Variational Manifold Alignment for Noisy Multilabel Prediction Correction

Label noise is ubiquitous in machine learning applications and usually leads to a geometric displacement in a trained classifier’s latent space. We propose LSNPC (Latent-Shift Noisy Prediction Correction), a post-hoc correction method that refines the multilabel predictions of a classifier trained on noisy labels, without retraining it. LSNPC is a variational autoencoder that aligns clean and noisy label distributions on a shared latent manifold by decoding both through the same decoder; this alignment is the primary corrective mechanism, which we design so that decoding a noisy prediction recovers most of the lost signal. A heavy-tailed Student-t transition models the noise-induced displacement, and a Gaussian shift from the noisy toward the clean representation then closes the residual displacement, yielding a smaller secondary refinement. We prove that the learned correction posterior approximates the true posterior over clean representations, that the Student-t shift yields a Kullback-Leibler divergence bound linear in the label discrepancy (a Gaussian alternative adds a quadratic term), and that the label-covariance reconstruction error is controlled by the latent displacement and label sparsity. Experiments on four synthetic-noise benchmarks, with real-world evaluation in the appendix, show that LSNPC improves prediction performance in most settings, with the largest gains observed under severe corruption.