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Transient dynamics of associative memory models
1Columbia University, Columbia University, Zuckerman Institute, New York, New York 10027, USA and Kavli Institute for Brain Science, New York, New York 10027, USA.
Physical Review. E
|June 19, 2026
Summary
Associative memory networks can retrieve patterns even above capacity limits. New analysis shows transient dynamics, not a blackout catastrophe, govern memory retrieval in these models.
Area of Science:
- Computational Neuroscience
- Statistical Physics
- Machine Learning
Background:
- Associative memory models like the Hopfield network face a 'blackout catastrophe,' losing stable memory states above critical capacity.
- This is often interpreted as a hard limit on network usability.
Purpose of the Study:
- To challenge the equilibrium perspective on associative memory capacity limits.
- To investigate transient memory retrieval dynamics in dense associative memory models.
Main Methods:
- Derivation of dynamical mean-field equations for graded-activity dense associative memory models using a bipartite cavity approach.
- Solving self-consistent equations via an iterative numerical scheme.
- Introduction of 'transient-recovery curves' to visualize retrieval behavior.
Main Results:
- Patterns can be accurately retrieved transiently even above critical capacity, despite the absence of stable attractors.
- Persistent slow regions in the energy landscape near stored patterns enable this transient retrieval.
- This dynamical perspective reveals energy landscape structures missed by equilibrium analysis.
Conclusions:
- The 'blackout catastrophe' is an artifact of the equilibrium perspective; transient dynamics allow for graceful performance above capacity.
- Biological neural circuits may leverage these transient dynamics for memory retrieval.
- The study offers new theoretical insights into generalized Hopfield models and neural computation beyond fixed points.
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