MathBrush: A System for Doing Math on Pen-Based Devices
Bibliographic record
Abstract
Many on-line (interactive) mathematics recognition systems allow the creation of typeset equations, normally in LaTeX, but they do not support mathematical problem solving. In this paper, we present MathBrush, a system that allows users to draw math input using a pen-input device on a tablet computer, recognizes the math expression, and then supports mathematical transformation and problem solving using back-end Computer Algebra Systems (CAS). We describe the architecture of the MathBrush system, which includes modules that support symbol recognition, semantic analysis, the transfer of recognized expressions to back-end CAS, and interface techniques for interacting with CAS output. We also identify unique challenges associated with recognition for math problem solving, such as the need for deeper semantic analysis than is required by LATEX, and the need to deal with ambiguities in user input. Our experiences serve to inform researchers seeking to design interactive mathematics recognition systems geared toward mathematical problem solving.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.082 | 0.025 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".