Graph Vector Field: A Unified Framework for Multimodal Health Risk Assessment from Heterogeneous Wearable and Environmental Data Streams

• URL: http://arxiv.org/abs/2603.28115v1
• Date: Mon, 30 Mar 2026 07:26:44 GMT
• Title: Graph Vector Field: A Unified Framework for Multimodal Health Risk Assessment from Heterogeneous Wearable and Environmental Data Streams
• Abstract summary: Graph Vector Field (GVF) is a framework that models health risk as a vector-valued field on time-varying simplicial complexes.<n>Risk is represented as a vector-valued cochain whose evolution is parameterised with Hodge Laplacians and discrete exterior calculus operators.<n>This paper develops the mathematical foundations, architectural design, and formal guarantees; empirical validation is the subject of ongoing work.
• Score: 0.7018547803286913
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Dementia Etiology Diagnosis via Collaborative Meta Knowledge Enhancement [81.27196033392559]
  We propose a Collaborative Meta Knowledge Enhancement (COME) framework for dementia etiology diagnosis.<n>COME injects multi-center acquisition semantics, source identifiers, and modality indicators as heterogeneity-aware embeddings into a unified Transformer architecture for scale-up training.<n>Our method achieves state-of-the-art in-domain performance with a mean macro-averaged AUC of 85.62% and a 4.29-point gain over the strongest baseline.
  arXiv  Detail & Related papers  (2026-07-24T04:26:47Z)
• PathAR: Structure-First Autoregressive Synthesis of Multimodal Pathology Images [51.428093790826814]
  We propose pathology Autorgressive modeling (PathAR) to factorize structure and appearance for modality-label-conditioned pathology generation.<n>PathAR stabilizes morphology under heterogeneous modality-specific appearances and enables spatially aligned image-mask pair generation.
  arXiv  Detail & Related papers  (2026-06-01T01:43:48Z)
• Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processes [8.718310015165025]
  Dynamical modelling is central to many scientific domains, including pharmacometrics, systems biology, physiology, and epidemiology.<n>We propose MEGPODE, a nonparametric mixed-effect ODE model in which each subject's vector field is quantified into a shared population component and a subject-specific deviation.
  arXiv  Detail & Related papers  (2026-05-13T06:57:01Z)
• Proteo-R1: Reasoning Foundation Models for De Novo Protein Design [129.2825640976092]
  We introduce bfProteo-R1, a reasoning-guided protein design framework.<n>It decouples emphmolecular understanding from emphgeometric generation.<n>Proteo-R1 achieves stable, interpretable, and modular integration of reasoning with state-of-the-art geometric generative models.
  arXiv  Detail & Related papers  (2026-05-01T06:52:27Z)
• Mixture-of-experts Wishart model for covariance matrices with an application to Cancer drug screening [0.8594140167290097]
  We introduce a comprehensive Bayesian framework for analyzing heterogeneous covariance data through both classical mixture models and a novel mixture-of-experts Wishart model.<n>We develop an efficient Gibbs-within-Metropolis-Hastings sampling algorithm tailored to the geometry of the Wishart likelihood and the gating network.<n>We present an innovative application of our methodology to a challenging dataset: cancer drug sensitivity profiles.
  arXiv  Detail & Related papers  (2026-02-14T21:07:14Z)
• SIGMA: Scalable Spectral Insights for LLM Collapse [51.863164847253366]
  We introduce SIGMA (Spectral Inequalities for Gram Matrix Analysis), a unified framework for model collapse.<n>By utilizing benchmarks that deriving and deterministic bounds on the matrix's spectrum, SIGMA provides a mathematically grounded metric to track the contraction of the representation space.<n>We demonstrate that SIGMA effectively captures the transition towards states, offering both theoretical insights into the mechanics of collapse.
  arXiv  Detail & Related papers  (2026-01-06T19:47:11Z)
• Supervised Learning of Random Neural Architectures Structured by Latent Random Fields on Compact Boundaryless Multiply-Connected Manifolds [0.0]
  This paper introduces a new probabilistic framework for supervised learning in neural systems.<n>It is designed to model complex, uncertain random outputs whose outputs are strongly non-Gaussian given deterministic inputs.<n>The goal is to establish a novel conceptual and mathematical framework in which neural systems are realizations of a geometry-aware, field-driven generative process.
  arXiv  Detail & Related papers  (2025-12-11T08:17:12Z)
• Geometric-Stochastic Multimodal Deep Learning for Predictive Modeling of SUDEP and Stroke Vulnerability [0.0]
  We present a unified geometric-stochastic multimodal deep learning framework that integrates EEG, ECG, respiration, SpO2, EMG, and fMRI signals.<n>We show improved predictive accuracy and interpretable biomarkers derived from manifold curvature, fractional memory indices, attention entropy, and diffusion centrality.
  arXiv  Detail & Related papers  (2025-12-09T05:28:09Z)
• scMRDR: A scalable and flexible framework for unpaired single-cell multi-omics data integration [53.683726781791385]
  We introduce a scalable and flexible generative framework called single-cell Multi-omics Regularized Disentangled Representations (scMRDR) for unpaired multi-omics integration.<n>Our method achieves excellent performance on benchmark datasets in terms of batch correction, modality alignment, and biological signal preservation.
  arXiv  Detail & Related papers  (2025-10-28T21:28:39Z)
• Information-theoretic Quantification of High-order Feature Effects in Classification Problems [0.19791587637442676]
  We present an information-theoretic extension of the High-order interactions for Feature importance (Hi-Fi) method.<n>Our framework decomposes feature contributions into unique, synergistic, and redundant components.<n>Results indicate that the proposed estimator accurately recovers theoretical and expected findings.
  arXiv  Detail & Related papers  (2025-07-06T11:50:30Z)
• MIRROR: Multi-Modal Pathological Self-Supervised Representation Learning via Modality Alignment and Retention [57.044719143401664]
  Histopathology and transcriptomics are fundamental modalities in oncology, encapsulating the morphological and molecular aspects of the disease.<n>We present MIRROR, a novel multi-modal representation learning method designed to foster both modality alignment and retention.<n>Extensive evaluations on TCGA cohorts for cancer subtyping and survival analysis highlight MIRROR's superior performance.
  arXiv  Detail & Related papers  (2025-03-01T07:02:30Z)
• Geometric Constraints in Probabilistic Manifolds: A Bridge from Molecular Dynamics to Structured Diffusion Processes [0.0]
  We propose a method that enables sampling from distributions that rigorously adhere to arbitrary sets of geometric constraints in Euclidean spaces. This is achieved by integrating a constraint projection operator within the well-regarded architecture of Denoising Diffusion Probabilistic Models.
  arXiv  Detail & Related papers  (2023-07-10T11:31:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.