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README.md
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- misconception-detection
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- k-12
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- math
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- misconception-detection
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- k-12
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- math
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---
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# qlm-map-classifier
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**A DeBERTa-v3 misconception-detection classifier for K-12 mathematics tutoring, in production at Quantum Learning Machines since April 2026.** It classifies student utterances and worked steps against a taxonomy of documented math misconceptions, and serves as an *observation model* feeding a Bayesian student-state layer — not as a standalone judge of student thinking. We publish it, with its honest numbers, because the field's progress depends on knowing what this class of model can and cannot do.
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## What it does in production
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Given a student turn (utterance, answer, or worked step) in a math tutoring context, the model emits misconception-class probabilities over 34 production classes drawn from QLM's 481-construct misconception ontology (423 constructs public under CC-BY-4.0 via our export API). Its outputs are **not** used to label students directly. They enter a persistent Bayesian posterior alongside triage signals that distinguish misconception-driven errors from slips and disengagement; instructional decisions condition on the accumulated state, not on any single classifier call.
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## Evaluation — read the limitations first
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Evaluated on an internal MathTutorBench-derived error-detection probe (unseen, GSM8K-based). All figures below are from versioned result files.
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| Variant | Detection recall | Mistake-location accuracy | Notes |
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|---|---|---|---|
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| **MAP-34 (this model, deployed)** | **25.1%** | **19.0%** | conservative by design; low over-flagging |
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| Combined-39 (research retrain, not deployed) | 86.2% | 16.3% | 8,207 mixed examples (EEDI public + expert-pattern-derived synthetic); **49.5% solution-correctness accuracy — severe over-flagging** |
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| EEDI-only retrain (not deployed) | 72.1% | 15.7% | same over-flagging pattern |
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| Bare LLM baseline (no classifier) | 78.3% | 14.7% (F1 micro) | flags nearly everything |
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**The pattern that matters:** every high-recall variant achieves its recall by over-flagging — calling correct or merely-slipped work "misconception." The training corpora available to this task (misconception-labeled datasets, expert-authored trigger patterns) contain, by construction, **no negative space**: no slips, no disengagement, no correct-but-unconventional work. A classifier trained only on what misconceptions look like cannot learn what they *don't* look like. This is a data-ecology finding about the field, not an implementation artifact — and it is why the deployed configuration is conservative and why the architecture treats the classifier as one observation source among several.
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## The architecture lesson (ablation)
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In controlled ablation, injecting this classifier's outputs directly into a tutor model's per-turn prompt **reduced** tutoring quality (solution-correctness evaluation: 60% → 55%). Classifier signal helps when integrated as evidence into persistent student state; it hurts when bolted onto generation. Build state layers, not prompt decorations.
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## Training data
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Production K-12 tutoring interaction data (private; de-identified), labeled against the misconception ontology. We do not publish interaction counts or corpus composition. The ontology's public tier — 423 constructs with descriptions, diagnostic questions, and research citations — is available CC-BY-4.0 via the QLM export API.
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## Intended use
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- Research on misconception detection, error-type triage, and tutoring-system evaluation
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- As an observation component inside stateful student-modeling systems
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- Reproducing and extending the negative-space findings above
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## Out-of-scope use
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- Grading, placement, or any consequential decision about an individual student
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- Standalone "misconception detector" products without state-level integration and human oversight
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- Non-mathematics domains; languages other than English (untested)
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## Bias, risks, and limitations
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Detection behavior has not been separately validated across demographic subgroups; measurement-invariance testing on authentic classroom data is planned, funded work. Low recall means many real misconceptions pass undetected; downstream systems must not treat absence of a flag as evidence of understanding. Trained on production interactions from QLM platforms; distribution shift to other tutoring contexts is untested.
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## Citation
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@software{qlm_map_classifier_2026,
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author = {Quantum Learning Machines},
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title = {qlm-map-classifier: misconception detection as an observation model},
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year = {2026},
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url = {https://huggingface.co/QuantumLearningMachines/qlm-map-classifier},
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license = {Apache-2.0}
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}
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## Contact: hello@quantumlearningmachines.com · quantumlearningmachines.com
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