Using information fractal dimension as temperature in restricted Boltzmann Machine
Bibliographic record
Abstract
Contrastive Divergence (CD) has shown success in estimating the parameters of Markov Random Fields. Restricted Boltzmann Machine (RBM) updates weights of RBM architecture using CD to minimize the reconstruction error. Minimization of CD is fundamentally equivalent of finding the self-similarity among the training data and the estimated data. However, this self-similarity is measured at single measurement scale. Using fractal dimension, self-similarity at multiple scales is obtained and is denoted by a noninteger value. Fractal dimension provides a way to extract complexity features of an object using multiscale probabilistic measures and represents self-similar relationship in terms of a loglog scale. Also, CD algorithm is based on temperature based Boltzmann distribution but it does not incorporate the effects of temperature in the calculations. In this paper, the authors propose an information fractal dimension based temperature factor in RBM that is theoretically analogous to minimization of temperature based CD and provides better error optimization due to the inclusion of temperature dynamics between the visible and hidden states of RBM. Experimental results on standard data sets of MNIST and SVHN demonstrate promising performance showing better convergence of error and better generalization on validation data.
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How this classification was reachedexpand
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 | 0.001 | 0.004 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".