In-context learning (ICL) is highly sensitive to which demonstrations appear in the prompt, but selecting them is expensive because the space of possible demonstration contexts and combinations is enormous. We argue that demonstration selection is \emph{easier to judge than to find}: predicting whether a specific query--context pair (q,D) will succeed is cheaper and more general than searching for an optimal D⋆. Based on this insight, we propose DiSP, a sample-and-judge framework that stratifies queries by difficulty. DiSP runs random demonstration trials to estimate success rate of each training query, trains a lightweight router to predict difficulty from the query, and trains level-specific judges for sampled demonstrations. At inference, DiSP performs stop-on-acceptance judging under an explicit budget, emitting diagnostic risk tags when no suitable context is found. Across five classification datasets with Llama3--8B and Qwen2.5--7B, DiSP achieves the best average accuracy, improving over strong learned selection baselines by up to 3.4%, while achieving up to 23× end-to-end wall-clock speedup.
In-context learning (ICL) is an emerging paradigm that employs the semantic information inherent in large language models (LLMs) for generating answers to user queries. While the remarkable performance of ICL has been widely known, a general modeling and a rigorous theoretical analysis of this paradigm are still lacking. This work presents a probabilistic model for ICL and derives the performance of ICL for both general parametric distributions and exponential families. Based on the derived results, the work explains the impact of multiple factors such as the number of demonstrations, the sensitivity of the probabilistic model to the variation of its parameters, as well as the similarity between the demonstrations and the query on the performance of ICL.
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.
While many-shot ICL achieves remarkable performance, prior studies of its scaling behavior have mainly focused on non-reasoning tasks. In this work, we study many-shot ICL on reasoning tasks, with a particular focus on many-shot chain-of-thought in-context learning (CoT-ICL). Analyzing across non-reasoning and reasoning tasks and across non-reasoning and reasoning-oriented LLMs, we identify several distinctive properties of many-shot CoT-ICL. We further interpret these findings by viewing many-shot CoT-ICL as in-context test-time learning rather than scaled pattern matching, and suggest two principles: (i) demonstrations should be easy for the target model to understand, and (ii) they should be ordered to support a smooth conceptual progression. Guided by the principle, we propose Curvilinear Demonstration Selection (CDS), a simple ordering method that yields up to a 5.42 percentage-point gain on a math task with 64 demonstrations. Overall, our results reframe the long context window from a retrieval buffer into a structured curriculum for in-context test-time learning.