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Similarity Field Theory: A Mathematical Framework for Intelligence

Created by
  • Haebom

Author

Kei-Sing Ng

Outline

This paper argues that persistent and transformable similarity relations form the structural foundation of understandable dynamical systems, and presents a mathematical framework, similarity field theory, to formalize this. This theory addresses similarity values and their evolution between entities, defining similarity fields, the evolution of systems, concepts, and operators that generate new entities. Specifically, it defines intelligence as an operator that generates new entities within a similarity field, belonging to a specific conceptual fiber. Similarity field theory provides a fundamental language for characterizing, comparing, and constructing intelligent systems, reframing intelligence and interpretability as geometric problems within a similarity field, rather than as statistical problems.

Takeaways, Limitations

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Approaching Intelligence and Interpretability from a New Perspective: Similarity Field Theory provides a geometrical approach to intelligence and interpretability through similarity relationships, offering a different perspective from conventional statistical approaches.
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Interpreting and Utilizing Large-Scale Language Models (LLMs): We present a novel approach to using LLMs as a tool for social cognitive experiments, broadening the scope of interpretation and utilization of LLMs.
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Theoretical rigor: We strengthen the theoretical foundation by proving two theorems related to asymmetry and stability, and we impose constraints on the evolution of the similarity field.
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Applications to Social Cognitive Research: Preliminary evidence across various consumer categories demonstrates the potential for use in social cognition research.
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Limitations: The paper may lack detailed information about the specific experimental methods, data, and results.
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Limitations: Further verification of the generalizability of the presented theory and its application to real systems is needed.
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