Enhanced storage capacity with errors in scale-free Hopfield neural networks: An analytical study

Area of Science:

• Computational Neuroscience
• Artificial Neural Networks
• Network Science

Background:

• The Hopfield model, a foundational neural network, demonstrates associative memory retrieval with a limited storage capacity.
• Traditional neural network models assume full connectivity, contradicting experimental findings of heterogeneous neuron connections in real brains.

Purpose of the Study:

• To investigate the impact of scale-free networks on the Hopfield model's associative memory retrieval.
• To compare memory retrieval patterns and storage capacity in scale-free versus fully connected networks.

Main Methods:

• Analysis of the Hopfield model adapted to scale-free network topologies.
• Mathematical derivation of storage capacity and error rates in heterogeneous networks.
• Comparison with error rates observed in real neural network data.

Main Results:

• Hopfield networks on scale-free networks exhibit significantly enhanced storage capacity compared to fully connected networks.
• Increased connection heterogeneity in scale-free networks leads to a trade-off: higher capacity but with memory retrieval errors.
• Observed error rates in real neural networks align with those predicted by scale-free network models.

Conclusions:

• Network topology, specifically scale-free properties, profoundly influences neural network memory capacity and retrieval fidelity.
• The findings suggest that heterogeneous connectivity, characteristic of real neural systems, can be modeled using scale-free networks to understand memory dynamics.