Title: Toward Adversarial Training on Contextualized Language Representation. Abstract: Beyond the success story of adversarial training (AT) in the recent text domain on top of pre-trained language models (PLMs), our empirical study showcases the inconsistent gains from AT on some tasks, e.g. commonsense reasoning, named entity recognition. This paper investigates AT from the perspective of the contextualized language representation outputted by PLM encoders. We find the current AT attacks lean to generate sub-optimal adversarial examples that can fool the decoder part but have a minor effect on the encoder. However, we find it necessary to effectively deviate the latter one to allow AT to gain. Based on the observation, we propose simple yet effective \textit{Contextualized representation-Adversarial Training} (CreAT), in which the attack is explicitly optimized to deviate the contextualized representation of the encoder. It allows a global optimization of adversarial examples that can fool the entire model. We also find CreAT gives rise to a better direction to optimize the adversarial examples, to let them less sensitive to hyperparameters. Compared to AT, CreAT produces consistent performance gains on a wider range of tasks and is proven to be more effective for language pre-training where only the encoder part is kept for downstream tasks. We achieve the new state-of-the-art performances on a series of challenging benchmarks, e.g. AdvGLUE (59.1 $ \rightarrow $ 61.1), HellaSWAG (93.0  $ \rightarrow $ 94.9), ANLI (68.1  $ \rightarrow $ 69.3).