Identifying latent representations or causal structures is important for good generalization and downstream task performance. However, both fields have been developed rather independently. We observe that several methods in both representation and causal structure learning rely on the same data-generating process (DGP), namely, exchangeable but not i.i.d. (independent and identically distributed) data. We provide a unified framework, termed Identifiable Exchangeable Mechanisms (IEM), for representation and structure learning under the lens of exchangeability. IEM provides new insights that let us relax the necessary conditions for causal structure identification in exchangeable non--i.i.d. data. We also demonstrate the existence of a duality condition in identifiable representation learning, leading to new identifiability results. We hope this work will pave the way for further research in causal representation learning.

翻译：识别潜在表示或因果结构对于实现良好泛化性能与下游任务表现至关重要。然而，这两个领域的发展长期相对独立。我们观察到，在表示学习与因果结构学习领域中，多种方法均依赖于相同的数据生成过程，即可交换但非独立同分布数据。本文提出一个统一框架——可辨识可交换机制，从可交换性视角为表示与结构学习提供理论支撑。该框架通过新视角放宽了可交换非独立同分布数据中因果结构辨识的必要条件。我们同时证明了可辨识表示学习中存在对偶条件，并由此推导出新的可辨识性结论。本研究期望为因果表示学习领域的后续探索奠定理论基础。