Reproducible macroscopic dynamics in a closed-loop human-AI learning system
2026-08-31 • Machine Learning
Machine Learning
AI summaryⓘ
The authors studied how people learn using an AI tutoring system by analyzing a large set of learner behavior data. They found patterns in how learners move through different learning states, showing consistent flows and stable behaviors over time. By creating and testing mathematical models, the authors could predict how learner progress drifts and changes. Their work links these observed learning patterns to mechanisms that resemble neural computation, providing a way to understand complex learning dynamics.
closed-loop systemsadaptive tutoringbehavioral trajectoriesmetastable kineticspopulation driftself-supervised learningneural computationstate-space modelingflow dynamicsbootstrap confidence interval
Authors
Minlin Wu, Xu Fang, Yicheng Zhang, Chenyu Zhou, Zhiyi Liu
Abstract
Closed-loop human-AI systems generate high-dimensional behavioural trajectories whose collective dynamics remain obscure. Using 297,915 learners' adaptive-tutoring histories, we define semantic order variables before model fitting and test them in user-disjoint cohorts. The state exhibits reproducible basin-like flow and operationally defined, state-heterogeneous metastable-like kinetics. A construction-matched null distinguishes normalised-memory relaxation from a reproducible excess field. A four-term conditional mechanism recovers population drift (r = 0.946; learner-bootstrap 95% CI, 0.935-0.955). Predictive event-level self-supervised learning recovers the state and learned-plane flow; null-referenced corrections retain directional, partial-amplitude excess-field structure without full calibration. Shuffled-order training reverses learned-plane flow on ordered trajectories; support-alignment randomisation selectively reduces inward transport. Both axes remain linearly accessible without state supervision. Without cross-model fitting, the models share leading population drift (r = 0.866; learner-bootstrap 95% CI, 0.857-0.875) and persistence ordering; residual directions remain model-specific. These results identify an externally anchored leading-order effective field linking empirical dynamics, an interpretable mechanism and neural computation.