The goal of generality in machine learning is to achieve excellent performance on various unseen tasks and domains. Recently, self-supervised learning (SSL) has been regarded as an effective method to achieve this goal. It can learn high-quality representations from unlabeled data and achieve promising empirical performance on multiple downstream tasks. Existing SSL methods mainly constrain generality from two aspects: (i) large-scale training data, and (ii) learning task-level shared knowledge. However, these methods lack explicit modeling of the SSL generality in the learning objective, and the theoretical understanding of SSL's generality remains limited. This may cause SSL models to overfit in data-scarce situations and generalize poorly in the real world, making it difficult to achieve true generality. To address these issues, we provide a theoretical definition of generality in SSL and define a $\sigma$-measurement to help quantify it. Based on this insight, we explicitly model generality into self-supervised learning and further propose a novel SSL framework, called GeSSL. It introduces a self-motivated target based on $\sigma$-measurement, which enables the model to find the optimal update direction towards generality. Extensive theoretical and empirical evaluations demonstrate the superior performance of the proposed GeSSL.

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