FACTS: A Factored State-Space Framework For World Modelling

2024-10-28

arXiv.org

AI Summary

Existing world modeling approaches—such as Transformer- and Mamba-based architectures—face efficiency bottlenecks and limited structural expressivity when modeling long-horizon, high-dimensional spatiotemporal sequences. To address this, we propose FACTored State-space (FACTS), a novel recurrent architecture that uniquely integrates graph-structured memory with permutation-invariant routing, enabling order-agnostic joint spatiotemporal modeling. FACTS employs recursive factorized state representations, selective state-space propagation, and parallelizable design to substantially improve modeling efficiency. Evaluated on three benchmark tasks—multivariate time series forecasting, object-centric world modeling, and spatiotemporal graph forecasting—FACTS matches or surpasses task-specific state-of-the-art models. It establishes a unified, efficient, and scalable framework for modeling complex dynamic systems, advancing the frontier of general-purpose spatiotemporal representation learning.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Deep Neural Architectures and Foundation Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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 extbf{FACT}ored extbf{S}tate-space ( extbf{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.

Problem

• Efficiently encoding spatial and temporal structures in complex systems.
• Overcoming limitations of current frameworks in long-term high-dimensional sequence modelling.
• Developing a general-purpose model for spatial-temporal world modelling tasks.

Innovation

• Graph-structured memory with routing mechanism
• Permutable memory representations for invariance
• Parallel computation for high-dimensional sequences