# SCAN: Learning Hierarchical Compositional Visual Concepts

arXiv: https://arxiv.org/abs/1707.03389 · HTML: https://mlsanity.com/paper/1707.03389/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2017.

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

- [LogiDynamics: Unraveling the Dynamics of Inductive, Abductive and Deductive Logical Inferences in LLM Reasoning](https://mlsanity.com/paper/2502.11176/) (2025)
- [Visual Referential Games Further the Emergence of Disentangled Representations](https://mlsanity.com/paper/2304.14511/) (2023)
- [Multimodal Variational Autoencoder: a Barycentric View](https://mlsanity.com/paper/2412.20487/) (2024)
- [Meta-Referential Games to Learn Compositional Learning Behaviours](https://mlsanity.com/paper/2207.08012/) (2022)
- [RotLSTM: Rotating Memories in Recurrent Neural Networks](https://mlsanity.com/paper/2105.00357/) (2021)
- [ETHER: Aligning Emergent Communication for Hindsight Experience Replay](https://mlsanity.com/paper/2307.15494/) (2023)

## Abstract (arXiv)

The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such representations are compositional and hierarchical, they can be recombined into an exponentially large set of new concepts. This paper describes SCAN (Symbol-Concept Association Network), a new framework for learning such abstractions in the visual domain. SCAN learns concepts through fast symbol association, grounding them in disentangled visual primitives that are discovered in an unsupervised manner. Unlike state of the art multimodal generative model baselines, our approach requires very few pairings between symbols and images and makes no assumptions about the form of symbol representations. Once trained, SCAN is capable of multimodal bi-directional inference, generating a diverse set of image samples from symbolic descriptions and vice versa. It also allows for traversal and manipulation of the implicit hierarchy of visual concepts through symbolic instructions and learnt logical recombination operations. Such manipulations enable SCAN to break away from its training data distribution and imagine novel visual concepts through symbolically instructed recombination of previously learnt concepts.