Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models
Beren Millidge1, Tommaso Salvatori2, Yuhang Song1,2
1MRC Brain Network Dynamics Unit, University of Oxford, UK.
Proceedings of Machine Learning Research
|February 8, 2023
Summary
This study introduces a unified framework for associative memory networks, revealing that Euclidean or Manhattan distance metrics enhance memory capacity and retrieval robustness beyond traditional dot product methods.
Area of Science:
- Computational Neuroscience
- Machine Learning
- Artificial Intelligence
Background:
- Numerous neural network models for associative memory exist, including Hopfield Networks (HN), Sparse Distributed Memories (SDM), and Modern Continuous Hopfield Networks (MCHN).
- MCHNs show strong connections to self-attention mechanisms in machine learning.
- Existing models often rely on specific similarity measures, limiting their adaptability and performance.
Purpose of the Study:
- To propose a general framework for understanding associative memory network operations.
- To unify existing models under this framework by defining differing similarity and separation functions.
- To investigate the impact of various similarity metrics on memory capacity and retrieval performance.
Main Methods:
- Developed a general framework describing memory network operations as similarity, separation, and projection.
- Extended the Krotov & Hopfield (2020) mathematical framework for neural network dynamics with local computation.
- Derived a general energy function that serves as a Lyapunov function for the network dynamics.
- Empirically evaluated different similarity functions (Euclidean, Manhattan, dot product) within the proposed framework.
Main Results:
- All previously proposed associative memory models were derived as instances of the general framework.
- Euclidean and Manhattan distance similarity metrics demonstrated substantially better performance compared to dot product.
- Alternative similarity metrics led to more robust retrieval and significantly higher memory capacity in practical applications.
Conclusions:
- The proposed general framework provides a unified perspective on diverse associative memory models.
- Non-dot product similarity metrics offer a promising avenue for enhancing the performance of associative memory networks.
- This research enables more robust memory retrieval and increased capacity in artificial memory systems.
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