TopoForce: Learning Topology-Revealing Representations across Multiple Scales

Topology provides a fundamental description of high-dimensional data, yet the underlying topological organization is typically latent and can contain structures emerging at heterogeneous intrinsic scales. Conventional dimensionality-reduction methods optimize geometric or neighborhood fidelity, which need not preserve collective topology. Persistent-homology (PH)-guided methods use persistent structure inferred from the observed metric as a target for topology preservation, but this structure can become unreliable in high-dimensional noisy observations. We introduce TopoForce, a PH-free graph-based method for learning multiscale topology-revealing representations. TopoForce uses density-normalized multiscale diffusion to infer a pairwise topology scale that characterizes the structural scale relevant to each relationship, and translates these scales into adaptive force-directed interactions. Across controlled simulations, TopoForce recovers topological features spanning heterogeneous scales and remains robust to nonuniform sampling and high-dimensional nuisance variation. Across real-world applications in single-cell genomics, image analysis, and neural population activity, TopoForce reveals cyclic and toroidal organization consistent with known underlying structure. Together, these results demonstrate that TopoForce can reveal latent topological structure across multiple intrinsic scales in high-dimensional data.Our code is available at https://anonymous.4open.science/r/topoforce_2026-34CE/.