Proficiency Control Task (PCT)

• Proficiency Control Task (PCT) is a framework that explicitly estimates and adapts proficiency levels across domains such as language generation, education, and robotics.
• PCT utilizes statistical modeling, adaptive difficulty control, and real-time feedback mechanisms to align outputs with target proficiency using methods like regression and SOM.
• Evaluation protocols and performance metrics in PCT demonstrate reduced error rates, improved task execution, and promising avenues for transfer learning in complex skill domains.

The Proficiency Control Task (PCT) is a formalized framework for quantifying, tracking, and guiding skill acquisition and proficiency adaptation across a range of domains, including human-computer interaction, robotics, and machine learning. PCT frameworks integrate mathematical modeling, task-difficulty control, behavioral performance measurement, and feedback strategies to align system output or learning trajectories with target proficiency levels, whether in human learners, robots, or generative models.

1. Formal Definitions Across Domains

PCT is instantiated differently according to domain, but centers on three core tenets: the explicit estimation of current proficiency, controlled assignment of task difficulty or output level, and adaptive feedback to realign actions or outputs toward target proficiency strata.

• Language Generation (LLMs): PCT formalizes controlled text generation as sampling $y \in \Sigma^*$ conditioned on a prompt $p \in \Sigma^*$ and target proficiency $t \in \{1, \ldots, 6\}$, where the model implements $p_\theta(y \mid p, t)$ and proficiency is scored via a regression-based CEFR mapping $s_{\mathrm{cefr}}(y) \in [1, 6]$ (Malik et al., 2024).
• Adaptive Language Assessment: In personalized question-generation, proficiency is explicitly estimated per round as a continuous score $\hat\theta_t$ within a discrete scale (e.g., $1$–$6$), representing educational stages (Huang et al., 2018).
• Human-Robot Interaction: PCTs are framed as Markov Decision Processes (MDPs) with internal robot proficiency self-assessment, outputting trust-calibrated recommendations or control suggestions (Conlon et al., 2022).
• Manual Robot Control: PCT operates on high-dimensional grip-force telemetry, using unsupervised learning (Self-Organizing Maps, or SOMs) to differentiate between novice and expert skill via quantization error (QE) in spatiotemporal force patterns (Liu et al., 2023).

2. Proficiency Estimation and Task-Level Control

A unifying feature of PCT implementations is probabilistic or statistical proficiency modeling, driving dynamic control over task assignment or output difficulty.

• Language Proficiency Scoring: Regression over lexical and syntactic features, trained on large CEFR-annotated corpora, yields $s_{\mathrm{cefr}}: \Sigma^* \to [1,6]$ with out-of-domain $R^2 \approx 0.8$ (Malik et al., 2024).
• Education Systems: Proficiency updates follow EWMA-style smoothing: $$\hat\theta_{t+1} = \alpha S_t + (1-\alpha)\hat\theta_t$$, with $S_t$ the quiz score and $\alpha$ a smoothing constant (empirically set to 0.3), then discretized for item selection (Huang et al., 2018).
• Human-Robot Collaboration: The robot computes an Outome Assessment ($OA$) by Monte Carlo rollouts, deriving confidence scores through upper/lower partial moments of simulated reward distributions, which are then mapped to a calibrated [–1, +1] scale (Conlon et al., 2022).
• Dexterity Tasks: SOM-QE and grip-force standard deviation (STD) serve as proficiency markers; lower, more stable values indicate higher expertise (Liu et al., 2023).

3. Methodologies and Implementation Strategies

PCT methodologies encompass supervised and reinforcement learning, adaptive item or task selection, and sensorimotor analytics.

Domain	Proficiency Marker	Control Mechanism
LLMs	$s_{\mathrm{cefr}}(y)$	Prompt/preference tokens, RL
Edu. quizzes	$\hat\theta_t$	20:60:20 adaptive quiz split
Robotics	$OA$ ($\in$ [–1,+1])	Trust/self-assessment display
Dexterity	SOM-QE, windowed AmV, STD	Feedback dashboard, thresholds

• Language Generation: Training regimes include prompt engineering, supervised fine-tuning (conditional on target proficiency tokens), and PPO-based RL alignment, with reward $R(y, t) = -\big(s_{\mathrm{cefr}}(y) - t\big)^2$ (Malik et al., 2024).
• Question Generation: A multi-type, multi-level item bank supports the stratified 20–60–20 selection algorithm: 20% review ($d=\theta-1$), 60% fit ($d=\theta$), 20% challenge ($d=\theta+1$), with dynamic re-exercise of incorrectly answered concepts (Huang et al., 2018).
• Robotics: Monte Carlo OA reporting and “control proportion” measurement ($$\frac{a_{\mathrm{robot}} - a_{\mathrm{participant}}}{a_{\mathrm{robot}} + a_{\mathrm{participant}}}$$) dynamically adapt operator-autonomy allocation (Conlon et al., 2022).
• Grip-Force Analytics: Data from FSR sensor gloves (12 channels per hand, 50 Hz sampling) feeds into a 49-neuron SOM with winner-take-all learning, generating QE profiles per session. Fixed 2 s windows yield finger-specific amplitude means (AmV), and statistical significance is assessed via two-way ANOVA (Liu et al., 2023).

4. Evaluation Protocols and Quantitative Results

Standardized metrics for PCT assessment emphasize sensitivity, reliability, and efficacy in either human learning, output adaptation, or collaborative task performance.

• LLMs: ControlError $(s_{\mathrm{cefr}}(y) - t)^2$ averaged over generations, with fluency/consistency ratings by GPT-4 and humans. CALM (7B LLaMa-2) + RL yields ControlError ≈ 0.15, surpassing GPT-4 prompting at a fraction of computational cost (Malik et al., 2024).
• Education: Key measures include rectification rate (proportion of prior incorrect concepts later answered correctly; 0.54 experimental vs 0.10 control), pre/posttest gain (paired $t$-test $p < 0.01$), and shifts in difficulty-wise accuracy distribution (significant $\chi^2$ effects for PCT group) (Huang et al., 2018).
• Human-Robot Teaming: Task failures are sharply reduced by high robot proficiency ($\chi^2(2,1237)=164.02, p<.0001$) and informed OA reports ($\chi^2(2,904)=19.813, p<.0001$). Operator trust is measured both subjectively (MDMT) and objectively (control proportion) (Conlon et al., 2022).
• Dexterity Monitoring: Experts display lower, stable STD and QE across sessions ($t(18)=9.27, p<.001$ dominant), and reduced completion times ($10.2 \to 7.5$ s expert vs $24.6 \to 18.8$ s novice), with incident counts $3$ vs $20$ (Liu et al., 2023).

5. Real-Time Operation, Feedback, and Extensions

PCT frameworks increasingly emphasize real-time or online operation, immediate feedback, and extensibility to novel domains.

• Language: CALM allows instant generation at any CEFR level via prefix token; top-$k$ sampling sharpens control (Malik et al., 2024).
• Adaptive Quizzing: Immediate re-exercise of “unclear” concepts accelerates rectification; personalization strategies (e.g., easier grammar/reading, on-level vocabulary) optimize gain (Huang et al., 2018).
• Robot Confidence: OA reports, displayed directly above control interfaces, powerfully shift operator control allocation toward optimal autonomy/teleoperation tradeoffs, and a plausible implication is that real-time self-assessment would address task drift not covered by a priori OA (Conlon et al., 2022).
• Real-Time Monitoring: Continuous 50 Hz sensor data drive sliding-window updates of STD, AmV, and SOM-QE; thresholds based on expert baselines trigger auditory/visual feedback, enabling rapid correction toward parsimonious force deployment (Liu et al., 2023).

6. Implications, Limitations, and Future Directions

PCT provides robust infrastructure for evidence-driven proficiency control, but several developmental fronts remain:

• Task Generalization and Transfer: Transfer learning (pre-trained SOM weights, model distillation) can seed proficiency calibration in related but novel domains (Liu et al., 2023, Malik et al., 2024).
• Multi-Modal Proficiency Sensing: Integration of haptic/force, computational, and behavioral signals enables richer, context-sensitive assessment, crucial for high-uncertainty environments such as NOTES/SILS surgery or stochastic robotics (Liu et al., 2023).
• Personalization Algorithms: Optimal challenge calibration depends on item type and individual learning curves; combining explicit proficiency grounding with fragile-concept tracking is essential for maximum rectification (Huang et al., 2018).
• Expanded Trust Metrics: In human–robot interaction, the multidimensionality of trust suggests that future PCTs may integrate cognitive, affective, and task-based trust components beyond performance and confidence (Conlon et al., 2022).

Across fields, PCT establishes a quantitatively anchored, adaptive process for mapping actions and system outputs to learner- or operator-specific proficiency levels, facilitating accelerated learning, trust calibration, and optimal task execution.