# Reproducible macroscopic dynamics in a closed-loop human-AI learning system

arXiv: https://arxiv.org/abs/2608.30946 · HTML: https://mlsanity.com/paper/2608.30946/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 49 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [EdNet: A Large-Scale Hierarchical Dataset in Education](https://mlsanity.com/paper/1912.03072/) (2019)
- [There Will Be a Scientific Theory of Deep Learning](https://mlsanity.com/paper/2604.21691/) (2026)
- [Constructing Custom Thermodynamics Using Deep Learning](https://mlsanity.com/paper/2308.04119/) (2023)
- [Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings](https://mlsanity.com/paper/2411.00989/) (2024)

## Abstract (arXiv)

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.