A Theoretical Framework for Understanding and Building "Any-task inference" Capable Foundation Models

arXiv:2610.40934v1 Announce Type: new Abstract: In this work, we provide a formal framework and mathematical definition for the subset of foundation models focused on enabling the property of "any-task inference" (ATI) (similar to zero-shot inference), rather than those designed for pre-training fine-tuning. To achieve this mathematical definition, we formalize the notion of a "space of tasks of interest," which we include in the problem domain, then provide an interface-based formal definition for ATI foundation models as those that map samples of data $x$ and tasks $t$ to predictions over the space of labels directly.