# Temporal Complexity and Self-Organization in an Exponential Dense Associative Memory Model

arXiv: https://arxiv.org/abs/2601.11478 · HTML: https://mlsanity.com/paper/2601.11478/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 113 references that are in the map.
- First posted on arXiv 16 Jan 2026.

## 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)
- [The structure and dynamics of multilayer networks](https://mlsanity.com/paper/1407.0742/) (2014)
- [Unsupervised Learning by Competing Hidden Units](https://mlsanity.com/paper/1806.10181/) (2018)
- [Dense Hebbian neural networks: a replica symmetric picture of unsupervised learning](https://mlsanity.com/paper/2211.14067/) (2022)
- [Dynamical stability and chaos in artificial neural network trajectories along training](https://mlsanity.com/paper/2404.05782/) (2024)
- [Dense Hopfield Networks in the Teacher-Student Setting](https://mlsanity.com/paper/2401.04191/) (2024)
- [Neural Avalanches at the Critical Point between Replay and Non-Replay of Spatiotemporal Patterns](https://mlsanity.com/paper/1310.2024/) (2013)

## Abstract (arXiv)

Dense Associative Memory (DAM) models generalize the classical Hopfield model by incorporating n-body or exponential interactions that greatly enhance storage capacity. While the criticality of DAM models has been largely investigated, mainly within a statistical equilibrium picture, little attention has been devoted to the temporal self-organizing behavior induced by learning. In this work, we investigate the behavior of a stochastic exponential DAM (SEDAM) model through the lens of Temporal Complexity (TC), a framework that characterizes complex systems by intermittent transition events between order and disorder and by scale-free temporal statistics. Transition events associated with birth-death of neural avalanche structures are exploited for the TC analyses and compared with analogous transition events based on coincidence structures. We systematically explore how TC indicators depend on control parameters, i.e., noise intensity and memory load. Our results reveal that the SEDAM model exhibits regimes of complex intermittency characterized by nontrivial temporal correlations and scale-free behavior, indicating the spontaneous emergence of self-organizing dynamics. Notably, such regimes arise over finite intervals of noise intensity rather than at a single critical point, consistent with the concept of extended criticality. Further, the noise intensity range needed to reach the critical region, where self-organizing behavior emerges, slightly decreases as the memory load increases. This study highlights the relevance of TC as a complementary framework for understanding learning and information processing in artificial and biological neural systems, revealing the link between the memory load and the self-organizing capacity of the network.