Phase Transitions Discovered in Stochastic Dense Associative Memory Networks with Exponential Interactions
Researchers have characterized the phase transition behavior of a stochastic exponential Dense Associative Memory (SEDAM) model trained on the MNIST dataset, finding a critical noise threshold at which the network shifts from short-time to long-time correlated dynamics. Dense Associative Memory models extend the classical Hopfield network by incorporating higher-order neuron interactions and exponential interaction functions, substantially increasing memory storage capacity. The findings shed light on out-of-equilibrium dynamics in modern associative memory models, a dimension that had previously received little systematic study.
The study introduces and analyzes a Stochastic Exponential Dense Associative Memory (SEDAM) model, using multiplicative salt-and-pepper noise probability as a control parameter and examining two order parameters: the time-averaged overlap Q and the diffusion scaling exponent H, the latter capturing temporal correlation structure. Experiments were conducted on networks trained on the MNIST handwritten digit dataset and compared against networks trained on standard Rademacher random patterns, as well as against a classical stochastic Hopfield network. Results show a clear phase transition in both Q and H as noise increases, with the critical noise level decreasing as the number of stored patterns (load K) grows. Most notably, at the critical regime the MNIST-trained SEDAM exhibits anomalously long-time correlated dynamics with a Hurst-like exponent H around 1.25, indicative of highly persistent temporal memory, while Rademacher-trained models show a slightly higher index of approximately 1.5. Below and above the critical point, dynamics revert to short-time correlations, underscoring the special nature of the critical regime for memory retrieval and network behavior.
What's missing
The paper does not address whether the identified critical noise levels have practical implications for hardware or software implementations of associative memory systems. As a preprint, the work has not yet undergone formal peer review.
What different sources said
- arXiv physicsCenter
Criticality of a Stochastic Dense Associative Memory Model with Exponential Interaction Function
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