Can We Break the Loop? Active Boundary Restoration for Learning with Noisy Labels

Most methods for learning with noisy labels identify reliable samples through training loss, predictive confidence, or model agreement. These reliability estimates depend on an evolving representation: as noisy supervision distorts class geometry, hard clean examples and mislabeled examples can become increasingly difficult to distinguish near class boundaries. Robust learning therefore requires maintaining a representation in which sample reliability remains identifiable. We propose HamBR, an active boundary restoration framework that explores low-support inter-class regions and constructs virtual boundary anchors. Constrained spherical Hamiltonian trajectories generate structured candidates along the current feature geometry, while an explicit density-retention rule controls their support relative to inter-class initialization. Geometric regularization then draws reliable features toward their class cores and away from the anchors. Theoretical analysis establishes a relative support-density bound, characterizes optimization of prototype–outlier margins, and provides an anchor-induced boundary-separation guarantee. Our evaluation examines classification performance, representation geometry, and alternative candidate-generation strategies under noisy supervision. Across synthetic- and real-noise benchmarks, the reported results support the benefits of active geometric intervention for robust learning. These findings motivate considering sample selection and representation geometry jointly, with active boundary restoration complementing advances in selection rules.