TabPFN Through The Looking Glass: An interpretability study of TabPFN and its internal representations

Tabular foundational models are pre-trained models designed for a wide range of tabular data tasks. They have shown strong performance across domains, yet their internal representations and learned concepts remain poorly understood. This lack of interpretability makes it important to study how these models process and transform input features. In this work, we analyze the information encoded inside the model's hidden representations and examine how these representations evolve across layers. We run a set of probing experiments that test for the presence of linear regression coefficients, intermediate values from complex expressions, and the final answer in early layers. These experiments allow us to reason about the computations the model performs internally. Our results provide evidence that meaningful and structured information is stored inside the representations of tabular foundational models. We observe clear signals that correspond to both intermediate and final quantities involved in the model's prediction process. This gives insight into how the model refines its inputs and how the final output emerges. Our findings contribute to a deeper understanding of the internal mechanics of tabular foundational models. They show that these models encode concrete and interpretable information, which moves us closer to making their decision processes more transparent and trustworthy.