# A Generalized Language Model in Tensor Space

arXiv: https://arxiv.org/abs/1901.11167 · HTML: https://mlsanity.com/paper/1901.11167/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2019.

## Built on by (most cited first, 6 of 6)

- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [Language Modeling Using Tensor Trains](https://mlsanity.com/paper/2405.04590/) (2024)
- [DisCoCLIP: A Distributional Compositional Tensor Network Encoder for Vision-Language Understanding](https://mlsanity.com/paper/2509.21287/) (2025)
- [Tensor Methods for Language Models: From Token Representation to Training, Adaptation, Inference, Compression, and Interpretability](https://mlsanity.com/paper/2608.30505/) (2026)
- [A quatum inspired neural network for geometric modeling](https://mlsanity.com/paper/2401.01801/) (2024)
- [Traitement quantique des langues : 'etat de l'art](https://mlsanity.com/paper/2406.15370/) (2024)

## Abstract (arXiv)

In the literature, tensors have been effectively used for capturing the context information in language models. However, the existing methods usually adopt relatively-low order tensors, which have limited expressive power in modeling language. Developing a higher-order tensor representation is challenging, in terms of deriving an effective solution and showing its generality. In this paper, we propose a language model named Tensor Space Language Model (TSLM), by utilizing tensor networks and tensor decomposition. In TSLM, we build a high-dimensional semantic space constructed by the tensor product of word vectors. Theoretically, we prove that such tensor representation is a generalization of the n-gram language model. We further show that this high-order tensor representation can be decomposed to a recursive calculation of conditional probability for language modeling. The experimental results on Penn Tree Bank (PTB) dataset and WikiText benchmark demonstrate the effectiveness of TSLM.