Learned representations at the level of characters, sub-words, words, and sentences, have each contributed to advances in understanding different NLP tasks and linguistic phenomena. However, learning textual embeddings is costly as they are tokenization specific and require different models to be trained for each level of abstraction. We introduce a novel language representation model which can learn to compress to different levels of abstraction at different layers of the same model. We apply Nonparametric Variational Information Bottleneck (NVIB) to stacked Transformer self-attention layers in the encoder, which encourages an information-theoretic compression of the representations through the model. We find that the layers within the model correspond to increasing levels of abstraction and that their representations are more linguistically informed. Finally, we show that NVIB compression results in a model which is more robust to adversarial perturbations.