# A Generalized Language Model in Tensor Space

## TL;DR

This paper introduces Tensor Space Language Model (TSLM), a high-dimensional tensor-based language model that generalizes n-gram models and effectively captures context, showing promising results on standard benchmarks.

## Contribution

The paper proposes a novel high-order tensor language model using tensor networks and decomposition, extending traditional n-gram models with greater expressive power.

## Key findings

- TSLM generalizes n-gram models through tensor representations.
- Experimental results on PTB and WikiText datasets demonstrate TSLM's effectiveness.
- High-dimensional tensor space improves language modeling capabilities.

## Abstract

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.