# Associative Memories via Predictive Coding

arXiv: https://arxiv.org/abs/2109.08063 · HTML: https://mlsanity.com/paper/2109.08063/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 16 Sep 2021.

## Builds on (most cited first, 14 of 14)

- [Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models](https://mlsanity.com/paper/1505.04870/) (2015)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning](https://mlsanity.com/paper/1605.08104/) (2016)
- [Large Associative Memory Problem in Neurobiology and Machine Learning](https://mlsanity.com/paper/2008.06996/) (2020)
- [Predictive Coding Approximates Backprop along Arbitrary Computation Graphs](https://mlsanity.com/paper/2006.04182/) (2020)
- [Every Model Learned by Gradient Descent Is Approximately a Kernel Machine](https://mlsanity.com/paper/2012.00152/) (2020)
- [Modern Hopfield Networks and Attention for Immune Repertoire Classification](https://mlsanity.com/paper/2007.13505/) (2020)
- [Overparameterized Neural Networks Implement Associative Memory](https://mlsanity.com/paper/1909.12362/) (2019)
- [Unsupervised Learning by Competing Hidden Units](https://mlsanity.com/paper/1806.10181/) (2018)
- [The Neural Coding Framework for Learning Generative Models](https://mlsanity.com/paper/2012.03405/) (2020)
- [Predictive Coding Can Do Exact Backpropagation on Convolutional and Recurrent Neural Networks](https://mlsanity.com/paper/2103.03725/) (2021)
- [Meta-Learning Deep Energy-Based Memory Models](https://mlsanity.com/paper/1910.02720/) (2019)

## Built on by (most cited first, 30 of 44)

- [Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models](https://mlsanity.com/paper/2202.04557/) (2022)
- [Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?](https://mlsanity.com/paper/2202.09467/) (2022)
- [In search of dispersed memories: Generative diffusion models are associative memory networks](https://mlsanity.com/paper/2309.17290/) (2023)
- [Uniform Memory Retrieval with Larger Capacity for Modern Hopfield Models](https://mlsanity.com/paper/2404.03827/) (2024)
- [The Predictive Forward-Forward Algorithm](https://mlsanity.com/paper/2301.01452/) (2023)
- [Learning on Arbitrary Graph Topologies via Predictive Coding](https://mlsanity.com/paper/2201.13180/) (2022)
- [Brain-inspired Computational Intelligence via Predictive Coding](https://mlsanity.com/paper/2308.07870/) (2023)
- [Benchmarking Predictive Coding Networks -- Made Simple](https://mlsanity.com/paper/2407.01163/) (2024)
- [Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learning](https://mlsanity.com/paper/2206.02629/) (2022)
- [A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networks](https://mlsanity.com/paper/2212.00720/) (2022)
- [A Theoretical Framework for Inference Learning](https://mlsanity.com/paper/2206.00164/) (2022)
- [Predictive Coding beyond Gaussian Distributions](https://mlsanity.com/paper/2211.03481/) (2022)
- [Sequential Memory with Temporal Predictive Coding](https://mlsanity.com/paper/2305.11982/) (2023)
- [BayesPCN: A Continually Learnable Predictive Coding Associative Memory](https://mlsanity.com/paper/2205.09930/) (2022)
- [Convolutional Neural Generative Coding: Scaling Predictive Coding to Natural Images](https://mlsanity.com/paper/2211.12047/) (2022)
- [Predictive Coding Networks and Inference Learning: Tutorial and Survey](https://mlsanity.com/paper/2407.04117/) (2024)
- [Towards the Training of Deeper Predictive Coding Neural Networks](https://mlsanity.com/paper/2506.23800/) (2025)
- [Predictive Coding beyond Correlations](https://mlsanity.com/paper/2306.15479/) (2023)
- [A Review of Neuroscience-Inspired Machine Learning](https://mlsanity.com/paper/2403.18929/) (2024)
- [Robust Graph Representation Learning via Predictive Coding](https://mlsanity.com/paper/2212.04656/) (2022)
- [A Sparse Quantized Hopfield Network for Online-Continual Memory](https://mlsanity.com/paper/2307.15040/) (2023)
- [Saliency-Guided Hidden Associative Replay for Continual Learning](https://mlsanity.com/paper/2310.04334/) (2023)
- [Bidirectional predictive coding](https://mlsanity.com/paper/2505.23415/) (2025)
- [On the Relationship Between Variational Inference and Auto-Associative Memory](https://mlsanity.com/paper/2210.08013/) (2022)
- [Neural Sampling in Hierarchical Exponential-family Energy-based Models](https://mlsanity.com/paper/2310.08431/) (2023)
- [Improving deep learning with prior knowledge and cognitive models: A survey on enhancing explainability, adversarial robustness and zero-shot learning](https://mlsanity.com/paper/2403.07078/) (2024)
- [Tight Stability, Convergence, and Robustness Bounds for Predictive Coding Networks](https://mlsanity.com/paper/2410.04708/) (2024)
- [Faster Predictive Coding Networks via Better Initialization](https://mlsanity.com/paper/2601.20895/) (2026)
- [Autoencoder Attractors for Uncertainty Estimation](https://mlsanity.com/paper/2204.00382/) (2022)
- [Associative Memories in the Feature Space](https://mlsanity.com/paper/2402.10814/) (2024)

## Abstract (arXiv)

Associative memories in the brain receive and store patterns of activity registered by the sensory neurons, and are able to retrieve them when necessary. Due to their importance in human intelligence, computational models of associative memories have been developed for several decades now. They include autoassociative memories, which allow for storing data points and retrieving a stored data point s when provided with a noisy or partial variant of s, and heteroassociative memories, able to store and recall multi-modal data. In this paper, we present a novel neural model for realizing associative memories, based on a hierarchical generative network that receives external stimuli via sensory neurons. This model is trained using predictive coding, an error-based learning algorithm inspired by information processing in the cortex. To test the capabilities of this model, we perform multiple retrieval experiments from both corrupted and incomplete data points. In an extensive comparison, we show that this new model outperforms in retrieval accuracy and robustness popular associative memory models, such as autoencoders trained via backpropagation, and modern Hopfield networks. In particular, in completing partial data points, our model achieves remarkable results on natural image datasets, such as ImageNet, with a surprisingly high accuracy, even when only a tiny fraction of pixels of the original images is presented. Furthermore, we show that this method is able to handle multi-modal data, retrieving images from descriptions, and vice versa. We conclude by discussing the possible impact of this work in the neuroscience community, by showing that our model provides a plausible framework to study learning and retrieval of memories in the brain, as it closely mimics the behavior of the hippocampus as a memory index and generative model.