Restricted Hopfield Networks are Robust to Adversarial Attack
Bibliographic record
Abstract
The Restricted Hopfield Network (RHN) builds upon the classical Hopfield Neural Network (HNN) by introducing multiple hidden layers and employing the Subspace Rotation Algorithm (SRA) for training. These advancements address the limitations of traditional HNNs, such as limited storage capacity and vulnerability to noise and adversarial perturbations. RHNs with orthogonal weight matrices trained by SRA can form stable attraction basins, enhancing their capacity and adversarial resilience. This paper systematically evaluates RHN against Dense Associative Memory (DAM), Predictive Coding Network (PCN), and Multilayer Perceptron (MLP) in terms of adversarial robustness and retrieval performance using incomplete patterns. Experiments using alphabet and character datasets demonstrate that RHN consistently outperforms the other models across a variety of adversarial scenarios, including Fast Gradient Sign Method (FGSM), Basic Iterative Method (BIM), Projected Gradient Descent (PGD), and Gaussian Noise (GN) attacks. The results show that RHNs trained with SRA not only enhance model capacity but also ensure high retrieval accuracy under adversarial conditions. These findings highlight the robustness and versatility of RHN as an effective solution for adversarially resilient memory systems.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".