# Input-Driven Dynamics for Robust Memory Retrieval in Hopfield Networks

arXiv: https://arxiv.org/abs/2411.05849 · HTML: https://mlsanity.com/paper/2411.05849/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## 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)
- [Continual Learning for Robotics: Definition, Framework, Learning Strategies, Opportunities and Challenges](https://mlsanity.com/paper/1907.00182/) (2019)
- [Long Sequence Hopfield Memory](https://mlsanity.com/paper/2306.04532/) (2023)
- [Metastable dynamics of neural circuits and networks](https://mlsanity.com/paper/2110.03025/) (2021)
- [Robust retrieval of dynamic sequences through interaction modulation](https://mlsanity.com/paper/2211.17152/) (2022)
- [Reducing a cortical network to a Potts model yields storage capacity estimates](https://mlsanity.com/paper/1710.04897/) (2017)

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

- [DeepInsert: Early Layer Bypass for Efficient and Performant Multimodal Understanding](https://mlsanity.com/paper/2504.19327/) (2025)
- [Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization](https://mlsanity.com/paper/2604.05042/) (2026)
- [Dynamic Manifold Hopfield Networks for Context-Dependent Associative Memory](https://mlsanity.com/paper/2506.01303/) (2025)
- [A Geometric Theory of Cognition for Machine Intelligence](https://mlsanity.com/paper/2512.12225/) (2025)
- [Context-Gated Associative Retrieval: From Theory to Transformers](https://mlsanity.com/paper/2605.10970/) (2026)

## Abstract (arXiv)

The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and retrieval dynamics, capacity estimates, and sequential transitions among memories. Notably, the role and impact of external inputs has been largely underexplored, from their effects on neural dynamics to how they facilitate effective memory retrieval. To bridge this gap, we propose a novel dynamical system framework in which the external input directly influences the neural synapses and shapes the energy landscape of the Hopfield model. This plasticity-based mechanism provides a clear energetic interpretation of the memory retrieval process and proves effective at correctly classifying highly mixed inputs. Furthermore, we integrate this model within the framework of modern Hopfield architectures, using this connection to elucidate how current and past information are combined during the retrieval process. Finally, we embed both the classic and the new model in an environment disrupted by noise and compare their robustness during memory retrieval.