Simplex Clustering via sBeta With Applications to Online Adjustment of Black-Box Predictions
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Bibliographic record
Abstract
We explore clustering the softmax predictions of deep neural networks and introduce a novel probabilistic clustering method, referred to as <small>k-sBetas</small>. In the general context of clustering discrete distributions, the existing methods focused on exploring distortion measures tailored to simplex data, such as the KL divergence, as alternatives to the standard euclidean distance. We provide a general maximum a posteriori (MAP) perspective of clustering distributions, emphasizing that the statistical models underlying the existing distortion-based methods may not be descriptive enough. Instead, we optimize a mixed-variable objective measuring data conformity within each cluster to the introduced <inline-formula><tex-math notation="LaTeX">$\mathtt {sBeta}$</tex-math></inline-formula> density function, whose parameters are constrained and estimated jointly with binary assignment variables. Our versatile formulation approximates various parametric densities for modeling simplex data and enables the control of the cluster-balance bias. This yields highly competitive performances for the unsupervised adjustment of black-box model predictions in various scenarios.
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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 | 0.002 |
| 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