This paper proposes an unsupervised method for learning a unified representation that serves both discriminative and generative purposes. While most existing unsupervised learning approaches focus on a representation for only one of these two goals, we show that a unified representation can enjoy the mutual benefits of having both. Such a representation is attainable by generalizing the recently proposed \textit{closed-loop transcription} framework, known as CTRL, to the unsupervised setting. This entails solving a constrained maximin game over a rate reduction objective that expands features of all samples while compressing features of augmentations of each sample. Through this process, we see discriminative low-dimensional structures emerge in the resulting representations. Under comparable experimental conditions and network complexities, we demonstrate that these structured representations enable classification performance close to state-of-the-art unsupervised discriminative representations, and conditionally generated image quality significantly higher than that of state-of-the-art unsupervised generative models. Source code can be found at https://github.com/Delay-Xili/uCTRL.
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