Identifiability and Order-Dimension Limits of In-Context Learning on Partial Orders
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 semantics makes background knowledge and open- versus closed-world assumptions explicit. For finite open-world prompts with positive and negative comparisons, we prove an exact completion trichotomy: after taking the reflexive transitive closure of t...
| Authors | Faizanuddin Ansari, Debanjan Dutta, Swagatam Das |
|---|---|
| Primary category | cs.LG |
| Published | 14 August 2026 |
| Last updated at source | 14 August 2026 |
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