# EDGE: A Theoretical Framework for Misconception-Aware Adaptive Learning

arXiv: https://arxiv.org/abs/2508.07224 · HTML: https://mlsanity.com/paper/2508.07224/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 7 references that are in the map.
- First posted on arXiv 10 Aug 2025.

## Builds on (most cited first, 1 of 1)

- [Optimization Learning](https://mlsanity.com/paper/2501.03443/) (2025)

## Built on by (most cited first, 1 of 1)

- [Exam Readiness Index (ERI): A Theoretical Framework for a Composite, Explainable Index](https://mlsanity.com/paper/2509.00718/) (2025)

## Abstract (arXiv)

We present EDGE, a general-purpose, misconception-aware adaptive learning framework composed of four stages: Evaluate (ability and state estimation), Diagnose (posterior infer-ence of misconceptions), Generate (counterfactual item synthesis), and Exercise (index-based retrieval scheduling). EDGE unifies psychometrics (IRT/Bayesian state space models), cog-nitive diagnostics (misconception discovery from distractor patterns and response latencies), contrastive item generation (minimal perturbations that invalidate learner shortcuts while pre-serving psychometric validity), and principled scheduling (a restless bandit approximation to spaced retrieval). We formalize a composite readiness metric, EdgeScore, prove its monotonicity and Lipschitz continuity, and derive an index policy that is near-optimal under mild assumptions on forgetting and learning gains. We further establish conditions under which counterfactual items provably reduce the posterior probability of a targeted misconception faster than standard practice. The paper focuses on theory and implementable pseudocode; empirical study is left to future work.