On the mapping between Hopfield networks and Restricted Boltzmann\n Machines
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Bibliographic record
Abstract
Hopfield networks (HNs) and Restricted Boltzmann Machines (RBMs) are two\nimportant models at the interface of statistical physics, machine learning, and\nneuroscience. Recently, there has been interest in the relationship between HNs\nand RBMs, due to their similarity under the statistical mechanics formalism. An\nexact mapping between HNs and RBMs has been previously noted for the special\ncase of orthogonal (uncorrelated) encoded patterns. We present here an exact\nmapping in the case of correlated pattern HNs, which are more broadly\napplicable to existing datasets. Specifically, we show that any HN with $N$\nbinary variables and $p<N$ arbitrary binary patterns can be transformed into an\nRBM with $N$ binary visible variables and $p$ gaussian hidden variables. We\noutline the conditions under which the reverse mapping exists, and conduct\nexperiments on the MNIST dataset which suggest the mapping provides a useful\ninitialization to the RBM weights. We discuss extensions, the potential\nimportance of this correspondence for the training of RBMs, and for\nunderstanding the performance of deep architectures which utilize RBMs.\n
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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 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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