# Robust Auto-associative Memory via Convolutional Restricted Hopfield Networks

arXiv: https://arxiv.org/abs/2606.20666 · HTML: https://mlsanity.com/paper/2606.20666/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 48 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Builds on (most cited first, 19 of 19)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Improving Transferability of Adversarial Examples with Input Diversity](https://mlsanity.com/paper/1803.06978/) (2018)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Nesterov Accelerated Gradient and Scale Invariance for Adversarial Attacks](https://mlsanity.com/paper/1908.06281/) (2019)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [Large Associative Memory Problem in Neurobiology and Machine Learning](https://mlsanity.com/paper/2008.06996/) (2020)
- [Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network](https://mlsanity.com/paper/1810.01279/) (2018)
- [Dense Associative Memory is Robust to Adversarial Inputs](https://mlsanity.com/paper/1701.00939/) (2017)
- [Associative Memories via Predictive Coding](https://mlsanity.com/paper/2109.08063/) (2021)
- [On Sparse Modern Hopfield Model](https://mlsanity.com/paper/2309.12673/) (2023)
- [Hybrid Predictive Coding: Inferring, Fast and Slow](https://mlsanity.com/paper/2204.02169/) (2022)
- [BayesPCN: A Continually Learnable Predictive Coding Associative Memory](https://mlsanity.com/paper/2205.09930/) (2022)
- [Adversarial Attacks to Machine Learning-Based Smart Healthcare Systems](https://mlsanity.com/paper/2010.03671/) (2020)
- [Back to the Continuous Attractor](https://mlsanity.com/paper/2408.00109/) (2024)
- [Hopfield-Fenchel-Young Networks: A Unified Framework for Associative Memory Retrieval](https://mlsanity.com/paper/2411.08590/) (2024)
- [Associative Memories in the Feature Space](https://mlsanity.com/paper/2402.10814/) (2024)

## Abstract (arXiv)

Associative memory models play a fundamental role in pattern retrieval, but their performance often degrades under adversarial perturbations and severe input corruptions. Existing approaches, including Modern Hopfield Networks (MHNs), and Predictive Coding Networks (PCNs), exhibit limitations in balancing storage capacity, computational efficiency, and robustness. In this paper, we propose a Convolutional Restricted Hopfield Networks (CRHNs), which integrates convolutional feature extraction with attractor-based memory retrieval in a structured latent space. The proposed model leverages subspace representations and fixed-point dynamics, trained via a gradient-free Subspace Rotation Algorithm (SRA), to enhance both robustness and memory capacity. Extensive experiments on Self-Taught Learning (STL) dataset demonstrate that CRHNs consistently achieve significantly lower reconstruction error compared to MHNs and PCNs across a wide range of adversarial attacks and input degradations. In many cases, CRHNs reduce reconstruction error by an order of magnitude and maintains stable retrieval performance under increasing perturbation strength. Statistical analysis further confirms that these improvements are significant (p < 0.01). These results highlight the effectiveness of attractor-based memory mechanisms and suggest that CRHNs provide a promising framework for building robust and scalable associative memory systems.