# Effects of Feature Correlations on Associative Memory Capacity

arXiv: https://arxiv.org/abs/2508.01395 · HTML: https://mlsanity.com/paper/2508.01395/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 16 references that are in the map.
- First posted on arXiv 2 Aug 2025.

## Builds on (most cited first, 6 of 6)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [Modern Hopfield Networks and Attention for Immune Repertoire Classification](https://mlsanity.com/paper/2007.13505/) (2020)
- [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)

## Abstract (arXiv)

We investigate how feature correlations influence the capacity of Dense Associative Memory (DAM), a Transformer attention-like model. Practical machine learning scenarios involve feature-correlated data and learn representations in the input space, but current capacity analyses do not account for this. We develop an empirical framework to analyze the effects of data structure on capacity dynamics. Specifically, we systematically construct datasets that vary in feature correlation and pattern separation using Hamming distance from information theory, and compute the model's corresponding storage capacity using a simple binary search algorithm. Our experiments confirm that memory capacity scales exponentially with increasing separation in the input space. Feature correlations do not alter this relationship fundamentally, but reduce capacity slightly at constant separation. This effect is amplified at higher polynomial degrees in the energy function, suggesting that Associative Memory is more limited in depicting higher-order interactions between features than patterns. Our findings bridge theoretical work and practical settings for DAM, and might inspire more data-centric methods.