# Density Matrices for Metaphor Understanding

arXiv: https://arxiv.org/abs/2408.11846 · HTML: https://mlsanity.com/paper/2408.11846/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 12 Aug 2024.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Supervised Learning of Universal Sentence Representations from Natural Language Inference Data](https://mlsanity.com/paper/1705.02364/) (2017)
- [QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer](https://mlsanity.com/paper/2102.12846/) (2021)
- [The Mathematics of Text Structure](https://mlsanity.com/paper/1904.03478/) (2019)
- [Open System Categorical Quantum Semantics in Natural Language Processing](https://mlsanity.com/paper/1502.00831/) (2015)
- [Modelling Lexical Ambiguity with Density Matrices](https://mlsanity.com/paper/2010.05670/) (2020)
- [Sentence Entailment in Compositional Distributional Semantics](https://mlsanity.com/paper/1512.04419/) (2015)
- [Meaning updating of density matrices](https://mlsanity.com/paper/2001.00862/) (2020)
- [Towards logical negation for compositional distributional semantics](https://mlsanity.com/paper/2005.04929/) (2020)
- [Conversational Negation using Worldly Context in Compositional Distributional Semantics](https://mlsanity.com/paper/2105.05748/) (2021)
- [Composing Conversational Negation](https://mlsanity.com/paper/2107.06820/) (2021)
- [Cats climb entails mammals move: preserving hyponymy in compositional distributional semantics](https://mlsanity.com/paper/2005.14134/) (2020)
- [Language Modeling with Reduced Densities](https://mlsanity.com/paper/2007.03834/) (2020)
- [Compositional Distributional Semantics with Compact Closed Categories and Frobenius Algebras](https://mlsanity.com/paper/1505.00138/) (2015)
- [Distributional Sentence Entailment Using Density Matrices](https://mlsanity.com/paper/1506.06534/) (2015)

## Abstract (arXiv)

In physics, density matrices are used to represent mixed states, i.e. probabilistic mixtures of pure states. This concept has previously been used to model lexical ambiguity. In this paper, we consider metaphor as a type of lexical ambiguity, and examine whether metaphorical meaning can be effectively modelled using mixtures of word senses. We find that modelling metaphor is significantly more difficult than other kinds of lexical ambiguity, but that our best-performing density matrix method outperforms simple baselines as well as some neural language models.