Iterative In-Context Learning to Enhance LLMs Abstract Reasoning: The Case-Study of Algebraic Tasks

LLMs face significant challenges in systematic generalization, particularly when dealing with reasoning tasks requiring compositional rules and handling out-of-distribution examples. To address these challenges, we introduce an in-context learning methodology that improves the generalization capabilities of general purpose LLMs. Our approach employs an iterative example selection strategy, which incrementally constructs a tailored set of few-shot examples optimized to enhance model's performance on a given task. As a proof of concept, we apply this methodology to the resolution of algebraic expressions involving non-standard simplification rules, according to which the priority of addition and multiplication is changed. Our findings indicate that LLMs exhibit limited proficiency in these mathematical tasks. We further demonstrate that LLMs reasoning benefits from our iterative shot selection prompting strategy integrated with explicit reasoning instructions. Crucially, our experiments reveal that some LLMs achieve better generalization performances when prompted with simpler few-shot examples rather than complex ones following the test data distribution.