# Disentangling the independently controllable factors of variation by interacting with the world

arXiv: https://arxiv.org/abs/1802.09484 · HTML: https://mlsanity.com/paper/1802.09484/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2018.

## Built on by (most cited first, 16 of 16)

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- [A Survey of State Representation Learning for Deep Reinforcement Learning](https://mlsanity.com/paper/2506.17518/) (2025)
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- [Reinforcement Learning with Exogenous States and Rewards](https://mlsanity.com/paper/2303.12957/) (2023)
- [From Pixels to Factors: Learning Independently Controllable State Variables for Reinforcement Learning](https://mlsanity.com/paper/2510.02484/) (2025)
- [Algebras of actions in an agent's representations of the world](https://mlsanity.com/paper/2310.01536/) (2023)
- [Disentanglement by means of action-induced representations](https://mlsanity.com/paper/2602.06741/) (2026)
- [Dueling World Models: Advantage-Style Action Channels for Common-Mode Distractor Rejection](https://mlsanity.com/paper/2608.06706/) (2026)
- [Comparing Reconstruction- and Contrastive-based Models for Visual Task Planning](https://mlsanity.com/paper/2109.06737/) (2021)
- [Intervening to Learn and Compose Causally Disentangled Representations](https://mlsanity.com/paper/2507.04754/) (2025)
- [elBERto: Self-supervised Commonsense Learning for Question Answering](https://mlsanity.com/paper/2203.09424/) (2022)
- [Disentangled Representations for Causal Cognition](https://mlsanity.com/paper/2407.00744/) (2024)

## Abstract (arXiv)

It has been postulated that a good representation is one that disentangles the underlying explanatory factors of variation. However, it remains an open question what kind of training framework could potentially achieve that. Whereas most previous work focuses on the static setting (e.g., with images), we postulate that some of the causal factors could be discovered if the learner is allowed to interact with its environment. The agent can experiment with different actions and observe their effects. More specifically, we hypothesize that some of these factors correspond to aspects of the environment which are independently controllable, i.e., that there exists a policy and a learnable feature for each such aspect of the environment, such that this policy can yield changes in that feature with minimal changes to other features that explain the statistical variations in the observed data. We propose a specific objective function to find such factors, and verify experimentally that it can indeed disentangle independently controllable aspects of the environment without any extrinsic reward signal.