On the Origins of Linear Representations in Large Language Models
This provides theoretical insights into representation learning in LLMs, addressing a fundamental question for AI researchers, but it is incremental as it builds on prior observations of linearity.
The paper investigates why large language models develop linear representations of semantic concepts, showing that the next token prediction objective and gradient descent bias promote such linearity, with experiments confirming emergence in data matching a latent variable model and validation on LLaMA-2.
Recent works have argued that high-level semantic concepts are encoded "linearly" in the representation space of large language models. In this work, we study the origins of such linear representations. To that end, we introduce a simple latent variable model to abstract and formalize the concept dynamics of the next token prediction. We use this formalism to show that the next token prediction objective (softmax with cross-entropy) and the implicit bias of gradient descent together promote the linear representation of concepts. Experiments show that linear representations emerge when learning from data matching the latent variable model, confirming that this simple structure already suffices to yield linear representations. We additionally confirm some predictions of the theory using the LLaMA-2 large language model, giving evidence that the simplified model yields generalizable insights.