Title: Language Modeling Using Tensor Trains. Abstract: Tensor networks have previously been shown to have potential in language modelling in theory, but lack of practical evidence support.  We propose a novel Tensor Train Language Model (TTLM) based on Tensor-Train decomposition.  We prove that TTLM generalizes  Second-order Recurrent Neural Networks (RNNs),  Recurrent Arithmetic Circuits and Multiplicative Integration RNNs in the sense that the architecture of all of these are, essentially, special cases of that of TTLM. To show the usefulness of TTLM, we perform a principled experimental evaluation on language modeling tasks, showing that our proposed variants, TTLM-large and TTLM-Tiny, can be more effective than Vanilla RNN while TTLM-Tiny has the half of the model size.