FlowMixer: A Depth-Agnostic Neural Architecture for Interpretable Spatiotemporal Forecasting
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914570182852608 |
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| author | Mehouachi, Fares B. Jabari, Saif Eddin |
| author_facet | Mehouachi, Fares B. Jabari, Saif Eddin |
| contents | We introduce FlowMixer, a single-layer neural architecture that leverages constrained matrix operations to model structured spatiotemporal patterns with enhanced interpretability. FlowMixer incorporates non-negative matrix mixing layers within a reversible mapping framework - applying transforms before mixing and their inverses afterward. This shape-preserving design enables a Kronecker-Koopman eigenmodes framework that bridges statistical learning with dynamical systems theory, providing interpretable spatiotemporal patterns and facilitating direct algebraic manipulation of prediction horizons without retraining. The architecture's semi-group property enables this single layer to mathematically represent any depth through composition, eliminating depth search entirely. Extensive experiments across diverse domains demonstrate FlowMixer's long-horizon forecasting capabilities while effectively modeling physical phenomena such as chaotic attractors and turbulent flows. Our results achieve performance matching state-of-the-art methods while offering superior interpretability through directly extractable eigenmodes. This work suggests that architectural constraints can simultaneously maintain competitive performance and enhance mathematical interpretability in neural forecasting systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16786 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | FlowMixer: A Depth-Agnostic Neural Architecture for Interpretable Spatiotemporal Forecasting Mehouachi, Fares B. Jabari, Saif Eddin Machine Learning We introduce FlowMixer, a single-layer neural architecture that leverages constrained matrix operations to model structured spatiotemporal patterns with enhanced interpretability. FlowMixer incorporates non-negative matrix mixing layers within a reversible mapping framework - applying transforms before mixing and their inverses afterward. This shape-preserving design enables a Kronecker-Koopman eigenmodes framework that bridges statistical learning with dynamical systems theory, providing interpretable spatiotemporal patterns and facilitating direct algebraic manipulation of prediction horizons without retraining. The architecture's semi-group property enables this single layer to mathematically represent any depth through composition, eliminating depth search entirely. Extensive experiments across diverse domains demonstrate FlowMixer's long-horizon forecasting capabilities while effectively modeling physical phenomena such as chaotic attractors and turbulent flows. Our results achieve performance matching state-of-the-art methods while offering superior interpretability through directly extractable eigenmodes. This work suggests that architectural constraints can simultaneously maintain competitive performance and enhance mathematical interpretability in neural forecasting systems. |
| title | FlowMixer: A Depth-Agnostic Neural Architecture for Interpretable Spatiotemporal Forecasting |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.16786 |