Title: SHADE: SHAnnon DEcay Information-Based Regularization for Deep Learning. Abstract: Regularization is a big issue for training deep neural networks. In this paper, we propose a new information-theory-based regularization scheme named SHADE for SHAnnon DEcay. The originality of the approach is to define a prior based on conditional entropy, which explicitly decouples the learning of invariant representations in the regularizer and the learning of correlations between inputs and labels in the data fitting term. We explain why this quantity makes our model able to achieve invariance with respect to input variations. We empirically validate the efficiency of our approach to improve classification performances compared to standard regularization schemes on several standard architectures.