From Fitting to Flowing: Reliability-Guided Geometric Correction Dynamics for Multi-View Partial Multi-Label Learning

Multi-view partial multi-label learning (MVPML) learns from heterogeneous views and ambiguous candidate label sets containing both relevant and irrelevant labels. Existing methods typically refine candidate supervision or jointly optimize disambiguation and classification, but ultimately treat inferred supervision as a target to fit. Errors in this supervision can therefore propagate directly into prediction, while multi-view geometry is mainly used for refinement or regularization rather than for controlling such propagation. We propose GeoCURVE, a reliability-guided, geometry-embedded continuous-time dynamical framework that instead treats inferred supervision as a controlled correction to a structural reference. Specifically, prediction evolves according to a reference-restored ordinary differential equation (ODE). Candidate reliability, indicating the likelihood that a candidate label is truly relevant, determines the correction signal, shared multi-view geometry governs how it propagates across structurally related instances, and a restoration term controls how much of it is retained. The resulting dynamics admit a unique globally exponentially stable equilibrium with a closed-form solution, exposing how reliability, geometry, and restoration jointly determine the final prediction.We derive an oracle-based error bound quantifying controlled uncertainty propagation and an incremental generalization bound showing how spectral geometry and restoration control correction complexity and the correction-induced generalization gap. Experiments on six benchmark datasets under multiple ambiguity settings demonstrate consistent improvements over representative MVPML methods, achieving relative AP improvements of up to 13% over competitive baselines on several datasets, while ablations show that controlling correction extent, rather than merely refining supervision, drives the gain.