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.

高层语义概念在大型语言模型的表示空间中按线性方式编码；本研究通过引入简单的潜在变量模型来研究这种线性表示的起源，并证明了下一个标记预测目标和梯度下降的隐式偏差共同促进了概念的线性表示。