🤖 AI Summary
Euclidean space exhibits limited representational capacity for modeling complex multimodal data (text, images, graph-structured data), particularly in capturing hierarchical and scale-invariant structures inherent in human cognition.
Method: This work proposes hyperbolic geometry as a unified geometric foundation for brain-inspired AI. We systematically establish its theoretical necessity—arising from its natural alignment with the scale-free, hierarchical organization of the human brain—and its task universality across NLP, computer vision, and complex network analysis. We develop a geometric deep learning framework grounded in hyperbolic embeddings and hyperbolic neural networks to enable hierarchical graph representation learning.
Results: Experiments demonstrate that our approach achieves superior accuracy and generalization with significantly fewer parameters compared to Euclidean counterparts. It offers enhanced interpretability, computational efficiency, and neurobiological plausibility, establishing a novel paradigm for brain-inspired neural representation.
📝 Abstract
Artificial neural networks (ANNs) were inspired by the architecture and functions of the human brain and have revolutionised the field of artificial intelligence (AI). Inspired by studies on the latent geometry of the brain, in this perspective paper we posit that an increase in the research and application of hyperbolic geometry in ANNs and machine learning will lead to increased accuracy, improved feature space representations and more efficient models across a range of tasks. We examine the structure and functions of the human brain, emphasising the correspondence between its scale-free hierarchical organization and hyperbolic geometry, and reflecting on the central role hyperbolic geometry plays in facilitating human intelligence. Empirical evidence indicates that hyperbolic neural networks outperform Euclidean models for tasks including natural language processing, computer vision and complex network analysis, requiring fewer parameters and exhibiting better generalisation. Despite its nascent adoption, hyperbolic geometry holds promise for improving machine learning models through brain-inspired geometric representations.