# Interpretable Self-Supervised Learning via Representer Landmarks and Nystr\\"om Approximation Source: [Interpretable Self-Supervised Learning via Representer Landmarks and Nystr\\"om Approximation]() Collection index: [llms.txt]() Data updated: 2026-06-10T05:15:22.625Z Authors: Maedeh Zarvandi, Michael Timothy, Theresa Wasserer, Debarghya Ghoshdastidar Published: 2025-09-29T08:45:40.000Z ## Abstract Self-supervised learning (SSL) learns representations from massive unlabeled data, yet the resulting models typically operate as black boxes, necessitating domain-specific explanations. We introduce KREPES, a unified framework to analytically interpret the learned representations of SSL objectives, including SimCLR, BYOL, and VICReg. By bridging empirical neural tangent kernel approximations of neural networks with the Representer Theorem for kernels, we express the learned latent space directly via "Representer Landmarks", which are the representations of influential unlabeled training examples. We introduce novel metrics, "Sample-Specific Influence Score", "Concept-Conditioned Influence Score" and "Feature Alignment Gap", to quantify the transparency of the learned representations. KREPES enables direct audit of the latent space without supervision, for example, revealing an algorithmic bias in the Adult-1M dataset where SSL uses demographic proxies for income. Finally, to ensure scalability to benchmarks with 1M+ samples (ImageNet-1K, Adult-1M), KREPES introduces a novel Nystr\\"om approximation-based analytical inference framework for SSL objectives. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()