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Related Experiment Videos

Semantic Algorithmic Information Theory: From Kolmogorov Complexity to Semantic Equivalence.

Jiatong Wu1, Sen Wang2, Kai Niu3

  • 1State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China.

Entropy (Basel, Switzerland)
|May 26, 2026
PubMed
Summary

This study introduces Semantic Algorithmic Information Theory (SAIT) to measure meaning, not just syntax. It presents a computable method, Normalized Semantic Information Distance (NSID), for semantic similarity.

Keywords:
algorithmic information theorykolmogorov complexitynormalized semantic information distancesemantic information theoryset-theoretic metricssynonymous set

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Information Theory

Background:

  • Classical Algorithmic Information Theory (AIT) offers syntactic similarity measures but struggles with semantic equivalence.
  • Existing methods are sensitive to surface variations, limiting their ability to capture true meaning.

Purpose of the Study:

  • Introduce Semantic Algorithmic Information Theory (SAIT) to address limitations of classical AIT.
  • Develop a computable method for semantic similarity measurement.
  • Evaluate the effectiveness of the proposed semantic distance metric.

Main Methods:

  • Formalized the Semantic Turing Machine System (STMS) to decouple concepts from syntax.
  • Defined Semantic Complexity for compact meaning representation.
  • Developed a model-based direct estimator for Normalized Semantic Information Distance (NSID) using neural autoregressive models.

Main Results:

  • The NSID estimator effectively suppresses syntactic variance while preserving semantic structure.
  • Empirical validation shows NSID is a practical and computable surrogate for semantic distance.
  • NSID outperforms classical syntactic metrics in evaluating cross-representational equivalence.

Conclusions:

  • SAIT provides a rigorous foundation for semantic information measurement.
  • NSID offers a significant advancement over syntactic metrics for understanding meaning.
  • The proposed methods enable more robust semantic similarity assessments.