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Brain-Inspired AI with Hyperbolic Geometry

Alexander Joseph, Nathan Francis, Meijke Balay

TL;DR

The paper argues that artificial neural networks have largely relied on Euclidean latent spaces, whereas the brain’s latent geometry is plausibly hyperbolic due to its hierarchical organization. It surveys hyperbolic geometry and connects it to brain structure and cognition, arguing that hyperbolic models better capture hierarchical data and complex networks. It reviews existing hyperbolic machine learning work—showing improved performance and parameter efficiency across NLP, vision, graphs, and symbolic tasks—and discusses current limitations and tooling. It concludes with an agenda for future work, including model selection, tool maturation, precision handling, and application to LLMs and knowledge graphs, highlighting potential for brain-like, efficient AI.

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.

Brain-Inspired AI with Hyperbolic Geometry

TL;DR

The paper argues that artificial neural networks have largely relied on Euclidean latent spaces, whereas the brain’s latent geometry is plausibly hyperbolic due to its hierarchical organization. It surveys hyperbolic geometry and connects it to brain structure and cognition, arguing that hyperbolic models better capture hierarchical data and complex networks. It reviews existing hyperbolic machine learning work—showing improved performance and parameter efficiency across NLP, vision, graphs, and symbolic tasks—and discusses current limitations and tooling. It concludes with an agenda for future work, including model selection, tool maturation, precision handling, and application to LLMs and knowledge graphs, highlighting potential for brain-like, efficient AI.

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.
Paper Structure (18 sections, 3 figures, 1 table)

This paper contains 18 sections, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Hyperbolic geometry
  3. Hyperbolic geometry and the brain
  4. Physical brain structure
  5. Cognition
  6. Macroscopic Cognition
  7. Smell
  8. Spatial Representation
  9. Vision
  10. Language
  11. Other cognitive functions
  12. Hyperbolic Machine Learning
  13. Existing research
  14. Limitations and existing tools
  15. Future Work
  16. ...and 3 more sections

Figures (3)

  • Figure 1: A binary tree embedded in 2D hyperbolic space. Large trees can be embedded with low distortion in hyperbolic space, but not in Euclidean space of the same dimension.
  • Figure 2: Oversimplified graphical model of the information representation flow from sensory inputs to abstract representations in human cortex taylor2015global
  • Figure 3: Wordnet nouns embedded in hyperbolic space poincare_embeddings