Continual Release of Densest Subgraphs: Privacy Amplification & Sublinear Space via Subsampling
Bibliographic record
Abstract
We study the sublinear space continual release model for edge-differentially private (DP) graph algorithms, with a focus on the densest subgraph problem (DSG) in the insertion-only setting. Our main result is the first continual release DSG algorithm that matches the additive error of the best static DP algorithms and the space complexity of the best non-private streaming algorithms, up to constants. The key idea is a refined use of subsampling that simultaneously achieves privacy amplification and sparsification, a connection not previously formalized in graph DP. Via a simple black-box reduction to the static setting, we obtain both pure and approximate-DP algorithms with $O(\log n)$ additive error and $O(n\log n)$ space, improving both accuracy and space complexity over the previous state of the art. Along the way, we introduce graph densification in the graph DP setting, adding edges to trigger earlier subsampling, which removes the extra logarithmic factors in error and space incurred by prior work [ELMZ25]. We believe this simple idea may be of independent interest.
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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 | 0.006 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.010 |
| Open science | 0.004 | 0.007 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".