In this expository note we show that the learning parities with noise (LPN) assumption is robust to weak dependencies in the noise distribution of small batches of samples. This provides a partial converse to the linearization technique of [AG11]. The material in this note is drawn from a recent work by the authors [GMR24], where the robustness guarantee was a key component in a cryptographic separation between reinforcement learning and supervised learning.

翻译：本导引性笔记表明，学习带噪声的奇偶性（LPN）假设对于小批量样本噪声分布中的弱相关性具有鲁棒性。这为[AG11]的线性化技术提供了部分逆推结果。本笔记内容源自作者近期工作[GMR24]，其中该鲁棒性保证是强化学习与监督学习之间密码学分离的关键组成部分。