Title: Transformer-QL: A Step Towards Making Transformer Network Quadratically Large. Abstract: Transformer networks have shown outstanding performance on many natural language processing tasks. However the context length (the number of previous tokens on which the output states depend) of a Transformer network grows at best linearly with the memory and computational power used. This limitation prevents a transformer network to have very long context in a resource limited application. In this work, we propose a class of transformer networks, namely Transformer-QL (\bf{Q}uadratically \bf{L}arge), in which, the context length can grow at best quadratically with the memory and computational power used. We have empirically evaluated a Transformer-QL model in three long range language modeling datasets. The results show that Transformer-QL can provide significant improvements over other state of the art networks.