Identifiability and Order-Dimension Limits of In-Context Learning on Partial Orders

Excerpt

arXiv:2608.14004v1 Announce Type: new Abstract: In-context learning is commonly formalized as inference from examples of a function. Partial orders instead combine transitivity, antisymmetry, and incomparability, so a finite prompt may not determine a queried comparison. We develop a theory of in-context learning on partial orders that separates logical identifiability, prompt teaching cost, structural complexity, and the exact capacity of a formal coordinate-decoder class. A version-space seman