# Adaptive Hopfield Network: Rethinking Similarities in Associative Memory

arXiv: https://arxiv.org/abs/2511.20609 · HTML: https://mlsanity.com/paper/2511.20609/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 25 Nov 2025.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [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)
- [Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models](https://mlsanity.com/paper/2202.04557/) (2022)
- [On Sparse Modern Hopfield Model](https://mlsanity.com/paper/2309.12673/) (2023)
- [Uniform Memory Retrieval with Larger Capacity for Modern Hopfield Models](https://mlsanity.com/paper/2404.03827/) (2024)
- [Provably Optimal Memory Capacity for Modern Hopfield Models: Transformer-Compatible Dense Associative Memories as Spherical Codes](https://mlsanity.com/paper/2410.23126/) (2024)
- [Nonparametric Modern Hopfield Models](https://mlsanity.com/paper/2404.03900/) (2024)
- [End-to-end Differentiable Clustering with Associative Memories](https://mlsanity.com/paper/2306.03209/) (2023)
- [Modern Methods in Associative Memory](https://mlsanity.com/paper/2507.06211/) (2025)
- [Harnessing the Power of the Crowd to Increase Capacity for Data Science in the Social Sector](https://mlsanity.com/paper/1606.07781/) (2016)
- [DynFrs: An Efficient Framework for Machine Unlearning in Random Forest](https://mlsanity.com/paper/2410.01588/) (2024)

## Built on by (most cited first, 1 of 1)

- [Active Adversarial Perturbation-driven Associative Memory Retrieval for RGB-Event Visual Object Tracking](https://mlsanity.com/paper/2606.26455/) (2026)

## Abstract (arXiv)

Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which cannot guarantee that the retrieved pattern has the strongest association with the query, failing correctness. We reframe this problem by proposing that a query is a generative variant of a stored memory pattern, and define a variant distribution to model this subtle context-dependent generative process. Consequently, correct retrieval should return the memory pattern with the maximum a posteriori probability of being the query's origin. This perspective reveals that an ideal similarity measure should approximate the likelihood of each stored pattern generating the query in accordance with variant distribution, which is impossible for fixed and pre-defined similarities used by existing associative memories. To this end, we develop adaptive similarity, a novel mechanism that learns to approximate this insightful but unknown likelihood from samples drawn from context, aiming for correct retrieval. We theoretically prove that our proposed adaptive similarity achieves optimal correct retrieval under three canonical and widely applicable types of variants: noisy, masked, and biased. We integrate this mechanism into a novel adaptive Hopfield network (A-Hop), and empirical results show that it achieves state-of-the-art performance across diverse tasks, including memory retrieval, tabular classification, image classification, and multiple instance learning.