On Autoencoders and Score Matching for Energy Based Models
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Bibliographic record
Abstract
We consider estimation methods for the class of continuous-data energy based models (EBMs). Our main result shows that estimating the parameters of an EBM using score matching when the conditional distribution over the visible units is Gaussian corresponds to training a particular form of regularized autoencoder. We show how different Gaussian EBMs lead to different autoencoder architectures, providing deep links between these two families of models. We compare the score matching estimator for the mPoT model, a particular Gaussian EBM, to several other training methods on a variety of tasks including image denoising and unsupervised feature extraction. We show that the regularization function induced by score matching leads to superior classification performance relative to a standard autoencoder. We also show that score matching yields classification results that are indistinguishable from better-known stochastic approximation maximum likelihood estimators. 1.
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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 | 0.000 | 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