Title: Counterbalancing Teacher: Regularizing Batch Normalized Models for Robustness. Abstract: Batch normalization (BN) is a ubiquitous technique for training deep neural networks that accelerates their convergence to reach higher accuracy. However, we demonstrate that BN comes with a fundamental drawback: it incentivizes the model to rely on frequent low-variance features that are highly specific to the training (in-domain) data, and thus fails to generalize to out-of-domain examples. In this work, we investigate this phenomenon by first showing that removing BN layers across a wide range of architectures leads to lower out-of-domain and corruption errors at the cost of higher in-domain error. We then propose the Counterbalancing Teacher (CT) method, which leverages a frozen copy of the same model without BN as a teacher to enforce the student network's learning of robust representations by substantially adapting its weights through a consistency loss function. This regularization signal helps CT perform well in unforeseen data shifts, even without information from the target domain as in prior works. We theoretically show in an overparameterized linear regression setting why normalization leads a model's reliance on such in-domain features, and empirically demonstrate the efficacy of CT by outperforming several methods on standard robustness benchmark datasets such as CIFAR-10-C, CIFAR-100-C, and VLCS.