World modelling is essential for understanding and predicting the dynamics of complex systems by learning both spatial and temporal dependencies. However, current frameworks, such as Transformers and selective state-space models like Mambas, exhibit limitations in efficiently encoding spatial and temporal structures, particularly in scenarios requiring long-term high-dimensional sequence modelling. To address these issues, we propose a novel recurrent framework, the \textbf{FACT}ored \textbf{S}tate-space (\textbf{FACTS}) model, for spatial-temporal world modelling. The FACTS framework constructs a graph-structured memory with a routing mechanism that learns permutable memory representations, ensuring invariance to input permutations while adapting through selective state-space propagation. Furthermore, FACTS supports parallel computation of high-dimensional sequences. We empirically evaluate FACTS across diverse tasks, including multivariate time series forecasting, object-centric world modelling, and spatial-temporal graph prediction, demonstrating that it consistently outperforms or matches specialised state-of-the-art models, despite its general-purpose world modelling design.
View on arXiv@article{nanbo2025_2410.20922,
title={ FACTS: A Factored State-Space Framework For World Modelling },
author={ Li Nanbo and Firas Laakom and Yucheng Xu and Wenyi Wang and Jürgen Schmidhuber },
journal={arXiv preprint arXiv:2410.20922},
year={ 2025 }
}