I Predict Therefore I Am

Yuhang Liu, Dong Gong, Erdun Gao, Zhen Zhang, Biwei Huang, Mingming Gong, Anton van den Hengel, Javen Qinfeng Shi

Recent empirical evidence shows that LLM representations encode human-interpretable concepts. Nevertheless, the mechanisms by which these representations emerge remain largely unexplored. To shed further light on this, we introduce a novel generative model that generates tokens on the basis of such concepts formulated as latent discrete variables. Under mild conditions, even when the mapping from the latent space to the observed space is non-invertible, we establish rigorous 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 given input context, up to an invertible linear transformation. This theoretical finding: 1) provides evidence that LLMs capture essential underlying generative factors, 2) offers a unified and principled perspective for understanding the linear representation hypothesis, and 3) motivates a theoretically grounded approach for evaluating sparse autoencoders. Empirically, we validate our theoretical results through evaluations on both simulation data and the Pythia, Llama, and DeepSeek model families.

Paper

[arXiv] [Code]