Title: A Simple Sparse Denoising Layer for Robust Deep Learning. Abstract: Deep models have achieved great success in many applications. However, vanilla deep models are not well-designed against the input perturbation.   In this work, we take an initial step to designing a simple robust layer as a lightweight plug-in for vanilla deep models.  To achieve this goal, we first propose a fast sparse coding and dictionary learning algorithm for sparse coding problem with an exact $k$-sparse constraint or  $l_0$ norm regularization. Our method comes with a closed-form approximation for the sparse coding phase by taking advantage of a novel structured dictionary.   With this handy approximation,  we propose a simple sparse denoising layer (SDL) as a lightweight robust plug-in.   Extensive experiments on both classification and reinforcement learning tasks manifest the effectiveness of our methods.