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Semantic Phonons: Lattice Vibrations in AI Internals

This paper introduces the 'semantic phonon' framework, analogizing the geometry of word embeddings to lattice vibrations. By analyzing the eigenmodes of the PMI matrix, it explains how different boundary conditions shape semantic continua. Experiments validate the framework on GloVe and Gemma 2B.

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Semantic Phonons: Lattice Vibrations in AI Internals
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Key points and analysis

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Key points

  • Principal components of word embeddings correspond to eigenmodes of the PMI matrix, akin to lattice vibration patterns.
  • Different boundary conditions yield distinct geometries: periodic boundary gives circles, Neumann boundary gives parabolas.
  • Robin boundary conditions are generic for open-ended semantic scales, with Neumann as an idealized limit.
  • 2D Neumann boundary can describe the biaxial structure of emotion (valence and arousal).

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