Geometric Priors for Generalizable World Models via Vector Symbolic Architecture

TL;DR

This paper introduces a geometric prior-based world model using Vector Symbolic Architecture principles, enabling better generalization, interpretability, and robustness in modeling world dynamics through structured high-dimensional representations.

Contribution

The paper proposes a novel world modeling approach grounded in VSA and Fourier Holographic Reduced Representation encoders, formalizing its group theoretic foundation and demonstrating improved generalization and robustness.

Findings

Achieves 87.5% zero shot accuracy on unseen state-action pairs

Improves 20-timestep horizon rollout accuracy by 53.6%

Demonstrates 4x higher robustness to noise compared to baseline

Abstract

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.