In-Context Learning on Partial Orders: Identifiability and Limits
Key takeaways
- A new theory explores in-context learning on partial orders, a complex data structure.
- It defines logical identifiability, prompt teaching cost, and structural complexity.
- An exact completion trichotomy determines if a query is forced true, false, or ambiguous.
- The research characterizes the capacity limits of formal coordinate-decoder classes.
Who benefits
Summary
This research develops a theory of in-context learning (ICL) on partial orders, separating logical identifiability, prompt teaching cost, and structural complexity. It introduces a version-space semantics, proves an exact completion trichotomy, and characterizes teaching numbers and coordinate-decoder capacities.
Why it matters
For professionals working on advanced AI systems, particularly those involving reasoning, knowledge representation, or complex decision-making, this research provides fundamental insights into the capabilities and limitations of in-context learning for structured data. This can inform the design of more robust and interpretable AI agents.
How to implement this in your domain
- 1Analyze existing AI systems that perform reasoning over structured or relational data.
- 2Explore the theoretical implications of in-context learning on partial orders for knowledge representation.
- 3Consider how the concepts of identifiability and teaching cost apply to prompt engineering for complex tasks.
- 4Investigate the design of coordinate-decoders for tasks involving inferring relationships from examples.
Original post by Faizanuddin Ansari, Debanjan Dutta, Swagatam Das
"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 devel…"
View on XOriginally posted by Faizanuddin Ansari, Debanjan Dutta, Swagatam Das on X · view source
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