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Human cognition uses discrete features to represent complex phenomena. This study introduces information-theoretic tools to measure the fidelity and efficiency of these representations, offering new insights into mental compositionality.

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Area of Science:

  • Cognitive Science
  • Information Theory
  • Psychology

Background:

  • Human cognition effectively represents complex phenomena using discrete features.
  • The ability of discrete features to capture the probabilistic nature of the environment remains unclear.

Purpose of the Study:

  • Introduce information-theoretic tools to quantify the fidelity and efficiency of featural representations.
  • Explore how discrete features represent complex probabilistic environments and the concept of compositionality.

Main Methods:

  • Utilize information-theoretic frameworks to define and measure 'fidelity' and 'efficiency' of representations.
  • Analyze how feature fidelity depends on projection direction in multidimensional spaces.
  • Propose criteria for compositional representation: fidelity, simplicity, and robustness.

Main Results:

  • A feature is 'faithful' if it reduces uncertainty about the true state of the world.
  • In multidimensional spaces, feature fidelity is direction-dependent.
  • Compositionality allows for diverse representations with varying fidelity and complexity.

Conclusions:

  • Information-theoretic tools offer a novel perspective on compositionality in human mental representation.
  • The proposed framework provides criteria to evaluate different compositional forms.
  • Understanding featural representation is key to understanding cognitive processes.