Explosive neural networks via higher-order interactions in curved statistical manifolds

Area of Science:

• Complex Systems Science
• Computational Neuroscience
• Statistical Physics

Background:

• Higher-order interactions are crucial in complex systems like biological and artificial neural networks.
• Studying these interactions is difficult due to a lack of suitable models.
• Tractable models are needed to understand phenomena driven by higher-order interactions.

Purpose of the Study:

• To introduce a new class of models, curved neural networks, for studying higher-order phenomena.
• To analyze the properties and capabilities of these networks using analytical methods.
• To demonstrate their potential for enhanced memory retrieval and understanding complex network dynamics.

Main Methods:

• Generalization of the maximum entropy principle to define curved neural networks.
• Exact mean-field descriptions to analyze network dynamics.
• Analytical exploration of memory-retrieval capacity using the replica trick.

Main Results:

• Curved neural networks implement a self-regulating annealing process.
• These networks exhibit accelerated memory retrieval, leading to explosive order-disorder phase transitions.
• Demonstrated enhanced memory capacity and retrieval robustness compared to classical associative memory networks.
• Observed multi-stability and hysteresis effects in the network dynamics.

Conclusions:

• Curved neural networks offer parsimonious and analytically tractable models for higher-order phenomena.
• The proposed framework reveals insights into complex network dynamics, including phase transitions and memory retrieval.
• This work advances the study of complex systems by providing a novel modeling approach.