# A Sparse Quantized Hopfield Network for Online-Continual Memory

arXiv: https://arxiv.org/abs/2307.15040 · HTML: https://mlsanity.com/paper/2307.15040/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 70 references that are in the map.
- First posted on arXiv 27 Jul 2023.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Towards Continual Reinforcement Learning: A Review and Perspectives](https://mlsanity.com/paper/2012.13490/) (2020)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Online Continual Learning in Image Classification: An Empirical Survey](https://mlsanity.com/paper/2101.10423/) (2021)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1805.07810/) (2018)
- [A Neural Dirichlet Process Mixture Model for Task-Free Continual Learning](https://mlsanity.com/paper/2001.00689/) (2020)
- [Dendritic cortical microcircuits approximate the backpropagation algorithm](https://mlsanity.com/paper/1810.11393/) (2018)
- [A Tutorial on Learning With Bayesian Networks](https://mlsanity.com/paper/2002.00269/) (2020)
- [Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models](https://mlsanity.com/paper/2202.04557/) (2022)
- [Self-Supervised Training Enhances Online Continual Learning](https://mlsanity.com/paper/2103.14010/) (2021)
- [Online Continual Learning for Embedded Devices](https://mlsanity.com/paper/2203.10681/) (2022)
- [Associative Memories via Predictive Coding](https://mlsanity.com/paper/2109.08063/) (2021)
- [Accurate online training of dynamical spiking neural networks through Forward Propagation Through Time](https://mlsanity.com/paper/2112.11231/) (2021)
- [A Theoretical Framework for Inference and Learning in Predictive Coding Networks](https://mlsanity.com/paper/2207.12316/) (2022)
- [Sequential Memory with Temporal Predictive Coding](https://mlsanity.com/paper/2305.11982/) (2023)
- [Properties of Sparse Distributed Representations and their Application to Hierarchical Temporal Memory](https://mlsanity.com/paper/1503.07469/) (2015)

## Built on by (most cited first, 5 of 5)

- [HiCL: Hippocampal-Inspired Continual Learning](https://mlsanity.com/paper/2508.16651/) (2025)
- [Asymptotically Stable Quaternion-valued Hopfield-structured Neural Network with Periodic Projection-based Supervised Learning Rules](https://mlsanity.com/paper/2510.16607/) (2025)
- [Online Vector Quantized Attention](https://mlsanity.com/paper/2602.03922/) (2026)
- [Improved Robustness and Hyperparameter Selection in the Dense Associative Memory](https://mlsanity.com/paper/2407.08742/) (2024)
- [Benchmarking local Hebbian learning rules for memory storage and prototype extraction](https://mlsanity.com/paper/2605.01074/) (2026)

## Abstract (arXiv)

An important difference between brains and deep neural networks is the way they learn. Nervous systems learn online where a stream of noisy data points are presented in a non-independent, identically distributed (non-i.i.d.) way. Further, synaptic plasticity in the brain depends only on information local to synapses. Deep networks, on the other hand, typically use non-local learning algorithms and are trained in an offline, non-noisy, i.i.d. setting. Understanding how neural networks learn under the same constraints as the brain is an open problem for neuroscience and neuromorphic computing. A standard approach to this problem has yet to be established. In this paper, we propose that discrete graphical models that learn via an online maximum a posteriori learning algorithm could provide such an approach. We implement this kind of model in a novel neural network called the Sparse Quantized Hopfield Network (SQHN). We show that SQHNs outperform state-of-the-art neural networks on associative memory tasks, outperform these models in online, non-i.i.d. settings, learn efficiently with noisy inputs, and are better than baselines on a novel episodic memory task.