Discretely Relaxing Continuous Variables for tractable Variational Inference
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Bibliographic record
Abstract
We explore a new research direction in Bayesian variational inference with discrete latent variable priors where we exploit Kronecker matrix algebra for efficient and exact computations of the evidence lower bound (ELBO). The proposed "DIRECT" approach has several advantages over its predecessors; (i) it can exactly compute ELBO gradients (i.e. unbiased, zero-variance gradient estimates), eliminating the need for high-variance stochastic gradient estimators and enabling the use of quasi-Newton optimization methods; (ii) its training complexity is independent of the number of training points, permitting inference on large datasets; and (iii) its posterior samples consist of sparse and low-precision quantized integers which permit fast inference on hardware limited devices. In addition, our DIRECT models can exactly compute statistical moments of the parameterized predictive posterior without relying on Monte Carlo sampling. The DIRECT approach is not practical for all likelihoods, however, we identify a popular model structure which is practical, and demonstrate accurate inference using latent variables discretized as extremely low-precision 4-bit quantized integers. While the ELBO computations considered in the numerical studies require over $10^{2352}$ log-likelihood evaluations, we train on datasets with over two-million points in just seconds.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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