Algebraic Structures in Weakly Supervised Disentangled Representation Learning

在这个名为“弱监督解纠缠表示学习中的代数结构”的项目中，我们旨在开发用于学习抽象和有意义表示的理论工具和实用算法。作为第一步，我们对机器学习中解开纠缠的各种定义进行了元分析。以范畴论为统一框架，揭示了不同定义之间的异同。我们还介绍了分析不同设置下解纠缠的工具，包括等变映射和随机映射。我们的发现可以帮助研究人员为他们的特定任务选择最合适的解缠定义，并发现更好的度量、模型和算法。

In this project, "Algebraic Structures in Weakly Supervised Disentangled Representation Learning", we aimed to develop theoretical tools and practical algorithms for learning abstract and meaningful representations. As the first step, we conducted a meta-analysis of various definitions of disentanglement in machine learning. Using category theory as a unifying framework, we revealed the similarities and differences between different definitions. We also introduced tools to analyze disentanglement in different settings, including equivariant maps and stochastic maps. Our findings can help researchers choose the most appropriate definition of disentanglement for their specific task and discover better metrics, models, and algorithms.