תמיכה באופטימיות של פתרון ספקטרלי ללמידה חיפושית

תקציר מקורי באנגליתarXiv:2502.04312v3 Announce Type: replace Abstract: Contrastive learning leverages data augmentation to develop feature representation without relying on large labeled datasets. However, despite its empirical success, the theoretical foundations of contrastive learning remain incomplete, with many essential guarantees left unaddressed, particularly the realizability assumption concerning neural approximability of an optimal spectral contrastive loss solution. In this work, we overcome these limitations by analyzing pointwise and spectral consistency of the augmentation graph Laplacian. We establish that, under specific conditions for data generation and graph connectivity, as the augmented dataset size increases, the augmentation graph Laplacian converges to a weighted Laplace-Beltrami ope