On Learning Parities with Dependent Noise

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.