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Pretext-based self-supervised learning learns the semantic representation viaa handcrafted pretext task over unlabeled data and then uses the learnedrepresentation for downstream tasks, which effectively reduces the samplecomplexity of downstream tasks under Conditional Independence (CI) condition.However, the downstream sample complexity gets much worse if the CI conditiondoes not hold. One interesting question is whether we can make the CI conditionhold by using downstream data to refine the unlabeled data to boostself-supervised learning. At first glance, one might think that seeingdownstream data in advance would always boost the downstream performance.However, we show that it is not intuitively true and point out that in somecases, it hurts the final performance instead. In particular, we prove bothmodel-free and model-dependent lower bounds of the number of downstream samplesused for data refinement. Moreover, we conduct various experiments on bothsynthetic and real-world datasets to verify our theoretical results.

Can Pretext-Based Self-Supervised Learning Be Boosted by Downstream Data? A Theoretical Analysis