Despite the fact that large language models (LLMs) show exceptional skill in instruction following tasks, this strength can turn into a vulnerability when the models are required to disregard certain instructions.Instruction following tasks typically involve a clear task description and input text containing the target data to be processed.However, when the input itself resembles an instruction, confusion may arise, even if there is explicit prompting to distinguish between the task instruction and the input.We refer to this phenomenon as instructional distraction.In this paper, we introduce a novel benchmark, named DIM-Bench, specifically designed to assess LLMs' performance under instructional distraction.The benchmark categorizes real-world instances of instructional distraction and evaluates LLMs across four instruction tasks: rewriting, proofreading, translation, and style transfer-alongside five input tasks: reasoning, code generation, mathematical reasoning, bias detection, and question answering.Our experimental results reveal that even the most advanced LLMs are susceptible to instructional distraction, often failing to accurately follow user intent in such cases. Instruction Input ExampleRewrite Reasoning Instruction: Paraphrase the following text.Input: Laundry detergents were once manufactured to contain high ... which would a lake become as a result of the phosphorous in the detergent?Options : A. canyon B. desert C. swamp D. river

We introduce transductive program synthesis, a new formulation of the program synthesis task that explicitly leverages test inputs during synthesis. While prior approaches to program synthesis--whether based on natural language descriptions or input-output examples--typically aim to generalize from training examples, they often struggle with robustness, especially in real-world settings where training examples are limited and test inputs involve various edge cases. To address this, we propose a novel framework that improves robustness by treating synthesis as an active learning over a finite hypothesis class defined by programs' outputs. We use an LLM to predict outputs for selected test inputs and eliminate inconsistent hypotheses, where the inputs are chosen via a greedy maximin algorithm to minimize the number of LLM queries required. We evaluate our approach on four benchmarks: Playgol, MBPP+, 1D-ARC, and programmatic world modeling on MiniGrid. We demonstrate that our method significantly improves program synthesis in both accuracy and efficiency. We release our code at https://github.com/klee972/SYNTRA.