Phase Transitions for One-Vs-One and One-Vs-All Linear Separability in Multiclass Gaussian Mixtures
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We study a fundamental statistical question in multiclass classification: When are data linearly separable? Unlike binary classification, linear separability in multiclass settings can be defined in different ways. Here, we focus on the so called one-vs-one (OvO) and one-vs-all (OvA) linear separability. We consider data generated from a Gaussian mixture model (GMM) in a linear asymptotic high-dimensional regime. In this setting, we prove that both the OvO and OvA separability undergo a sharp phase-transition as a function of the overparameterization ratio. We present precise formulae characterizing the phase transitions as a function of the data geometry and the number of classes. Existing results on binary classification follow as special cases of our new formulae. Numerical simulations verify the validity of the asymptotic predictions in finite dimensions.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 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