论文标题
自由类别的概率生成模型
A Probabilistic Generative Model of Free Categories
论文作者
论文摘要
应用类别理论最近开发了用于计算有趣类别的形态的库，而机器学习则开发了有趣的语言学习程序的方式。认真对待类别和语言之间的类比，本文定义了在特定领域的生成对象和形态上的自由单体类别中形态学的概率生成模型。该论文显示了无环的定向接线图如何模拟形态的规格，该模型可以用来产生形态。然后，生成模型中的摊销变异推断可以学习参数（通过最大似然）和潜在变量的推断（通过贝叶斯倒置）。一个具体的实验表明，免费类别的先验在Omniglot数据集上实现了竞争性重建性能。
Applied category theory has recently developed libraries for computing with morphisms in interesting categories, while machine learning has developed ways of learning programs in interesting languages. Taking the analogy between categories and languages seriously, this paper defines a probabilistic generative model of morphisms in free monoidal categories over domain-specific generating objects and morphisms. The paper shows how acyclic directed wiring diagrams can model specifications for morphisms, which the model can use to generate morphisms. Amortized variational inference in the generative model then enables learning of parameters (by maximum likelihood) and inference of latent variables (by Bayesian inversion). A concrete experiment shows that the free category prior achieves competitive reconstruction performance on the Omniglot dataset.
