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Summary
This summary is machine-generated.

This study clarifies the ambiguous concept of redundancy in information theory by distinguishing between operational redundancy (task-based prediction) and informational redundancy (content overlap). Separating these concepts resolves paradoxes and guides future research.

Keywords:
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Area of Science:

  • Multivariate Information Theory
  • Computational Neuroscience
  • Machine Learning

Background:

  • The concept of redundancy in multivariate information theory is ambiguously defined, leading to confusion.
  • Existing literature conflates operational and informational redundancy, causing paradoxes, especially with independent inputs.

Purpose of the Study:

  • To formally distinguish between operational and informational redundancy.
  • To resolve conceptual ambiguities and apparent paradoxes in information theory.
  • To provide a clear framework for future research on redundancy.

Main Methods:

  • Formalizing two distinct classes of redundancy: operational and informational.
  • Analyzing functional examples and biased input ensembles.
  • Demonstrating distinctions using information theory principles.

Main Results:

  • Operational redundancy relates to input sufficiency/substitutability for prediction.
  • Informational redundancy concerns shared content among inputs, measured by mutual information.
  • Demonstrated that inputs lacking informational overlap can exhibit operational redundancy.

Conclusions:

  • A clear separation of operational and informational redundancy is proposed.
  • This distinction clarifies why redundancy is elusive and why single measures are insufficient.
  • Outlines minimal commitments for future theoretical and applied work.