# Generative Neurosymbolic Machines

arXiv: https://arxiv.org/abs/2010.12152 · HTML: https://mlsanity.com/paper/2010.12152/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 30 of 57)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
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- [Simple Unsupervised Object-Centric Learning for Complex and Naturalistic Videos](https://mlsanity.com/paper/2205.14065/) (2022)
- [GENESIS-V2: Inferring Unordered Object Representations without Iterative Refinement](https://mlsanity.com/paper/2104.09958/) (2021)
- [ClevrTex: A Texture-Rich Benchmark for Unsupervised Multi-Object Segmentation](https://mlsanity.com/paper/2111.10265/) (2021)
- [Object-Centric Slot Diffusion](https://mlsanity.com/paper/2303.10834/) (2023)
- [Neuro-Symbolic Artificial Intelligence: Current Trends](https://mlsanity.com/paper/2105.05330/) (2021)
- [Invariant Slot Attention: Object Discovery with Slot-Centric Reference Frames](https://mlsanity.com/paper/2302.04973/) (2023)
- [Guess What Moves: Unsupervised Video and Image Segmentation by Anticipating Motion](https://mlsanity.com/paper/2205.07844/) (2022)
- [Neural Systematic Binder](https://mlsanity.com/paper/2211.01177/) (2022)
- [Efficient Iterative Amortized Inference for Learning Symmetric and Disentangled Multi-Object Representations](https://mlsanity.com/paper/2106.03630/) (2021)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Compositional Scene Representation Learning via Reconstruction: A Survey](https://mlsanity.com/paper/2202.07135/) (2022)
- [Towards Unsupervised Object Detection From LiDAR Point Clouds](https://mlsanity.com/paper/2311.02007/) (2023)
- [Structured World Belief for Reinforcement Learning in POMDP](https://mlsanity.com/paper/2107.08577/) (2021)
- [Neuro-Symbolic Verification of Deep Neural Networks](https://mlsanity.com/paper/2203.00938/) (2022)
- [Learning What and Where: Disentangling Location and Identity Tracking Without Supervision](https://mlsanity.com/paper/2205.13349/) (2022)
- [Slot-VAE: Object-Centric Scene Generation with Slot Attention](https://mlsanity.com/paper/2306.06997/) (2023)
- [Unsupervised Multi-object Segmentation by Predicting Probable Motion Patterns](https://mlsanity.com/paper/2210.12148/) (2022)
- [Posterior Collapse of a Linear Latent Variable Model](https://mlsanity.com/paper/2205.04009/) (2022)
- [Boosting Object Representation Learning via Motion and Object Continuity](https://mlsanity.com/paper/2211.09771/) (2022)
- [MEWL: Few-shot multimodal word learning with referential uncertainty](https://mlsanity.com/paper/2306.00503/) (2023)
- [Slot State Space Models](https://mlsanity.com/paper/2406.12272/) (2024)
- [Promising or Elusive? Unsupervised Object Segmentation from Real-world Single Images](https://mlsanity.com/paper/2210.02324/) (2022)
- [Unlocking Slot Attention by Changing Optimal Transport Costs](https://mlsanity.com/paper/2301.13197/) (2023)
- [Multi-Object Discovery by Low-Dimensional Object Motion](https://mlsanity.com/paper/2307.08027/) (2023)
- [Motion-inductive Self-supervised Object Discovery in Videos](https://mlsanity.com/paper/2210.00221/) (2022)
- [Scalable Neural-Probabilistic Answer Set Programming](https://mlsanity.com/paper/2306.08397/) (2023)
- [Slot-Guided Adaptation of Pre-trained Diffusion Models for Object-Centric Learning and Compositional Generation](https://mlsanity.com/paper/2501.15878/) (2025)
- [Unsupervised Learning of Compositional Scene Representations from Multiple Unspecified Viewpoints](https://mlsanity.com/paper/2112.03568/) (2021)

## Abstract (arXiv)

Reconciling symbolic and distributed representations is a crucial challenge that can potentially resolve the limitations of current deep learning. Remarkable advances in this direction have been achieved recently via generative object-centric representation models. While learning a recognition model that infers object-centric symbolic representations like bounding boxes from raw images in an unsupervised way, no such model can provide another important ability of a generative model, i.e., generating (sampling) according to the structure of learned world density. In this paper, we propose Generative Neurosymbolic Machines, a generative model that combines the benefits of distributed and symbolic representations to support both structured representations of symbolic components and density-based generation. These two crucial properties are achieved by a two-layer latent hierarchy with the global distributed latent for flexible density modeling and the structured symbolic latent map. To increase the model flexibility in this hierarchical structure, we also propose the StructDRAW prior. In experiments, we show that the proposed model significantly outperforms the previous structured representation models as well as the state-of-the-art non-structured generative models in terms of both structure accuracy and image generation quality. Our code, datasets, and trained models are available at https://github.com/JindongJiang/GNM