# FACTS: A Factored State-Space Framework For World Modelling

arXiv: https://arxiv.org/abs/2410.20922 · HTML: https://mlsanity.com/paper/2410.20922/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in World models for language agents, one of 11 directions in World models.
- Builds on 86 of its 130 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Placed in

- World models / [World models for language agents](https://mlsanity.com/wm/world-models-for-language-agents/)
- State-space sequence models (S4, Mamba) / [Core SSM architectures for language](https://mlsanity.com/ssm/core-ssm-architectures-for-language/)

## Builds on (most cited first, 30 of 86)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)

## Built on by (most cited first, 4 of 4)

- [Transformers learn factored representations](https://mlsanity.com/paper/2602.02385/) (2026)
- [Graph World Models: Concepts, Taxonomy, and Future Directions](https://mlsanity.com/paper/2604.27895/) (2026)
- [Weight-Space Linear Recurrent Neural Networks](https://mlsanity.com/paper/2506.01153/) (2025)
- [Structural Prognostic Event Modeling for Multimodal Cancer Survival Analysis](https://mlsanity.com/paper/2512.01116/) (2025)

## Abstract (arXiv)

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 FACTored State-space (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.