Algebraic Structures in Weakly Supervised Disentangled Representation Learning

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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.