One Blade for One Purpose: Advancing Math Information Retrieval using Hybrid Search
Bibliographic record
Abstract
Neural retrievers have been shown to be effective for math-aware search. Their ability to cope with math symbol mismatches, to represent highly contextualized semantics, and to learn effective representations are critical to improving math information retrieval. However, the most effective retriever for math remains impractical as it depends on token-level dense representations for each math token, which leads to prohibitive storage demands, especially considering that math content generally consumes more tokens. In this work, we try to alleviate this efficiency bottleneck while boosting math information retrieval effectiveness via hybrid search. To this end, we propose MABOWDOR, a Math-Aware Bestof-Worlds Domain Optimized Retriever, which has an unsupervised structure search component, a dense retriever, and optionally a sparse retriever on top of a domain-adapted backbone learned by context-enhanced pretraining, each addressing a different need in retrieving heterogeneous data from math documents. Our hybrid search outperforms the previous state-of-the-art math IR system while eliminating efficiency bottlenecks. Our system is available at https://github.com/approach0/pya0.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.014 | 0.017 |
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".