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Planting a Latent Variable in Natural-Looking Text: a More Realistic Test of Belief States in LLMs and Their Link to Concept Geometry

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TL;DR - Researchers embed a controllable latent variable into natural-looking text and show that a small transformer trained on it tracks the variable’s Bayesian posterior. The model also reproduces the latent process’s ring geometry, linking learned concept geometry to underlying statistical dynamics.

  • An LLM teacher generates ordinary text while being steered along one of eight unrelated sparse-autoencoder directions at each token.
  • The active directions transition according to a ring-shaped Markov chain, creating a controlled latent process within realistic-looking language.
  • A small transformer trained on the corpus learns to represent posterior beliefs about the active latent state.
  • Its representations arrange the eight states in the Markov chain’s exact ring order, suggesting that latent-variable dynamics can shape feature geometry.

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Planting a Latent Variable in Natural-Looking Text: a More Realistic Test of Belief States in LLMs and Their Link to Concept Geometry

arXiv cs.CL Alexandru-Iulius Jerpelea 2026-08-27 arXiv:2608.26887
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Providers: Hugging Face · N/A OpenAlex · N/A Publisher · N/A Semantic Scholar · N/A X · N/A Fetched 2026-09-26 14:17:49.287088 UTC

TL;DR - Researchers embed a controllable latent variable into natural-looking text and show that a small transformer trained on it tracks the variable’s Bayesian posterior. The model also reproduces the latent process’s ring geometry, linking learned concept geometry to underlying statistical dynamics.

  • An LLM teacher generates ordinary text while being steered along one of eight unrelated sparse-autoencoder directions at each token.
  • The active directions transition according to a ring-shaped Markov chain, creating a controlled latent process within realistic-looking language.
  • A small transformer trained on the corpus learns to represent posterior beliefs about the active latent state.
  • Its representations arrange the eight states in the Markov chain’s exact ring order, suggesting that latent-variable dynamics can shape feature geometry.
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