Recognizing mathematical expressions using tree transformation
Why this work is in the frame
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Bibliographic record
Abstract
We describe a robust and efficient system for recognizing typeset and handwritten mathematical notation. From a list of symbols with bounding boxes the system analyzes an expression in three successive passes. The Layout Pass constructs a Baseline Structure Tree (BST) describing the two-dimensional arrangement of input symbols. Reading order and operator dominance are used to allow efficient recognition of symbol layout even when symbols deviate greatly from their ideal positions. Next, the Lexical Pass produces a Lexed BST from the initial BST by grouping tokens comprised of multiple input symbols; these include decimal numbers, function names, and symbols comprised of nonoverlapping primitives such as "=". The Lexical Pass also labels vertical structures such as fractions and accents. The Lexed BST is translated into L/sup A/T/sub E/X. Additional processing, necessary for producing output for symbolic algebra systems, is carried out in the Expression Analysis Pass. The Lexed BST is translated into an Operator Tree, which describes the order and scope of operations in the input expression. The tree manipulations used in each pass are represented compactly using tree transformations. The compiler-like architecture of the system allows robust handling of unexpected input, increases the scalability of the system, and provides the groundwork for handling dialects of mathematical notation.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it