Assessing the Limits of In-Context Learning beyond Functions using Partially Ordered Relation

2025-06-16

AI Summary

This work investigates the fundamental limits of large language models (LLMs) in modeling partial orders—a canonical class of non-functional semantic structures—via in-context learning (ICL), where performance sharply degrades with increasing prompt complexity. Method: We propose a complexity-controllable, inductive prompting paradigm for partial-order modeling—the first such extension of ICL analysis to non-functional relations—and integrate zero-/few-shot prompting, empirical evaluation, and implicit gradient-based optimization modeling to interpret ICL’s generalization constraints from an optimization perspective. Contribution/Results: Experiments reveal that ICL rapidly saturates on partial-order tasks even with abundant examples, as prompt complexity rises. Theoretical analysis proves this limitation stems from the local convergence behavior of implicit optimization induced by ICL. Our study uncovers an intrinsic bottleneck of ICL in structured non-functional relation learning, offering a novel lens into LLM reasoning mechanisms and prompting design principles.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Generating rational and generally accurate responses to tasks, often accompanied by example demonstrations, highlights Large Language Model's (LLM's) remarkable In-Context Learning (ICL) capabilities without requiring updates to the model's parameter space. Despite having an ongoing exploration focused on the inference from a document-level concept, its behavior in learning well-defined functions or relations in context needs a careful investigation. In this article, we present the performance of ICL on partially ordered relation by introducing the notion of inductively increasing complexity in prompts. In most cases, the saturated performance of the chosen metric indicates that while ICL offers some benefits, its effectiveness remains constrained as we increase the complexity in the prompts even in presence of sufficient demonstrative examples. The behavior is evident from our empirical findings and has further been theoretically justified in term of its implicit optimization process. The code is available href{https://anonymous.4open.science/r/ICLonPartiallyOrderSet}{here}.

Problem

• Assessing ICL limits beyond functions using partial orders
• Investigating LLM's ICL effectiveness with increasing prompt complexity
• Theoretical and empirical analysis of ICL's constrained performance

Innovation

• Assessing ICL limits with partially ordered relations
• Introducing inductively increasing complexity in prompts
• Empirical and theoretical analysis of ICL constraints