Further reading

The classical background for sheaves, descent, and topos semantics is given by Mac Lane and Moerdijk [ 1992 ] . Predictive state representations originate in early work on predictive representations and dynamical systems [ Littman et al. , 2001 , Singh et al. , 2004b ] ; later work connects prediction to planning and abstraction [ Boots et al. , 2011 , Soni and Singh , 2007 ] . These readings clarify the two ingredients SID combines: local-to-global consistency and state represented by observable predictions.

Machine-learning uses of sheaves include sheaf neural networks [ Hansen and Gebhart , 2020 ] , connection-Laplacian models [ Barbero et al. , 2022 ] , neural sheaf diffusion [ Bodnar et al. , 2022a ] , and nonlinear adaptive sheaf diffusion [ Zaghen et al. , 2024 ] . Copresheaf topological neural networks extend the architecture-level viewpoint [ Hajij et al. , 2025 ] . SID addresses a different layer: it treats the declared descent diagram as a constraint and repair interface, including effectivity and admission, rather than choosing a sheaf Laplacian as the predictive architecture.