# Geometric Priors for Generalizable World Models via Vector Symbolic Architecture

arXiv: https://arxiv.org/abs/2602.21467 · HTML: https://mlsanity.com/paper/2602.21467/

## 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 14 of its 28 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [Contrastive Learning of Structured World Models](https://mlsanity.com/paper/1911.12247/) (2019)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [A Survey on Interpretable Reinforcement Learning](https://mlsanity.com/paper/2112.13112/) (2021)
- [Learning Symmetric Embeddings for Equivariant World Models](https://mlsanity.com/paper/2204.11371/) (2022)
- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [A Novel Hyperdimensional Computing Framework for Online Time Series Forecasting on the Edge](https://mlsanity.com/paper/2402.01999/) (2024)
- [Spiking Hyperdimensional Network: Neuromorphic Models Integrated with Memory-Inspired Framework](https://mlsanity.com/paper/2110.00214/) (2021)
- [HEAL: Brain-inspired Hyperdimensional Efficient Active Learning](https://mlsanity.com/paper/2402.11223/) (2024)

## Abstract (arXiv)

A key challenge in artificial intelligence and neuroscience is understanding how neural systems learn representations that capture the underlying dynamics of the world. Most world models represent the transition function with unstructured neural networks, limiting interpretability, sample efficiency, and generalization to unseen states or action compositions. We address these issues with a generalizable world model grounded in Vector Symbolic Architecture (VSA) principles as geometric priors. Our approach utilizes learnable Fourier Holographic Reduced Representation (FHRR) encoders to map states and actions into a high dimensional complex vector space with learned group structure and models transitions with element-wise complex multiplication. We formalize the framework's group theoretic foundation and show how training such structured representations to be approximately invariant enables strong multi-step composition directly in latent space and generalization performances over various experiments. On a discrete grid world environment, our model achieves 87.5% zero shot accuracy to unseen state-action pairs, obtains 53.6% higher accuracy on 20-timestep horizon rollouts, and demonstrates 4x higher robustness to noise relative to an MLP baseline. These results highlight how training to have latent group structure yields generalizable, data-efficient, and interpretable world models, providing a principled pathway toward structured models for real-world planning and reasoning.