Planting a Latent Variable in Natural-Looking Text: a More Realistic Test of Belief States in LLMs and Their Link to Concept Geometry
TL;DR
This work plants a controllable latent variable inside natural-looking text and arranges the 8 states themselves on a ring, in the exact order of the Markov chain, which is supporting evidence that a concept's geometry can be formed by the statistical dynamics of the latent variable behind it.
Abstract
LLMs are thought to track"belief states,"i.e., running probability distributions over the latent variables that govern language (Shai et al., 2024; Sarfati et al., 2026), but so far this has only been comprehensively demonstrated on toy synthetic data and in a few isolated case studies. It has also never been empirically connected to the geometry of LLM features (the concepts interpretability finds in model activations). In this work, we plant a controllable latent variable inside natural-looking text. An LLM teacher writes ordinary text while we"subliminally"steer it along one of K = 8 unrelated sparse autoencoder directions at each token, with the active directions following a ring-shaped Markov chain. A small transformer model trained on this corpus does indeed track the Bayesian posterior belief about our planted latent variable. Moreover, it also arranges the 8 states themselves on a ring, in the exact order of the Markov chain, which is supporting evidence that a concept's geometry can be formed by the statistical dynamics of the latent variable behind it.
