# Compositionality as we see it, everywhere around us

arXiv: https://arxiv.org/abs/2110.05327 · HTML: https://mlsanity.com/paper/2110.05327/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 116 references that are in the map.
- First posted on arXiv 11 Oct 2021.

## Builds on (most cited first, 22 of 22)

- [QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer](https://mlsanity.com/paper/2102.12846/) (2021)
- [Foundations for Near-Term Quantum Natural Language Processing](https://mlsanity.com/paper/2012.03755/) (2020)
- [lambeq: An Efficient High-Level Python Library for Quantum NLP](https://mlsanity.com/paper/2110.04236/) (2021)
- [Quantum Natural Language Processing on Near-Term Quantum Computers](https://mlsanity.com/paper/2005.04147/) (2020)
- [Category Theory in Machine Learning](https://mlsanity.com/paper/2106.07032/) (2021)
- [The Frobenius anatomy of word meanings I: subject and object relative pronouns](https://mlsanity.com/paper/1404.5278/) (2014)
- [Quantum Algorithms for Compositional Natural Language Processing](https://mlsanity.com/paper/1608.01406/) (2016)
- [The Mathematics of Text Structure](https://mlsanity.com/paper/1904.03478/) (2019)
- [Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus](https://mlsanity.com/paper/1902.03178/) (2019)
- [Open System Categorical Quantum Semantics in Natural Language Processing](https://mlsanity.com/paper/1502.00831/) (2015)
- [Compositional game theory](https://mlsanity.com/paper/1603.04641/) (2016)
- [Interacting Conceptual Spaces I : Grammatical Composition of Concepts](https://mlsanity.com/paper/1703.08314/) (2017)
- [Meaning updating of density matrices](https://mlsanity.com/paper/2001.00862/) (2020)
- [Grammar Equations](https://mlsanity.com/paper/2106.07485/) (2021)
- [How to make qubits speak](https://mlsanity.com/paper/2107.06776/) (2021)
- [A quantum teleportation inspired algorithm produces sentence meaning from word meaning and grammatical structure](https://mlsanity.com/paper/1305.0556/) (2013)
- [A Diagrammatic Axiomatisation for Qubit Entanglement](https://mlsanity.com/paper/1501.07082/) (2015)
- [The ZX calculus is a language for surface code lattice surgery](https://mlsanity.com/paper/1704.08670/) (2017)
- [Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)](https://mlsanity.com/paper/2102.10984/) (2021)
- [Talking Space: inference from spatial linguistic meanings](https://mlsanity.com/paper/2109.06554/) (2021)
- [A categorical semantics for causal structure](https://mlsanity.com/paper/1701.04732/) (2017)
- [From quantum foundations via natural language meaning to a theory of everything](https://mlsanity.com/paper/1602.07618/) (2016)

## Built on by (most cited first, 11 of 11)

- [Towards Compositional Interpretability for XAI](https://mlsanity.com/paper/2406.17583/) (2024)
- [A Quantum Natural Language Processing Approach to Musical Intelligence](https://mlsanity.com/paper/2111.06741/) (2021)
- [Distilling Text into Circuits](https://mlsanity.com/paper/2301.10595/) (2023)
- [Compositionality Unlocks Deep Interpretable Models](https://mlsanity.com/paper/2504.02667/) (2025)
- [Categorical semantics of compositional reinforcement learning](https://mlsanity.com/paper/2208.13687/) (2022)
- [Finding Manifolds With Bilinear Autoencoders](https://mlsanity.com/paper/2510.16820/) (2025)
- [Quantum Algorithms for Compositional Text Processing](https://mlsanity.com/paper/2408.06061/) (2024)
- [Bilinear autoencoders find interpretable manifolds](https://mlsanity.com/paper/2605.08891/) (2026)
- [From Mechanistic to Compositional Interpretability](https://mlsanity.com/paper/2605.08934/) (2026)
- [Causal Models for Growing Networks](https://mlsanity.com/paper/2504.01012/) (2025)
- [Categorical AI phenomenology: A first-person approach](https://mlsanity.com/paper/2608.20420/) (2026)

## Abstract (arXiv)

There are different meanings of the term "compositionality" within science: what one researcher would call compositional, is not at all compositional for another researcher. The most established conception is usually attributed to Frege, and is characterised by a bottom-up flow of meanings: the meaning of the whole can be derived from the meanings of the parts, and how these parts are structured together. Inspired by work on compositionality in quantum theory, and categorical quantum mechanics in particular, we propose the notions of Schrodinger, Whitehead, and complete compositionality. Accounting for recent important developments in quantum technology and artificial intelligence, these do not have the bottom-up meaning flow as part of their definitions. Schrodinger compositionality accommodates quantum theory, and also meaning-as-context. Complete compositionality further strengthens Schrodinger compositionality in order to single out theories like ZX-calculus, that are complete with regard to the intended model. All together, our new notions aim to capture the fact that compositionality is at its best when it is `real', `non-trivial', and even more when it also is `complete'. At this point we only put forward the intuitive and/or restricted formal definitions, and leave a fully comprehensive definition to future collaborative work.