Implementing Restricted Hopfield Network as Robust Auto-associative Memory Using Subspace Rotation Algorithm
Bibliographic record
Abstract
Both the Restricted Hopfield Network (RHN) and Dense Associative Memory (DAM) are derived from the classical Hopfield Neural Network (HNN), but they improve upon HNN using different mechanisms. This paper presents a comparative analysis of RHN and DAM with respect to storage capacity, time complexity, training efficiency, and retrieval from incomplete or noisy patterns. The analysis reveals that RHN and DAM use different mechanisms for storing patterns. RHN, trained using the Subspace Rotation Algorithm (SRA), exhibits better time complexity than DAM, which is trained using the Energy-based Algorithm (EBA). Furthermore, in practice, RHN requires significantly less time than DAM to memorize the same number of patterns, as DAM needs more epochs to converge. The experimental results demonstrate that when storing 1,000 character patterns (825 bits), RHN with two hidden layers outperforms DAM in terms of retrieval from noisy and incomplete patterns. When memorizing 10, 50, and 100 patterns from both the MNIST and Fashion MNIST datasets, RHN shows a slight advantage over DAM in retrieval from incomplete and noisy patterns. However, the performance of both models degrades as the number of hidden nodes or stored patterns increases.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".