Jorge Bravo Abad’s Post

Curved neural networks: Efficiently capturing higher-order interactions for enhanced memory retrieval Higher-order interactions (HOIs) are complex interactions involving more than two components within a system, and they play a crucial role in determining collective behaviors in various physical, biological, and artificial networks. Unlike simple pairwise interactions, HOIs account for group effects where the system's collective state cannot be fully understood or predicted by examining individual or binary relationships alone. Despite their significance, modeling these interactions efficiently has been challenging due to computational complexity. In a recent paper, Miguel Aguilera and coauthors introduced "curved neural networks," a novel framework that employs the maximum entropy principle on curved statistical manifolds to parsimoniously model these intricate interactions. Their approach captures HOIs naturally, avoiding the combinatorial explosion typically encountered in traditional methods. Remarkably, these curved neural networks demonstrate intriguing behaviors such as explosive phase transitions, hysteresis effects, and accelerated memory retrieval dynamics. By implementing a self-regulated annealing mechanism, the authors show that these networks can dramatically enhance their memory capacity and robustness compared to classical associative memory models. This advancement provides new insights into how HOIs could underpin improved performance observed in cutting-edge deep learning architectures, like transformers and diffusion models. Paper: https://lnkd.in/dHbx6qJE #NeuralNetworks #HigherOrderInteractions #ComplexSystems #MachineLearning #StatisticalPhysics #DeepLearning #ArtificialIntelligence #ComputationalNeuroscience #AssociativeMemory #ExplosiveTransitions #CurvedNeuralNetworks #ResearchInnovation #InformationTheory #DataScience #AIforScience