Conceptual spaces - Geometry of thoughts

updated:

Book: Conceptual SpacesThe Geometry of Thought | Books Gateway | MIT Press
Video: Youtube

Key Points

• Conceptual spaces represent concepts as convex regions in geometric spaces with quality dimensions as axes. This allows for efficient learning from few examples and better generalization.
• Evidence shows color concepts across languages form convex regions in color spaces. Prepositions also map well to spatial coordinates.
• The hippocampus represents memories and experiences in grid cells that act as a spatial coordinate system. This provides a neural basis for the geometric spaces postulated in conceptual spaces theory.
• Conceptual spaces allow vague concepts to be modeled geometrically. Spatial representation supports pattern recognition and generalization in human cognition.

Summary

Conceptual spaces theory proposes that thoughts and concepts can be represented as geometric spaces instead of symbolic representations. Regions in conceptual spaces represent concepts, with quality dimensions as axes. Convexity of conceptual regions enables efficient learning from few examples. Evidence supports geometry of color concepts and prepositions. The hippocampus encodes memories in grid cell networks that act as a spatial coordinate system, providing a neural basis for conceptual spaces. Overall, the spatial nature of conceptual spaces accounts for pattern recognition and generalization in human cognition.

Note

• Two representations of thoughts:
  • Symbolic representation - fundamental mental code for computing
  • Connectionism - cognition is the input/output of neurons
  • Spatial models - cognition can be modeled geometrically/topologically
• Information is organized in spatial structures.
  • Example: Human color perception and similarity judgments form geometric color spaces
• The hippocampus learns information in geometric spaces
• Conceptual spaces theory (Gärdenfors, 2004):
  • Spaces have quality dimensions as axes.
  • Concepts are convex regions in domains.
  • Color concepts across languages form convex regions in color spaces.
  • Convexity enables efficient learning from a few examples
  • Connects to the prototype theory
• Evidence for convexity criterion:
  • Jaeger (2010) found color terminology across 110 languages fit convex partitioning of color space.
• Humans excel at pattern recognition.
  • The cognitive representation of actions is a spatial pattern of forces.
  • Similarity judgments of videos project consistently across languages.
• Geometry of prepositions described by spatial coordinates
• Neural basis:
  • The hippocampus represents memories spatially (Bellmund et al., 2018)
  • Grid cells provide a spatial coordinate system (Bush et al., 2015)
  • Explains generalization in cognition
  • Matches navigation in rats
• Benefits of conceptual spaces:
  • Model vague concepts geometrically
  • Enable pattern recognition and generalization

References

• Bellmund, J. L. S., Gärdenfors, P., Moser, E. I., & Doeller, C. F. (2018). Navigating cognition: Spatial codes for human thinking. Science, 362(6415).
• Bush, D., Barry, C., Manson, D., & Burgess, N. (2015). Using grid cells for navigation. Neuron, 87(3), 507-520.
• Gärdenfors, P. (2000). Conceptual spaces: The geometry of thought. MIT press.
• Jäger, G. (2009). Natural color categories are convex sets. Lecture Notes in Computer Science