach, leading to a novel paradigm for semidefinite optimization on quantum computers, in which the goal is to implement thermal measurements rather than prepare thermal states. Finally, we propose quantum algorithms for implementing Fermi-Dirac thermal measurements, and we also propose second-order hybrid quantum-classical optimization algorithms.
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