# Probabilistic World Modeling with Asymmetric Distance Measure

arXiv: https://arxiv.org/abs/2403.10875 · HTML: https://mlsanity.com/paper/2403.10875/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 16 Mar 2024.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 20 of 20)

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- [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)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [CURL: Contrastive Unsupervised Representations for Reinforcement Learning](https://mlsanity.com/paper/2004.04136/) (2020)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Search on the Replay Buffer: Bridging Planning and Reinforcement Learning](https://mlsanity.com/paper/1906.05253/) (2019)
- [Noise Contrastive Estimation and Negative Sampling for Conditional Models: Consistency and Statistical Efficiency](https://mlsanity.com/paper/1809.01812/) (2018)
- [Video as the New Language for Real-World Decision Making](https://mlsanity.com/paper/2402.17139/) (2024)
- [The Laplacian in RL: Learning Representations with Efficient Approximations](https://mlsanity.com/paper/1810.04586/) (2018)
- [InfoBot: Transfer and Exploration via the Information Bottleneck](https://mlsanity.com/paper/1901.10902/) (2019)
- [How Far I'll Go: Offline Goal-Conditioned Reinforcement Learning via f-Advantage Regression](https://mlsanity.com/paper/2206.03023/) (2022)
- [Learning Actionable Representations with Goal-Conditioned Policies](https://mlsanity.com/paper/1811.07819/) (2018)
- [C-Planning: An Automatic Curriculum for Learning Goal-Reaching Tasks](https://mlsanity.com/paper/2110.12080/) (2021)
- [Bag of Image Patch Embedding Behind the Success of Self-Supervised Learning](https://mlsanity.com/paper/2206.08954/) (2022)

## Abstract (arXiv)

Representation learning is a fundamental task in machine learning, aiming at uncovering structures from data to facilitate subsequent tasks. However, what is a good representation for planning and reasoning in a stochastic world remains an open problem. In this work, we posit that learning a distance function is essential to allow planning and reasoning in the representation space. We show that a geometric abstraction of the probabilistic world dynamics can be embedded into the representation space through asymmetric contrastive learning. Unlike previous approaches that focus on learning mutual similarity or compatibility measures, we instead learn an asymmetric similarity function that reflects the state reachability and allows multi-way probabilistic inference. Moreover, by conditioning on a common reference state (e.g. the observer's current state), the learned representation space allows us to discover the geometrically salient states that only a handful of paths can lead through. These states can naturally serve as subgoals to break down long-horizon planning tasks. We evaluate our method in gridworld environments with various layouts and demonstrate its effectiveness in discovering the subgoals.