One Blade for One Purpose: Advancing Math Information Retrieval using Hybrid Search
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 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