Subspace Rotation Algorithm for Training Restricted Hopfield Network
Bibliographic record
Abstract
This paper introduces the Subspace Rotation Algorithm (SRA) to train the Restricted Hopfield Network (RHN) as an auto-associative memory.Subspace Rotation Algorithm is a gradient-free subspace tracking approach based on the Singular Value Decomposition (SVD).In comparison with Back-propagation Through Time (BPTT) on training Restricted Hopfield Network (RHN), it is observed that Subspace Rotation Algorithm (SRA) could always converge to the optimal solution and Back-propagation Through Time (BPTT) could not achieve the same performance when the model becomes complex, and the number of patterns is large.The AU T S case study showed that the Restricted Hopfield Network (RHN) model trained by Subspace Rotation Algorithm (SRA) could achieve a better structure of attraction basin with larger radius(in general) than the Hopfield Network(HNN) model trained by Hebbian learning rule.Through learning 10000 patterns from MNIST dataset with Restricted Hopfield Network (RHN) models with different number of hidden nodes, it is observed that several components could be adjusted to achieve a balance between recovery accuracy and noise resistance.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".