I Predict Therefore I Am: Is Next Token Prediction Enough to Learn Human-Interpretable Concepts from Data?

The remarkable achievements of large language models (LLMs) have led many to conclude that they exhibit a form of intelligence. This is as opposed to explanations of their capabilities based on their ability to perform relatively simple manipulations of vast volumes of data. To illuminate the distinction between these explanations, we introduce a novel generative model that generates tokens on the basis of human interpretable concepts represented as latent discrete variables. Under mild conditions, even when the mapping from the latent space to the observed space is non-invertible, we establish an identifiability result: the representations learned by LLMs through next-token prediction can be approximately modeled as the logarithm of the posterior probabilities of these latent discrete concepts, up to an invertible linear transformation. This theoretical finding not only provides evidence that LLMs capture underlying generative factors, but also strongly reinforces the linear representation hypothesis, which posits that LLMs learn linear representations of human-interpretable concepts. Empirically, we validate our theoretical results through evaluations on both simulation data and the Pythia, Llama, and DeepSeek model families.