Universal approximation results for the temporal restricted Boltzmann machine and the recurrent temporal restricted Boltzmann machine
Bibliographic record
Abstract
The Restricted Boltzmann Machine (RBM) has proved to be a powerful tool in machine learning, both on its own and as the building block for Deep Belief Networks (multi-layer generative graphical models). The RBM and Deep Belief Network have been shown to be universal approximators for probability distributions on binary vectors. In this paper we prove several similar universal approximation results for two variations of the Restricted Boltzmann Machine with time dependence, the Temporal Restricted Boltzmann Machine (TRBM) and the Recurrent Temporal Restricted Boltzmann Machine (RTRBM). We show that the TRBM is a universal approximator for Markov chains and generalize the theorem to sequences with longer time dependence. We then prove that the RTRBM is a universal approximator for stochastic processes with nite time dependence. We conclude with a discussion on e ciency and how the constructions developed could explain some previous experimental results.
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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 | 0.004 | 0.019 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.007 | 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".