# Symbolic Disentangled Representations for Images

arXiv: https://arxiv.org/abs/2412.19847 · HTML: https://mlsanity.com/paper/2412.19847/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 96 references that are in the map.
- First posted on arXiv 25 Dec 2024.

## Builds on (most cited first, 30 of 60)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Conditional Object-Centric Learning from Video](https://mlsanity.com/paper/2111.12594/) (2021)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Bridging the Gap to Real-World Object-Centric Learning](https://mlsanity.com/paper/2209.14860/) (2022)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Illiterate DALL-E Learns to Compose](https://mlsanity.com/paper/2110.11405/) (2021)
- [SlotFormer: Unsupervised Visual Dynamics Simulation with Object-Centric Models](https://mlsanity.com/paper/2210.05861/) (2022)
- [xGen-MM (BLIP-3): A Family of Open Large Multimodal Models](https://mlsanity.com/paper/2408.08872/) (2024)

## Built on by (most cited first, 2 of 2)

- [Measuring and Guiding Monosemanticity](https://mlsanity.com/paper/2506.19382/) (2025)
- [KAGE-Bench: Fast Known-Axis Visual Generalization Evaluation for Reinforcement Learning](https://mlsanity.com/paper/2601.14232/) (2026)

## Abstract (arXiv)

The idea of disentangled representations is to reduce the data to a set of generative factors that produce it. Typically, such representations are vectors in latent space, where each coordinate corresponds to one of the generative factors. The object can then be modified by changing the value of a particular coordinate, but it is necessary to determine which coordinate corresponds to the desired generative factor -- a difficult task if the vector representation has a high dimension. In this article, we propose ArSyD (Architecture for Symbolic Disentanglement), which represents each generative factor as a vector of the same dimension as the resulting representation. In ArSyD, the object representation is obtained as a superposition of the generative factor vector representations. We call such a representation a textitsymbolic disentangled representation. We use the principles of Hyperdimensional Computing (also known as Vector Symbolic Architectures), where symbols are represented as hypervectors, allowing vector operations on them. Disentanglement is achieved by construction, no additional assumptions about the underlying distributions are made during training, and the model is only trained to reconstruct images in a weakly supervised manner. We study ArSyD on the dSprites and CLEVR datasets and provide a comprehensive analysis of the learned symbolic disentangled representations. We also propose new disentanglement metrics that allow comparison of methods using latent representations of different dimensions. ArSyD allows to edit the object properties in a controlled and interpretable way, and the dimensionality of the object property representation coincides with the dimensionality of the object representation itself.