Representation Synthesis by Probabilistic Many-Valued Logic Operation in Self-Supervised Learning

In this paper, we propose a new self-supervised learning (SSL) method for representations that enable logic operations. Representation learning has been applied to various tasks like image generation and retrieval. The logical controllability of representations is important for these tasks. Although some methods have been shown to enable the intuitive control of representations using natural languages as the inputs, representation control via logic operations between representations has not been demonstrated. Some SSL methods using representation synthesis (e.g., elementwise mean and maximum operations) have been proposed, but the operations performed in these methods do not incorporate logic operations. In this work, we propose a logic-operable self-supervised representation learning method by replacing the existing representation synthesis with the OR operation on the probabilistic extension of many-valued logic. The representations comprise a set of feature-possession degrees, which are truth values indicating the presence or absence of each feature in the image, and realize the logic operations (e.g., OR and AND). Our method can generate a representation that has the features of both representations or only those features common to both representations. Furthermore, the expression of the ambiguous presence of a feature is realized by indicating the feature-possession degree by the probability distribution of truth values of the many-valued logic. We showed that our method performs competitively in single and multi-label classification tasks compared with prior SSL methods using synthetic representations. Moreover, experiments on image retrieval using MNIST and PascalVOC showed the representations of our method can be operated by OR and AND operations.