Reason Analogically via Cross-domain Prior Knowledge: An Empirical Study of Cross-domain Knowledge Transfer for In-Context Learning

In-context retrieval (ICR) is a retrieval-based form of in-context learning (ICL) in which demonstrations are retrieved from a source database based on similarity to the query, rather than sampled independently. In this work, we formulate ICR as a type of domain adaptation problem, where the source distribution $P$ of the database may differ from the target distribution $Q$ of the test query-label pair. We investigate the performance of ICR under a flexible class of distributional shifts that substantially extends prior work \citep{li2024fine,guo2025retrieval}, and establish theoretical guarantees that quantify the benefits and pitfalls of this learning paradigm. Our theory is verified by experiments on synthetic and language tasks.

Large language models (LLMs) have made notable progress in logical reasoning, yet still fall short of human-level performance. Current boosting strategies rely on expert-crafted in-domain demonstrations, limiting their applicability in expertise-scarce domains, such as specialized mathematical reasoning, formal logic, or legal analysis. In this work, we demonstrate the feasibility of leveraging cross-domain demonstrating examples to boost the LLMs' reasoning performance. Despite substantial domain differences, many reusable implicit logical structures are shared across domains. In order to effectively retrieve cross-domain examples for unseen domains under investigation, in this work, we further propose an effective retrieval method, called domain-invariant neurons-based retrieval (DIN-Retrieval). Concisely, DIN-Retrieval first summarizes a hidden representation that is universal across different domains. Then, during the inference stage, we use the DIN vector to retrieve structurally compatible cross-domain demonstrations for the in-context learning. Experimental results in multiple settings for the transfer of mathematical and logical reasoning demonstrate that our method achieves an average improvement of 1.8 over the state-of-the-art methods \footnote{Our implementation is available at https://github.com/Leon221220/DIN-Retrieval}.

In-context learning (ICL) is often motivated by the intuition that demonstrations help because they provide correct input-output examples. However, we reveal a counterintuitive phenomenon: correctness does not guarantee exemplar utility, and some correct demonstrations can even reduce ICL accuracy. To study this correctness-utility gap, we introduce task-preserving perturbations, where only the exemplar input is changed, while the example remains a correct instance of the same task. Concretely, each perturbed exemplar is assigned the target induced by the task mapping. This framework covers both label-updating perturbations, where task-relevant semantics change and targets are recomputed, and stricter target-preserving perturbations, where the original target remains valid. We formalize the resulting failure mode as contextual evidence shift: task-preserving perturbations can change the effective mixture of evidence used by the model for contextual inference, thereby separating exemplar correctness from exemplar utility. Across sentiment classification, logical reasoning, and math word problems, we find that task-preserving perturbed demonstrations can substantially degrade ICL performance, especially for smaller models, harder tasks, and higher perturbation ratios. Our results show that robust ICL requires evaluating not only whether demonstrations are correct, but also how they influence contextual inference. Code is available at https://github.com/Chenghao-Qiu/Task-Preserving-ICL.