Fast Cosine Similarity Search in Binary Space with Angular Multi-Index Hashing
Why this work is in the frame
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Bibliographic record
Abstract
Given a large dataset of binary codes and a binary query point, we address how to efficiently find <inline-formula><tex-math notation="LaTeX">$K$</tex-math></inline-formula> codes in the dataset that yield the largest cosine similarities to the query. The straightforward answer to this problem is to compare the query with all items in the dataset, but this is practical only for small datasets. One potential solution to enhance the search time and achieve sublinear cost is to use a hash table populated with binary codes of the dataset and then look up the nearby buckets to the query to retrieve the nearest neighbors. However, if codes are compared in terms of cosine similarity rather than the Hamming distance, then the main issue is that the order of buckets to probe is not evident. To examine this issue, we first elaborate on the connection between the Hamming distance and the cosine similarity. Doing this allows us to systematically find the probing sequence in the hash table. However, solving the nearest neighbor search with a single table is only practical for short binary codes. To address this issue, we propose the angular multi-index hashing search algorithm which relies on building multiple hash tables on binary code substrings. The proposed search algorithm solves the exact angular <inline-formula><tex-math notation="LaTeX">$K$</tex-math></inline-formula> nearest neighbor problem in a time that is often orders of magnitude faster than the linear scan baseline and even approximation methods.
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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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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