Quantum-Inspired Rogue Variable Modeling (QRVM)

• QRVM is a framework that applies quantum decoherence concepts to model rogue variable dynamics in interactive human-AI systems.
• It integrates human and machine performance metrics through ablation studies to identify and address feedback misalignment.
• The approach offers practical strategies, enhancing system reliability by clarifying agency and recalibrating iterative interactions.

Human-in-the-loop decoherence refers to the gradual loss or breakdown of alignment, fidelity, or operational meaning in interactive systems where human feedback is tightly coupled to a machine learner or optimizer. Originating as an analogy to quantum decoherence—the loss of a well-defined phase relationship between components of a superposed state—in human-AI systems, it denotes the attenuation of the feedback signal’s informational coherence, leading to persistent oscillation, failure to converge, or divergence from optimal outcomes. Human-in-the-loop decoherence manifests both as a conceptual misalignment between labels and control within deployed systems, as well as as a technical challenge arising from human judgment noise, cognitive biases, and shifting objectives. Closely related phenomena are found in both human-feedback-driven optimization (Ou et al., 2022) and human-centered collaborative AI (Natarajan et al., 2024), underscoring challenges to sustained, reliable partnership between people and machines.

1. Formal Definitions and System Taxonomy

The interpretation of "human-in-the-loop" (HIL) in the literature is often ambiguous, masking critical distinctions in locus of control and system dynamics. In a canonical HIL system, the AI component (A) orchestrates data acquisition, model update, and inference, invoking the human (H) for supervision, advice, or labeling solely to improve its internal model. The functional structure is:

$$\text{Decision} \leftarrow A(\text{Data}, \text{Advice from } H)$$

Exemplars include active learning, weak/distant supervision frameworks, and advice integration in reinforcement learning.

By contrast, "AI-in-the-loop" ($AI^2L$) systems invert agency:

$$\text{Decision} \leftarrow H(\text{Recommendations from } A, \text{Personal Expertise})$$

Here, the human retains decision authority, integrating AI-generated recommendations, risk estimates, or evidence synthesis but retaining the ability to override, ignore, or recalibrate machine advice. $AI^2L$ subsumes collaborative clinical decision-making and operational domains where the human agent is epistemic and normative principal (Natarajan et al., 2024).

Human-in-the-loop decoherence thus arises when there is a mislabeling or loss of system-state alignment, either due to collapses in the intended feedback loop (technical decoherence) or due to rhetorical imprecision regarding who holds agency (label decoherence).

2. Quantitative Modeling and Performance Metrics

Absent closed-form analytic models, overall system performance can be abstracted as

$$P_\mathrm{total} = f(H_\mathrm{perf},\,A_\mathrm{perf})$$

with a typical weighted sum representation: $$P_\mathrm{total} = \alpha\,H_\mathrm{perf} + (1-\alpha)\,A_\mathrm{perf}, \qquad 0 \leq \alpha \leq 1$$

In classical HIL, $\alpha \approx 0$, making $A_\mathrm{perf}$ (machine-centric metrics like accuracy, F1) the principal axis of evaluation. $AI^2L$ yields $\alpha \approx 1$, shifting emphasis to human outcomes: task completion, trust calibration, operational latency, and human error correction rates.

Decoherence becomes evident when system designers overemphasize AI metrics while actual agency, control, and outcome quality are dominated by human determinants. Rigorous ablation studies are essential, measuring $P_\mathrm{total}$ with and without each component (H alone, A alone, and H$+$A) to reveal latent decoherence and true locus of performance (Natarajan et al., 2024).

Specific to preference-based optimization, empirical convergence is tracked via metrics:

• $\mu_r(t):=$ mean rating per iteration $t$
• $\sigma_r^2(t):=$ variance of ratings per iteration $t$

Convergence is indicated by a monotonic increase in $\mu_r$ and decrease in $\sigma_r^2$; stationarity or oscillation signal loop decoherence (Ou et al., 2022).

3. Empirical Manifestations and Failure Modes

In systems studied with real users, decoherence manifests as an inability of the interactive loop to steer towards a satisfactory or optimal solution. Field and lab studies in preference-guided design optimization reveal that human ratings often:

• Drift or contradict earlier judgments across iterations
• Exhibit strong cognitive biases (anchoring, availability, representativeness)
• Display loss aversion and diminished willingness to explore alternatives once a "good enough" solution is seen
• Accumulate substantial noise across levels: level, pattern, and transient noise (nomenclature as in Kahneman et al. 2021)

For example, in a 3-month deployment, only 11.9% of multi-step optimization sessions reached a satisfactory endpoint; in controlled studies, fewer than half converged within 11 iterations (Ou et al., 2022). Statistical tests (ADF, Mann–Kendall $\tau$) overwhelmingly fail to support desirable monotonic improvement.

Empirical decoherence examples include (a) rating identical objects differently due to drift; (b) penalizing obviously superior variants via representativeness bias; (c) misgrading due to limited visual framing, which UI tools might otherwise mitigate.

4. Conceptual and Operational Decoherence

A central form of decoherence, termed label-control decoherence (Editor's term), emerges when the system's purported architecture (e.g., HIL) is incoherent with its actual operational dynamics. The misalignment is amplified by:

• Misapplied or misleading system taxonomy (“HIL” when $AI^2L$ is descriptively accurate)
• Evaluation protocols that prioritize the wrong metrics (AI-centric when human agency dominates)
• Lack of appropriate ablation and interpretability studies, obscuring which subsystem dictates system behavior

This conceptual decoherence distorts system design, fosters misplaced trust, and hides loci of bias and error. It has been explicitly critiqued as creating a misleading “coherence” at design time that collapses in practical deployment (Natarajan et al., 2024).

5. Mitigation Strategies and System Design Guidelines

To restore and sustain coherence in human–machine cooperation, best practices have been distilled from empirical and critical analyses:

1. Clarify agency: Establish, pre-implementation, whether the human or the AI must ultimately control final decisions.
2. Align evaluation with control: Center metric selection on the true locus of agency—human-outcome metrics for $AI^2L$; machine-centric for HIL.
3. Ablation protocols: Evaluate H alone, A alone, and H$+$A combinations to disambiguate contributions.
4. Model credibility and reliability: In HIL, model human credibility as input; in $AI^2L$, quantify AI reliability and data-source dependability.
5. Prioritize transparency and explainability: Architect for interactive, interpretable affordances that allow effective judgment, override, and trust calibration.
6. Socio-technical context: Evaluate long-term impacts, not just short-term performance; include real-world deployments over static benchmarks (Natarajan et al., 2024).

Beyond these macro-guidelines, interface-level interventions can reduce judgment noise and restore feedback coherence:

• Chronological visualization of milestones counteracts level noise and loss aversion.
• Iteration phase indicators (“exploration” vs “exploitation”) help frame user context and mitigate representativeness bias.
• Consistency checks (re-rating past variants) and difference-highlighting discourage drift and context-blindness (Ou et al., 2022).

6. Broader Perspectives and Physical Analogies

The term "decoherence" has deep roots in quantum open systems, where environment-induced entanglement leads to rapid loss of pure quantum superpositions, with practical limits on achievable macroscopic coherence (Moustos et al., 2024). In the human–AI context, this analogy is deployed intentionally: just as gravity mediates in-principle unavoidable decoherence of macroscopic quantum systems (e.g., loss of a 100 kg, 1 m superposition occurs in $\sim$1 s due to coupling with Earth's quantum phonon bath), irreducible cognitive and behavioral noise in human agents can destroy the convergence of human-in-the-loop systems, especially at scale.

A plausible implication is that even in idealized architectures, persistent decoherence is to be expected unless designers build both technical and interactional affordances that preserve, measure, and realign the "phase" of the human–machine system at each iteration.

7. Illustrative Domains and Case Studies

Domain-specific characterizations of automation (HIL) versus collaboration ($AI^2L$) provide calibration points for system design:

Domain	Automate (HIL) Example	Collaborate ($AI^2L$) Example
Medicine	MRI anomaly detection prompting human review	Treatment-plan generation with physician in loop
Autonomous Driving	Route planning via AI optimization	Urban driving with human maneuvers, AI as assistant
Finance	Fraud detection flagging by AI	Investment portfolio constructed by human, AI advisory

Each collaborative example demonstrates the restoration of coherence—placing the human at the center of normative decision loops, with AI as an instrument rather than controller (Natarajan et al., 2024).

In summary, human-in-the-loop decoherence encompasses a spectrum of breakdowns in technical, evaluative, and conceptual alignment between humans and AI within interactive loops. Recognizing, diagnosing, and mitigating both label-control and feedback decoherence is essential for robust, trustworthy deployment of interactive human–machine systems. Robust design practice requires critical distinction of agency, appropriate metrics, practical ablation, and resilient interface affordances to sustain alignment and operational coherence.