# Beyond Disorder: Unveiling Cooperativeness in Multidirectional Associative Memories

arXiv: https://arxiv.org/abs/2503.04454 · HTML: https://mlsanity.com/paper/2503.04454/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 20 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 8 of 8)

- [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)
- [Large Associative Memory Problem in Neurobiology and Machine Learning](https://mlsanity.com/paper/2008.06996/) (2020)
- [Supervised Hebbian Learning](https://mlsanity.com/paper/2203.01304/) (2022)
- [Neural networks with redundant representation: detecting the undetectable](https://mlsanity.com/paper/1911.12689/) (2019)
- [Dense Hebbian neural networks: a replica symmetric picture of unsupervised learning](https://mlsanity.com/paper/2211.14067/) (2022)
- [Dense Hebbian neural networks: a replica symmetric picture of supervised learning](https://mlsanity.com/paper/2212.00606/) (2022)
- [Thermodynamics of bidirectional associative memories](https://mlsanity.com/paper/2211.09694/) (2022)

## Abstract (arXiv)

By leveraging tools from the statistical mechanics of complex systems, in these short notes we extend the architecture of a neural network for hetero-associative memory (called three-directional associative memories, TAM) to explore supervised and unsupervised learning protocols. In particular, by providing entropic-heterogeneous datasets to its various layers, we predict and quantify a new emergent phenomenon -- that we term em layer's cooperativeness -- where the interplay of dataset entropies across network's layers enhances their retrieval capabilities Beyond those they would have without reciprocal influence. Naively we would expect layers trained with less informative datasets to develop smaller retrieval regions compared to those pertaining to layers that experienced more information: this does not happen and all the retrieval regions settle to the same amplitude, allowing for optimal retrieval performance globally. This cooperative dynamics marks a significant advancement in understanding emergent computational capabilities within disordered systems.