Tensor Representation of Topographically Organized Semantic Spaces.

Area of Science:

• Neuroscience
• Cognitive Science
• Computational Neuroscience

Background:

• The human brain organizes object and action categories in a continuous semantic space across the cortical surface.
• This organization reflects category similarity and aligns with known topographic maps (somatotopic, retinotopic, tonotopic).

Purpose of the Study:

• To operationally represent semantic topographies using context-dependent associative memory models.
• To demonstrate how tensor methods can spatially organize semantic information in neural networks.

Main Methods:

• Utilizing context-dependent associative memories with Kronecker tensor products for spatial memory organization.
• Employing input and output tensor contexts to localize semantic category matrices within neural layers.
• Developing tensor representations to reproduce empirical neural topographic patterns.

Main Results:

• Demonstrated that tensor representations can spatially organize associative memories to mimic neural topographic patterns.
• Showcased how tensor contexts direct information flow to specific neural addresses.
• Achieved progressive approximations of topographic patterns by managing memory overlap and empty regions.

Conclusions:

• Context-dependent associative memories and tensor products offer a viable operational model for semantic brain organization.
• This approach provides a framework for understanding how topographic maps in the cortex represent semantic information.
• The findings support a spatially organized view of semantic representation in the brain.