Low-Dimensional Perturb-and-MAP Approach for Learning Restricted Boltzmann Machines
Bibliographic record
Abstract
This paper introduces a new approach to maximum likelihood learning of the parameters of a restricted Boltzmann machine (RBM). The proposed method is based on the Perturb-and-MAP (PM) paradigm that enables sampling from the Gibbs distribution. PM is a two step process: (i) perturb the model using Gumbel perturbations, then (ii) find the maximum a posteriori (MAP) assignment of the perturbed model. We show that under certain conditions the resulting MAP configuration of the perturbed model is an unbiased sample from the original distribution. However, this approach requires an exponential number of perturbations, which is computationally intractable. Here, we apply an approximate approach based on the first order (low-dimensional) PM to calculate the gradient of the log-likelihood in binary RBM. Our approach relies on optimizing the energy function with respect to observable and hidden variables using a greedy procedure. First, for each variable we determine whether flipping this value will decrease the energy, and then we utilize the new local maximum to approximate the gradient. Moreover, we show that in some cases our approach works better than the standard coordinate-descent procedure for finding the MAP assignment and compare it with the Contrastive Divergence algorithm. We investigate the quality of our approach empirically, first on toy problems, then on various image datasets and a text dataset.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".