Repair Before Veto, When Repair Is Hidden: Quantum-Accessible Features for Repair-Augmented Constraint Learning

Abstract: Hard-constraint decision systems usually veto infeasible candidates. This is too rigid when the system can act: if a known affordable repair would make an infeasible candidate feasible and valuable, rejection is a false veto rather than a ranking error. We introduce Q-RACL (Quantum Repair-Augmented Constraint Learning), a repair-before-veto framework that first defines RACL decision semantics and then identifies the single inference link where quantum feature access can be load-bearing. RACL accepts a candidate when a sequential repair plan restores feasibility and preference; otherwise it returns structured rejection credit. The hard link is repair-feasibility inference: which repair class restores feasibility from an observed candidate and context. We construct a discrete-logarithm-hidden RACL family where the repair class is a shifted interval rule in the latent exponent a = log_g(x), while the learner observes only x = g^a mod p. Under standard DLP-based learning separation, this coordinate is inaccessible to efficient raw-input classical policies but accessible to a quantum agent through Shor/Fourier structure. Across six primes and ten seeds, bounded raw-input classical policies and a wrong raw-Fourier encoding remain near chance, whereas the Q-DLP policy keeps false-veto rate below 1.1%, wins all paired seeds, and yields QNI_cond = 0.9777 to 0.9972. A classical DLog oracle matches it, isolating feature access rather than classifier capacity. Thus quantum AI is not added as a generic model upgrade; for this DLP-hidden repair family, it supplies the missing feature that closes the repair-before-veto loop.

• The paper demonstrates that integrating quantum-accessible features within RACL drastically reduces false veto rates compared to classical policies.
• It employs a DLP-hidden construction to obscure latent repair feasibility, which quantum models efficiently infer using Fourier-based techniques.
• Empirical evaluations show the Q-DLP policy achieves false veto rates below 1.1%, underscoring its advantage in privacy-preserving decision systems.

Quantum-Accessible Features in Repair-Augmented Constraint Learning

Problem Setting and Motivation

This work formalizes and investigates the "repair-before-veto" paradigm in constraint-based decision systems. Traditional hard-constraint pipelines unconditionally veto candidates that violate feasibility requirements, even when cost-effective, known repairs could render them valid and valuable. This rigid approach fails to leverage actionable recourse, resulting in avoidable false rejections.

The proposed framework, Repair-Augmented Constraint Learning (RACL), embeds potential repairs directly into the decision semantics, ensuring candidates are only vetoed if irreparably infeasible, unacceptably costly to repair, or suboptimal after all feasible repairs. Structured outputs, including repair plans and rejection credits, are returned, which provide actionable feedback and informative rejection reasons rather than binary accept/reject labels.

RACL stands in contrast to recourse and counterfactual methods that attempt post-hoc explanations or repairs after a veto has been committed. It also generalizes beyond constraint satisfaction and soft-constraint systems by integrating sequential repair planning and structured credit assignment into the decision loop.

Quantum Feature Access and DLP-Hidden RACL Construction

A pivotal challenge addressed is the repair-feasibility inference bottleneck: efficiently determining, from observed features, which repair class restores feasibility. In realistic deployed settings, candidate objects are often represented by encoded identifiers or opaque group codes, where operational feasibility classes are simple in an unobserved (latent) coordinate but hidden in the input data. The paper constructs a family of RACL instances where this structural barrier is formalized using the hardness of the Discrete Logarithm Problem (DLP).

Specifically, in the DLP-hidden RACL setting:

• Candidates are elements $x = g^a \bmod p$ for a known generator $g$ of $\mathbb{Z}_p^*$ and prime $p$, with $a$ as the hidden exponent.
• Repair feasibility is determined by predicates that are simple shifted intervals in $a$, but appear as scrambled, non-linear functions in the observed $x$.
• Efficient classical learners restricted to raw $x$ cannot recover the repair class without solving DLP, a presumed-hard problem.
• Quantum models can compute or operate in the Fourier basis over $a$, exploiting Shor's algorithm or variational circuits to access features unavailable to classical learners.

This construction localizes quantum advantage to a specific inference link within the repair-augmented pipeline: mapping observed encodings to their feasibility class for repair planning. The work does not posit generic quantum superiority for all constraint tasks; instead, it gives a theorem-backed and controlled demonstration of conditional quantum necessity for a classically-hard feature-inference bottleneck.

Policy Families, Controls, and Experimental Design

Empirical evaluation contrasts several policy families:

• Bounded raw-input classical policies: logistic regression, polynomial regression, random forest, MLP, and random Fourier features over $x$.
• Misaligned quantum-style policies: Fourier features over $g$0—not over the hidden $g$1 coordinate.
• Q-DLP policies: policies with explicit access to DLP/Fourier features over $g$2 and context shifts.
• DLog Oracle: classical access to the exponent, serving as an upper bound and control.

The target is the false-veto rate (FVR): the probability the policy falsely rejects a candidate that could feasibly be repaired. Evaluations are conducted across multiple primes ($g$3 to $g$4) and random seeds, ensuring robust generalization through test splits with disjoint exponents.

Results

Key results demonstrate:

• Bounded classical (raw-input and misaligned) policies remain at chance-level FVR ($g$50.41–0.50), exhibiting no capacity to efficiently learn the DLP-hidden predicate.
• The Q-DLP policy obtains FVR below 1.1% across all primes, with observed rates as low as 0.0014 (see Table 2 in the paper).
• The DLog oracle matches Q-DLP policy performance, confirming that once the critical coordinate is exposed, a simple policy head suffices.
• Paired tests (10 seeds per prime) show the Q-DLP policy universally outperforms the best classical baseline, with mean FVR reductions up to 0.48 and $g$6.

These outcomes exemplify the structural, conditional advantage quantum feature access provides when classical feature-based policies are information-theoretically blocked from inferring feasibility classes. The quantum necessity index (QNI), nearly $g$7 for all experiments, quantifies that quantum access closes essentially the entire classical false-veto gap.

Theoretical and Practical Implications

The theoretical implication is a precise characterization of when quantum machine learning is required for repair-augmented constrained decision-making: namely, when repair feasibility is a function of a latent coordinate hidden by a cryptographically hard transform such as DLP. The paper's construction and analysis clarify that quantum advantage is load-bearing at specifically these inference links, not as a general-purpose upgrade.

Practically, the findings are pertinent for systems that rely on obfuscated or privacy-preserving identifiers, such as fare codes, tokenized records, or anonymized features, where the operational class is simple in a non-observed domain. The localization of quantum advantage suggests strategic use of quantum learning modules within otherwise classical ML pipelines, focusing quantum resources where classical inference is structurally blocked.

The results also stress the need for rigorous structural and cryptographic separation-based analyses when assessing quantum utility—eschewing overbroad benchmarking in favor of identifying precise feature-access bottlenecks.

Limitations and Scope

The study employs proof-of-mechanism simulations on small primes and does not demonstrate large-scale quantum hardware advantage. The use of classical DLP tables for evaluation validates the principle in a controlled setting, with asymptotic claims tied to established classical and quantum algorithmic complexity.

The quantum-necessity argument is conditional: transparent or low-complexity feasibility rules are still solvable by classical methods, and no universal quantum advantage for all RACL problems is claimed.

Conclusion

This work formally instantiates and analyzes the repair-before-veto paradigm in constraint learning, introducing RACL as a framework that integrates actionable repair into structured decision-making. Through the DLP-hidden RACL family, it identifies and demonstrates that quantum feature access is needed—not as a model upgrade, but as a structural mechanism—for closing false-veto gaps in settings where repair feasibility is obfuscated by cryptographic hardness. The findings argue for quantum-classical hybrid pipelines that deploy quantum inference selectively at critical feature-access barriers, with broader applicability for privacy-preserving and encoded-feature decision systems.

Reference:

"Repair Before Veto, When Repair Is Hidden: Quantum-Accessible Features for Repair-Augmented Constraint Learning" (2606.08020)