Human-Centered Learning Mechanics: Observable Entropy Control under Protected-Risk Constraints
Abstract
Entropy reduction is not a safety criterion: it can leave predictions unchanged or accompany increasing risk for a protected group. We study entropy-regulated learning under separately specified task, risk, and intervention constraints. A noise-calibrated log-determinant functional yields an exact spectral force formula and a metric decomposition into observable and prediction-null velocities. For scalar feedback, we characterize the complete interval of coefficients preserving a task-descent fraction and meeting an entropy-rate request; restricting intervention to observable directions can make that interval empty. For several protected risks, we derive an exact minimax certificate of feasibility within a specified subspace and norm budget, an exact robust extension for uncertain constraint rows, and a cone-projection formula for the entropy reduction remaining after protection. These formulas use standard convex geometry but identify when apparently active entropy control has no admissible effect. Barrier comparisons, finite-step curvature and gradient-error margins, and fresh-data audits give distinct conditional guarantees for risk thresholds. Human authority enters through the specification and release policy; the mathematics does not identify compression with alignment or certify human well-being. A memorization counterexample separates fresh-input information from sample-level information, and a noisy sample-code assumption supports a conditional generalization bound. Reproducible mathematical checks and a small real-data experiment expose both feasible interventions and failures. The resulting theory characterizes admissible entropy regulation and its limitations, rather than asserting universal accuracy or safety improvements.
Related
- A Structure-Preserving and Thermodynamically Compatible Cell-Centered Lagrangian Finite Volume Scheme for Continuum Mechanics
- Ramp Metering Control via Hybrid State Deep Reinforcement Learning in Partially Observable Connected Vehicle Environments
- Learning Topology-Aware Representations for Mechanics-Relevant TPMS Metamaterials
- Reassessing adult surfactant replacement therapy with mechanics-informed reinforcement learning
- Distributed Consensus, Optimization, and Learning under Communication Constraints
BibTeX
@misc{tran2026humancentered,
title = {{Human-Centered Learning Mechanics: Observable Entropy Control under Protected-Risk Constraints}},
author = {Kim Phuc Tran},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.22940},
eprint = {2605.22940},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.22940},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Human-Centered Learning Mechanics: Observable Entropy Control under Protected-Risk Constraints
AU - Kim Phuc Tran
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2605.22940
UR - https://arxiv.org/abs/2605.22940
AB - Entropy reduction is not a safety criterion: it can leave predictions unchanged or accompany increasing risk for a protected group. We study entropy-regulated learning under separately specified task, risk, and intervention constraints. A noise-calibrated log-determinant functional yields an exact spectral force formula and a metric decomposition into observable and prediction-null velocities. For scalar feedback, we characterize the complete interval of coefficients preserving a task-descent fraction and meeting an entropy-rate request; restricting intervention to observable directions can make that interval empty. For several protected risks, we derive an exact minimax certificate of feasibility within a specified subspace and norm budget, an exact robust extension for uncertain constraint rows, and a cone-projection formula for the entropy reduction remaining after protection. These formulas use standard convex geometry but identify when apparently active entropy control has no admissible effect. Barrier comparisons, finite-step curvature and gradient-error margins, and fresh-data audits give distinct conditional guarantees for risk thresholds. Human authority enters through the specification and release policy; the mathematics does not identify compression with alignment or certify human well-being. A memorization counterexample separates fresh-input information from sample-level information, and a noisy sample-code assumption supports a conditional generalization bound. Reproducible mathematical checks and a small real-data experiment expose both feasible interventions and failures. The resulting theory characterizes admissible entropy regulation and its limitations, rather than asserting universal accuracy or safety improvements.
ER -