Geometric Priors for Generalizable World Models via Vector Symbolic Architecture
arXiv:2602.21467v1 Announce Type: new 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
arXiv:2602.21467v1 Announce Type: new 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.
Executive Summary
This article explores the development of generalizable world models through the application of Vector Symbolic Architecture (VSA) principles as geometric priors. The authors propose a novel approach using learnable Fourier Holographic Reduced Representation (FHRR) encoders to map states and actions into a high-dimensional complex vector space. This structured representation enables strong multi-step composition directly in latent space and generalization performances over various experiments. The authors demonstrate the efficacy of their approach through experiments on a discrete grid world environment, achieving superior performance compared to an MLP baseline. The study highlights the potential of training latent group structure to yield generalizable, data-efficient, and interpretable world models, providing a principled pathway toward structured models for real-world planning and reasoning.
Key Points
- ▸ The authors leverage Vector Symbolic Architecture (VSA) principles to develop generalizable world models.
- ▸ Learnable Fourier Holographic Reduced Representation (FHRR) encoders are used to map states and actions into a high-dimensional complex vector space.
- ▸ The structured representation enables strong multi-step composition directly in latent space and generalization performances.
Merits
Strength in Geometric Priors
The use of geometric priors in VSA provides a principled approach to learning structured representations, enabling generalizability and interpretability.
Improved Robustness
The approach demonstrates 4x higher robustness to noise relative to an MLP baseline, suggesting improved resilience to environmental uncertainties.
Demerits
Limited Domain
The study is conducted on a discrete grid world environment, limiting the generalizability of the results to real-world scenarios with complex dynamics.
Computational Complexity
The learnable FHRR encoders introduce additional computational complexity, which may hinder the scalability of the approach to larger or more complex environments.
Expert Commentary
The article presents a significant contribution to the field of artificial intelligence, leveraging Vector Symbolic Architecture (VSA) principles to develop generalizable world models. The use of learnable Fourier Holographic Reduced Representation (FHRR) encoders enables strong multi-step composition directly in latent space, demonstrating improved robustness and generalization performances. However, the study is limited to a discrete grid world environment, and the computational complexity of the approach may hinder its scalability. Nevertheless, the findings have significant implications for real-world planning and reasoning systems, highlighting the importance of developing principled approaches to learning structured representations.
Recommendations
- ✓ Future research should focus on applying the approach to more complex and dynamic environments, such as real-world robotics or autonomous systems.
- ✓ The development of more efficient and scalable algorithms for learnable FHRR encoders is essential for the widespread adoption of the approach.
