# The Conceptual VAE

arXiv: https://arxiv.org/abs/2203.11216 · HTML: https://mlsanity.com/paper/2203.11216/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 21 Mar 2022.

## Builds on (most cited first, 11 of 11)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Word Representations via Gaussian Embedding](https://mlsanity.com/paper/1412.6623/) (2014)
- [Quantum Variational Autoencoder](https://mlsanity.com/paper/1802.05779/) (2018)
- [Interacting Conceptual Spaces I : Grammatical Composition of Concepts](https://mlsanity.com/paper/1703.08314/) (2017)
- [Embedding Words as Distributions with a Bayesian Skip-gram Model](https://mlsanity.com/paper/1711.11027/) (2017)
- [A Thorough Formalization of Conceptual Spaces](https://mlsanity.com/paper/1706.06366/) (2017)
- [A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces](https://mlsanity.com/paper/2110.05985/) (2021)
- [Formalising Concepts as Grounded Abstractions](https://mlsanity.com/paper/2101.05125/) (2021)

## Built on by (most cited first, 3 of 3)

- [A Pattern Language for Machine Learning Tasks](https://mlsanity.com/paper/2407.02424/) (2024)
- [Formalising and Learning a Quantum Model of Concepts](https://mlsanity.com/paper/2302.14822/) (2023)
- [Interpretable Anomaly Detection in Cellular Networks by Learning Concepts in Variational Autoencoders](https://mlsanity.com/paper/2306.15938/) (2023)

## Abstract (arXiv)

In this report we present a new model of concepts, based on the framework of variational autoencoders, which is designed to have attractive properties such as factored conceptual domains, and at the same time be learnable from data. The model is inspired by, and closely related to, the Beta-VAE model of concepts, but is designed to be more closely connected with language, so that the names of concepts form part of the graphical model. We provide evidence that our model -- which we call the Conceptual VAE -- is able to learn interpretable conceptual representations from simple images of coloured shapes together with the corresponding concept labels. We also show how the model can be used as a concept classifier, and how it can be adapted to learn from fewer labels per instance. Finally, we formally relate our model to Gardenfors' theory of conceptual spaces, showing how the Gaussians we use to represent concepts can be formalised in terms of "fuzzy concepts" in such a space.