Fast Graph Sampling for Short Video Summarization Using Gershgorin Disc Alignment
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Bibliographic record
Abstract
We study the problem of efficiently summarizing a short video into several keyframes, leveraging recent progress in fast graph sampling. Specifically, we first construct a similarity path graph (SPG) G, represented by graph Laplacian matrix L, where the similarities between adjacent frames are encoded as positive edge weights. We show that maximizing the smallest eigenvalue λ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</inf> (B) of a coefficient matrix B = diag(a) + µL, where a is the binary keyframe selection vector, is equivalent to minimizing a worst-case signal reconstruction error. We prove that, after partitioning $\mathcal{G}$ into Q sub-graphs $\left\{ {{\mathcal{G}^q}} \right\}_{q = 1}^Q$, the smallest Gershgorin circle theorem (GCT) lower bound of Q corresponding coefficient matrices—${\min _q}\lambda _{\min }^ - \left( {{{\mathbf{B}}^q}} \right)$—is a lower bound for λ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</inf> (B). This inspires a fast graph sampling algorithm to iteratively partition $\mathcal{G}$ into Q sub-graphs using Q samples (keyframes), while maximizing $\lambda _{\min }^ - \left( {{{\mathbf{B}}^q}} \right)$ for each sub-graph ${\mathcal{G}^q}$. Experimental results show that our algorithm achieves comparable video summarization performance as state-of-the-art methods, at a substantially reduced complexity.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 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