Self-Supervised Reconstruction Knockoffs for Calibrated Unsupervised Feature Selection

Unsupervised feature selection is widely used as a discovery tool, yet most methods return only absolute rankings: a selected gene, pixel, or sensor is never compared against a feature-wise null. We introduce Self-Supervised Reconstruction Knockoffs (SSRK), a calibrated proxy-discovery framework for unlabeled data. SSRK defines relevance through masked reconstruction: a feature is deemed useful only when replacing it with a matched knockoff degrades reconstruction of other masked coordinates. The method trains a symmetric knockoff-gated masked autoencoder and converts the learned gates into a slot-aware signed statistic that satisfies the knockoff sign-flip property under Model-X exchangeability and coupled implementation. We formalize the estimation target as knockoff-relative masked information, prove immunity to self-copy and marginal-variance artifacts, derive an entropy-regularized population fixed point for correlated gates, and establish finite-sample margin and defect-robust false discovery rate bounds. Oracle synthetic experiments validate knockoff+ control at q = 0.10 with full support recovery in the reported regimes. On Peripheral Blood Mononuclear Cells, MNIST, Fashion-MNIST, and UCI Human Activity Recognition, where learned knockoffs are approximate, the same statistic is evaluated as a ranking and recovers biologically, spatially, and sensor-structurally meaningful subsets. SSRK thereby turns masked self-supervision into a feature-wise null comparison while clearly separating controlled discoveries from exploratory rankings.