Active Learning as Nullspace Regulation: A Spectral Representation Perspective

Most active learning (AL) methods estimate sample value through empirical criteria such as prediction ambiguity, diversity, or distributional coverage. We revisit AL from a spectral-geometric perspective by regarding the feature span of the current labeled set as the modeled subspace and its orthogonal complement as an operational residual subspace. The projected residual component of an unlabeled sample then reflects its relation to representation components weakly expressed by the labeled-feature spectrum. Based on this formulation, we propose a spectrally driven nullspace regulation framework that unifies spectrum-induced subspace decomposition, cross-cycle residual persistence estimation, and coverage-aware acquisition in the residual-coordinate space. This yields an acquisition criterion that favors samples whose residual components are both persistent across cycles and complementary to already selected samples. Experiments on visual benchmarks show competitive or improved sample efficiency over strong baselines. Further analyses support the proposed view by showing that residual components shrink anisotropically and that acquisition rankings vary substantially across backbones, indicating that sample value is conditioned on the current representation state rather than being purely data-intrinsic.