In the quest for unveiling novel categories at test time, we confront the inherent limitations of traditional supervised recognition models that are restricted by a predefined category set. While strides have been made in the realms of self-supervised and open-world learning towards test-time category discovery, a crucial yet often overlooked question persists: what exactly delineates a \textit{category}? In this paper, we conceptualize a \textit{category} through the lens of optimization, viewing it as an optimal solution to a well-defined problem. Harnessing this unique conceptualization, we propose a novel, efficient and self-supervised method capable of discovering previously unknown categories at test time. A salient feature of our approach is the assignment of minimum length category codes to individual data instances, which encapsulates the implicit category hierarchy prevalent in real-world datasets. This mechanism affords us enhanced control over category granularity, thereby equipping our model to handle fine-grained categories adeptly. Experimental evaluations, bolstered by state-of-the-art benchmark comparisons, testify to the efficacy of our solution in managing unknown categories at test time. Furthermore, we fortify our proposition with a theoretical foundation, providing proof of its optimality. Our code is available at: \url{https://github.com/SarahRastegar/InfoSieve}.

翻译：在测试阶段探索未知类别的过程中，我们面临着传统监督识别模型受限于预定义类别集的固有局限性。尽管自监督和开放世界学习领域在测试时类别发现方面已取得进展，但一个关键却常被忽视的问题依然存在：究竟是什么定义了“类别”？本文通过优化视角将“类别”概念化为一个明确定义问题的最优解。基于这一独特概念，我们提出了一种新颖、高效且自监督的方法，能够在测试时发现先前未知的类别。该方法的核心特征是为每个数据实例分配最小长度的类别编码，这封装了现实数据集中普遍存在的隐式类别层级。这一机制赋予我们对类别粒度的增强控制，从而使模型能够精准处理细粒度类别。通过最先进基准测试对比的实验评估验证了我们的解决方案在测试时处理未知类别的有效性。此外，我们为这一命题提供了理论支撑，证明了其最优性。代码开源地址：\url{https://github.com/SarahRastegar/InfoSieve}