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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.28115 |
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| _version_ | 1866908920564416512 |
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| author | Coletti, Silvano Fallucchi, Francesca |
| author_facet | Coletti, Silvano Fallucchi, Francesca |
| contents | Digital health research has advanced dynamic graph-based disease models, topological learning on simplicial complexes, and multimodal mixture-of-experts architectures, but these strands remain largely disconnected. We propose Graph Vector Field (GVF), a framework that models health risk as a vector-valued field on time-varying simplicial complexes, coupling discrete differential-geometric operators with modality-structured mixture-of-experts. Risk is represented as a vector-valued cochain whose evolution is parameterised with Hodge Laplacians and discrete exterior calculus operators, yielding a Helmholtz-Hodge decomposition into potential-driven (exact), circulation-like (coexact), and topologically constrained (harmonic) components linked to interpretable propagation, cyclic, and persistent risk mechanisms. Multimodal inputs from wearable sensors, behavioural/environmental context, and clinical/genomic data are incorporated through a bundle-structured mixture-of-experts in which modality-specific latent spaces are attached as fibres to the base complex. This separates modality-specific from shared contributions and offers a principled route toward modality-level identifiability. GVF integrates geometric dynamical systems, higher-order topology (enforced indirectly via geometric regularisation and Hodge decomposition), and structured multimodal fusion into a single framework for interpretable, modality-resolved risk modelling. This paper develops the mathematical foundations, architectural design, and formal guarantees; empirical validation is the subject of ongoing work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28115 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Graph Vector Field: A Unified Framework for Multimodal Health Risk Assessment from Heterogeneous Wearable and Environmental Data Streams Coletti, Silvano Fallucchi, Francesca Machine Learning Primary 68T07, Secondary 55N31, 58A15, 62R40, 92C50 Digital health research has advanced dynamic graph-based disease models, topological learning on simplicial complexes, and multimodal mixture-of-experts architectures, but these strands remain largely disconnected. We propose Graph Vector Field (GVF), a framework that models health risk as a vector-valued field on time-varying simplicial complexes, coupling discrete differential-geometric operators with modality-structured mixture-of-experts. Risk is represented as a vector-valued cochain whose evolution is parameterised with Hodge Laplacians and discrete exterior calculus operators, yielding a Helmholtz-Hodge decomposition into potential-driven (exact), circulation-like (coexact), and topologically constrained (harmonic) components linked to interpretable propagation, cyclic, and persistent risk mechanisms. Multimodal inputs from wearable sensors, behavioural/environmental context, and clinical/genomic data are incorporated through a bundle-structured mixture-of-experts in which modality-specific latent spaces are attached as fibres to the base complex. This separates modality-specific from shared contributions and offers a principled route toward modality-level identifiability. GVF integrates geometric dynamical systems, higher-order topology (enforced indirectly via geometric regularisation and Hodge decomposition), and structured multimodal fusion into a single framework for interpretable, modality-resolved risk modelling. This paper develops the mathematical foundations, architectural design, and formal guarantees; empirical validation is the subject of ongoing work. |
| title | Graph Vector Field: A Unified Framework for Multimodal Health Risk Assessment from Heterogeneous Wearable and Environmental Data Streams |
| topic | Machine Learning Primary 68T07, Secondary 55N31, 58A15, 62R40, 92C50 |
| url | https://arxiv.org/abs/2603.28115 |