Curse of Dimensionality in Pivot Based Indexes
Why this work is in the frame
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Bibliographic record
Abstract
We offer a theoretical validation of the curse of dimensionality in the pivot based indexing of datasets for similarity search, by proving, in the framework of statistical learning, that in high dimensions no pivot based indexing scheme can essentially outperform the linear scan. A study of the asymptotic performance of pivot based indexing schemes is performed on a sequence of datasets modeled as samples picked in i.i.d. fashion from a sequence of metric spaces. We allow the size of the dataset to grow in relation to dimension, such that the dimension is superlogarithmic but subpolynomial in the size of the dataset. The number of pivots is sublinear in the size of the dataset. We pick the least restrictive cost model of similarity search where we count each distance calculation as a single computation and disregard the rest. We demonstrate that if the intrinsic dimension of the spaces in the sense of concentration of measure phenomenon is linear in dimension, then the performance of similarity search pivot based indexes is asymptotically linear in the size of the dataset.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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