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Similarity Field Theory: A General Mathematical Framework for Intelligence

Created by
  • Haebom

Author

Kei-Sing Ng

Outline

This paper presents a mathematical framework called Similarity Field Theory, which assumes that the persistence and transformation of similarity relations form the structural basis of any intelligible dynamical system. This framework formalizes the similarity values between individuals and the principles that govern their evolution. Its main components are: (1) a similarity field S defined on a set of individuals U: U × U → [0, 1] (which satisfies reflexivity S(E,E) = 1 and allows for asymmetry and nontransitivity), (2) an evolutionary process Zp = (Xp, S(p)) of the system indexed by p = 0, 1, 2, …, (3) a fiber Fα(K) = {E ∈ U | S(E,K) ≥ α} (the super-level set of the unary mapping S_K(E) := S(E,K)), (4) a generative operator G that creates new entities. Within this framework, we define intelligence generatively and prove two theorems: (i) asymmetry prevents mutual inclusion, and (ii) stability requires ultimate bounds within the reference coordinate or level set. Finally, we use this framework to interpret large-scale language models and present empirical results using large-scale language models as an experimental tool for experimental exploration of social cognition.

Takeaways, Limitations

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Takeaways:
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It provides a new framework for understanding the structural basis of dynamic systems through changes in similarity relationships.
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Define intelligence from a generative perspective and formalize it mathematically.
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We present a novel methodology for applying large-scale language models to social cognition research.
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We present mathematical results that ensure the constraints and interpretability of the evolution of pseudogrowth.
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Limitations:
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Further research is needed to determine the practical applicability and generalizability of the proposed theory.
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The scope of empirical research using large-scale language models may be limited.
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There may be a lack of a concrete definition and algorithm for the generating operator G of pseudogrowth.
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Further validation is needed to determine how well the properties of pseudogrowth, which allow for asymmetry and non-transitivity, are suitable for real systems.
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