Emergence of Linear Truth Encodings in Language Models
Authors: name: Shauli Ravfogel, name: Gilad Yehudai, name: Tal Linzen, name: Joan Bruna, name: Alberto Bietti

Recent probing studies reveal that large language models exhibit linear
subspaces that separate true from false statements, yet the mechanism behind
their emergence is unclear. We introduce a transparent, one-layer transformer
toy model that reproduces such truth subspaces end-to-end and exposes one
concrete route by which they can arise. We study one simple setting in which
truth encoding can emerge: a data distribution where factual statements
co-occur with other factual statements (and vice-versa), encouraging the model
to learn this distinction in order to lower the LM loss on future tokens. We
corroborate this pattern with experiments in pretrained language models.
Finally, in the toy setting we observe a two-phase learning dynamic: networks
first memorize individual factual associations in a few steps, then -- over a
longer horizon -- learn to linearly separate true from false, which in turn
lowers language-modeling loss. Together, these results provide both a
mechanistic demonstration and an empirical motivation for how and why linear
truth representations can emerge in language models.