Category theory has been successfully applied in various domains of science, shedding light on universal principles unifying diverse phenomena and thereby enabling knowledge transfer between them. Applications to machine learning have been pursued recently, and yet there is still a gap between abstract mathematical foundations and concrete applications to machine learning tasks. In this paper we introduce DisCoPyro as a categorical structure learning framework, which combines categorical structures (such as symmetric monoidal categories and operads) with amortized variational inference, and can be applied, e.g., in program learning for variational autoencoders. We provide both mathematical foundations and concrete applications together with comparison of experimental performance with other models (e.g., neuro-symbolic models). We speculate that DisCoPyro could ultimately contribute to the development of artificial general intelligence.

翻译：范畴论已成功应用于多个科学领域，揭示了统一不同现象的普遍原理，从而促进了这些领域之间的知识迁移。近年来，其在机器学习中的应用已得到探索，但抽象数学基础与机器学习任务的具体应用之间仍存在差距。本文介绍DisCoPyro作为一种范畴结构学习框架，该框架将范畴结构（如对称幺半范畴和操作元）与摊销变分推理相结合，可应用于变分自编码器的程序学习等场景。我们提供了数学基础与具体应用，并与其他模型（如神经符号模型）进行了实验性能比较。我们推测，DisCoPyro最终可能为人工通用智能的发展做出贡献。