Large Language Models (LLMs) enable a new form of digital experimentation where treatments combine human and model-generated content in increasingly sophisticated ways. The main methodological challenge in this setting is representing these high-dimensional treatments without losing their semantic meaning or rendering analysis intractable. Here, we address this problem by focusing on learning low-dimensional representations that capture the underlying structure of such treatments. These representations enable downstream applications such as guiding generative models to produce meaningful treatment variants and facilitating adaptive assignment in online experiments. We propose double kernel representation learning, which models the causal effect through the inner product of kernel-based representations of treatments and user covariates. We develop an alternating-minimization algorithm that learns these representations efficiently from data and provides convergence guarantees under a low-rank factor model. As an application of this framework, we introduce an adaptive design strategy for online experimentation and demonstrate the method's effectiveness through numerical experiments.

翻译：大型语言模型（LLMs）催生了一种新型数字实验形式，其中干预措施以日益复杂的方式结合人类与模型生成的内容。在此情境下的主要方法学挑战在于如何表征这些高维干预，同时不丢失其语义含义或导致分析难以处理。本文通过聚焦于学习能够捕捉此类干预底层结构的低维表征来解决该问题。这些表征支持下游应用，例如引导生成模型产生有意义的干预变体，并促进在线实验中的自适应分配。我们提出双重核表征学习方法，该方法通过基于核的干预表征与用户协变量表征的内积来建模因果效应。我们开发了一种交替最小化算法，能够高效地从数据中学习这些表征，并在低秩因子模型下提供收敛性保证。作为该框架的应用，我们引入了一种用于在线实验的自适应设计策略，并通过数值实验证明了该方法的有效性。