# Skill Learning via Policy Diversity Yields Identifiable Representations for Reinforcement Learning

arXiv: https://arxiv.org/abs/2507.14748 · HTML: https://mlsanity.com/paper/2507.14748/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 52 of its 73 references that are in the map.
- First posted on arXiv 19 Jul 2025.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 30 of 52)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Planning to Explore via Self-Supervised World Models](https://mlsanity.com/paper/2005.05960/) (2020)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Dynamics-Aware Unsupervised Discovery of Skills](https://mlsanity.com/paper/1907.01657/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Large-Scale Study of Curiosity-Driven Learning](https://mlsanity.com/paper/1808.04355/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Variational Intrinsic Control](https://mlsanity.com/paper/1611.07507/) (2016)
- [Self-Supervised Exploration via Disagreement](https://mlsanity.com/paper/1906.04161/) (2019)
- [Contrastive Learning as Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2206.07568/) (2022)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [Variational Information Maximisation for Intrinsically Motivated Reinforcement Learning](https://mlsanity.com/paper/1509.08731/) (2015)
- [Fast Task Inference with Variational Intrinsic Successor Features](https://mlsanity.com/paper/1906.05030/) (2019)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Variational Option Discovery Algorithms](https://mlsanity.com/paper/1807.10299/) (2018)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [Chaos is a Ladder: A New Theoretical Understanding of Contrastive Learning via Augmentation Overlap](https://mlsanity.com/paper/2203.13457/) (2022)

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

- [VendiRL: A Framework for Self-Supervised Reinforcement Learning of Diversely Diverse Skills](https://mlsanity.com/paper/2509.02930/) (2025)
- [Unifying Goal-Conditioned RL and Unsupervised Skill Learning via Control-Maximization](https://mlsanity.com/paper/2605.06145/) (2026)
- [On the Emergence and Test-Time Use of Structural Information in Large Language Models](https://mlsanity.com/paper/2601.17869/) (2026)
- [Learning to Perceive the World Through Control: Empowerment-Based Representation Learning](https://mlsanity.com/paper/2605.30656/) (2026)

## Abstract (arXiv)

Self-supervised feature learning and pretraining methods in reinforcement learning (RL) often rely on information-theoretic principles, termed mutual information skill learning (MISL). These methods aim to learn a representation of the environment while also incentivizing exploration thereof. However, the role of the representation and mutual information parametrization in MISL is not yet well understood theoretically. Our work investigates MISL through the lens of identifiable representation learning by focusing on the Contrastive Successor Features (CSF) method. We prove that CSF can provably recover the environment's ground-truth features up to a linear transformation due to the inner product parametrization of the features and skill diversity in a discriminative sense. This first identifiability guarantee for representation learning in RL also helps explain the implications of different mutual information objectives and the downsides of entropy regularizers. We empirically validate our claims in MuJoCo and DeepMind Control and show how CSF provably recovers the ground-truth features both from states and pixels.