Is similarity actually a structural mapping problem?

[weite76]

🚀 The feature, motivation and pitch

Hi, I’ve been working on a theoretical framework about knowledge and cognition.

Core idea (very compressed):

• Knowledge = structured commonality
• Cognition = forming mappings between relational structures
• The strongest form of commonality is what I call “parallel mapping”

In most ML systems:

• similarity is treated as a metric or loss objective

In my view:

• similarity is not a tool
• it is the essence of knowledge itself

More specifically:
When two systems share structure, their internal relations can form a near-parallel mapping.
This “parallel structure” is what we actually recognize as knowledge.

Rough analogy:

• nodes → elements
• edges → relations
• knowledge → stable mapping between two relational graphs

Question:

Do current architectures (e.g. transformers, GNNs, embedding spaces) already approximate this kind of “parallel mapping” implicitly?

Or is this perspective fundamentally missing from current ML?

I’m not sure if this belongs more to representation learning, graph learning, or something else — would appreciate any direction.

Attached materials
Chinese original: 人工智能的几何原理.pdf
English translation (AI-assisted, may contain inaccuracies): Geometric Principles of Artificial Intelligence.docx

Alternatives

No response

Additional context

No response