Inferring Latent Geometries in Weighted Spatio-Functional Networks
Abstract
Complex networks balance metric wiring costs against functional routing demands, rarely conforming to idealized dichotomies of pure planar grids or unconstrained topologies. Yet, existing latent-space models remain computationally bottlenecked by stochastic sampling on small, unweighted graphs. Here, we formulate a scalable generative framework to solve the inverse problem of spatio-functional inference in weighted networks. By coupling explicit metric spaces with an unobserved latent geometry, we jointly reconstruct hidden coordinates and infer a coupling parameter λ∈ [0, 1], quantifying the connectivity propensity explained by functional affinity conditioned on metric distance decay. Our deterministic pipeline pairs a physics-informed spectral residual initialization with hybrid first- and quasi-Newton optimization. Across diverse empirical systems, the framework reveals a continuous spatio-functional spectrum. In the Drosophila melanogaster whole-brain connectome, it resolves an architectural progression from metric-constrained sensory circuits to specialized associative and chemo-affinity neuropils. In the continental European power grid, line pruning preserves a strictly metric baseline (λ̂ ≈ 0), whereas topological rewiring drives a sharp surge in λ̂, demonstrating that macroscopic component connectivity can mask spatial degradation. Finally, tracking global aviation throughout the COVID-19 pandemic captures dynamic regime shifts toward localized metric connectivity, establishing a unified diagnostic to probe structural organization and resilience in spatially embedded networks.
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BibTeX
@misc{cerioli2026inferring,
title = {{Inferring Latent Geometries in Weighted Spatio-Functional Networks}},
author = {Gabriele Cerioli and Adamo Cerioli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23933},
eprint = {2609.23933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23933},
}
RIS
TY - UNPB
TI - Inferring Latent Geometries in Weighted Spatio-Functional Networks
AU - Gabriele Cerioli
AU - Adamo Cerioli
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.23933
UR - https://arxiv.org/abs/2609.23933
AB - Complex networks balance metric wiring costs against functional routing demands, rarely conforming to idealized dichotomies of pure planar grids or unconstrained topologies. Yet, existing latent-space models remain computationally bottlenecked by stochastic sampling on small, unweighted graphs. Here, we formulate a scalable generative framework to solve the inverse problem of spatio-functional inference in weighted networks. By coupling explicit metric spaces with an unobserved latent geometry, we jointly reconstruct hidden coordinates and infer a coupling parameter λ∈ [0, 1], quantifying the connectivity propensity explained by functional affinity conditioned on metric distance decay. Our deterministic pipeline pairs a physics-informed spectral residual initialization with hybrid first- and quasi-Newton optimization. Across diverse empirical systems, the framework reveals a continuous spatio-functional spectrum. In the Drosophila melanogaster whole-brain connectome, it resolves an architectural progression from metric-constrained sensory circuits to specialized associative and chemo-affinity neuropils. In the continental European power grid, line pruning preserves a strictly metric baseline (λ̂ ≈ 0), whereas topological rewiring drives a sharp surge in λ̂, demonstrating that macroscopic component connectivity can mask spatial degradation. Finally, tracking global aviation throughout the COVID-19 pandemic captures dynamic regime shifts toward localized metric connectivity, establishing a unified diagnostic to probe structural organization and resilience in spatially embedded networks.
ER -