Determining whether large language models derive answers from context or prior knowledge remains a fundamental challenge. Self-contained linguistic olympiad puzzles provide a controlled setting where all answers derive solely from expert-designed context examples without external knowledge. Removing individual context examples can eliminate information needed for specific questions while leaving the rest of the puzzle unchanged. We leverage this to introduce a diagnostic framework for analyzing individual context examples. Using 53 UK Linguistics Olympiad puzzles, we generate two modified variants by deleting a single context example: (1) uniform random deletion, and (2) targeted deletion (inspired by error-correcting codes) to remove a structurally load-bearing example uniquely carrying necessary information. We formalize this impact using a Question Damage Score to classify puzzles as fragile or robust. Evaluating three frontier LLMs under instructions to abstain when information is insufficient, we find they rarely abstain, often continuing to produce correct answers after load-bearing context is removed. These findings motivate further investigation into context-based reasoning, prior knowledge, memorization, and linguistic inference. Beyond abstention, the framework enables fine-grained analyses of context reliance, including causal interventions, stopping-set analysis, targeted contamination studies, and mechanistic interpretability.
Large language models (LLMs) offer a promising approach to machine translation (MT) for extremely low-resource languages by incorporating linguistic resources through in-context learning. However, LLMs often struggle to apply grammatical information effectively during translation. Inspired by recent progress in chain-of-thought reasoning, we investigate whether low-resource MT can benefit from structured intermediate steps of linguistic analysis and grammatical reasoning. We propose a pipeline for automatically generating step-by-step linguistic reasoning traces from Universal Dependencies treebanks, dictionaries, and grammar-rule banks. We evaluate these traces in three settings: in-context learning (ICL), supervised fine-tuning (SFT), and reinforcement fine-tuning (RFT), on Xibe and Chintang as test cases. Our results show that linguistic reasoning traces are most effective as inference-time guidance: in ICL, reliable linguistic reasoning traces substantially improve translation performance across models, languages, and metrics. In contrast, using these traces as training data yields smaller and less consistent gains, as models learn the format but often generate error-prone content. These findings suggest that LLMs can leverage grammatical information for low-resource MT when given reliable linguistic analyses, while learning to generate such analyses remains a major bottleneck.