# Symmetry and Complexity in Object-Centric Deep Active Inference Models

arXiv: https://arxiv.org/abs/2304.14493 · HTML: https://mlsanity.com/paper/2304.14493/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 14 Apr 2023.

## Builds on (most cited first, 10 of 10)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [Are Disentangled Representations Helpful for Abstract Visual Reasoning?](https://mlsanity.com/paper/1905.12506/) (2019)
- [Explorations in Homeomorphic Variational Auto-Encoding](https://mlsanity.com/paper/1807.04689/) (2018)
- [Improving Generalization for Abstract Reasoning Tasks Using Disentangled Feature Representations](https://mlsanity.com/paper/1811.04784/) (2018)
- [Symmetry-Based Representations for Artificial and Biological General Intelligence](https://mlsanity.com/paper/2203.09250/) (2022)
- [The Free Energy Principle for Perception and Action: A Deep Learning Perspective](https://mlsanity.com/paper/2207.06415/) (2022)
- [Disentangling Shape and Pose for Object-Centric Deep Active Inference Models](https://mlsanity.com/paper/2209.09097/) (2022)

## Built on by (most cited first, 4 of 4)

- [Rethinking the Evaluating Framework for Natural Language Understanding in AI Systems: Language Acquisition as a Core for Future Metrics](https://mlsanity.com/paper/2309.11981/) (2023)
- [Object-Centric World Models Meet Monte Carlo Tree Search](https://mlsanity.com/paper/2601.06604/) (2026)
- [Learning to Navigate from Scratch using World Models and Curiosity: the Good, the Bad, and the Ugly](https://mlsanity.com/paper/2308.15852/) (2023)
- [Dynamic planning in hierarchical active inference](https://mlsanity.com/paper/2402.11658/) (2024)

## Abstract (arXiv)

Humans perceive and interact with hundreds of objects every day. In doing so, they need to employ mental models of these objects and often exploit symmetries in the object's shape and appearance in order to learn generalizable and transferable skills. Active inference is a first principles approach to understanding and modeling sentient agents. It states that agents entertain a generative model of their environment, and learn and act by minimizing an upper bound on their surprisal, i.e. their Free Energy. The Free Energy decomposes into an accuracy and complexity term, meaning that agents favor the least complex model, that can accurately explain their sensory observations. In this paper, we investigate how inherent symmetries of particular objects also emerge as symmetries in the latent state space of the generative model learnt under deep active inference. In particular, we focus on object-centric representations, which are trained from pixels to predict novel object views as the agent moves its viewpoint. First, we investigate the relation between model complexity and symmetry exploitation in the state space. Second, we do a principal component analysis to demonstrate how the model encodes the principal axis of symmetry of the object in the latent space. Finally, we also demonstrate how more symmetrical representations can be exploited for better generalization in the context of manipulation.