Structured and Efficient Variational Deep Learning with Matrix Gaussian\n Posteriors
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Bibliographic record
Abstract
We introduce a variational Bayesian neural network where the parameters are\ngoverned via a probability distribution on random matrices. Specifically, we\nemploy a matrix variate Gaussian \\cite{gupta1999matrix} parameter posterior\ndistribution where we explicitly model the covariance among the input and\noutput dimensions of each layer. Furthermore, with approximate covariance\nmatrices we can achieve a more efficient way to represent those correlations\nthat is also cheaper than fully factorized parameter posteriors. We further\nshow that with the "local reprarametrization trick"\n\\cite{kingma2015variational} on this posterior distribution we arrive at a\nGaussian Process \\cite{rasmussen2006gaussian} interpretation of the hidden\nunits in each layer and we, similarly with \\cite{gal2015dropout}, provide\nconnections with deep Gaussian processes. We continue in taking advantage of\nthis duality and incorporate "pseudo-data" \\cite{snelson2005sparse} in our\nmodel, which in turn allows for more efficient sampling while maintaining the\nproperties of the original model. The validity of the proposed approach is\nverified through extensive experiments.\n
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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 | 0.001 | 0.001 |
| 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