arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2205.04545cs.AIcs.LGmath.CTstat.ML
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自由范畴的概率生成模型

A Probabilistic Generative Model of Free Categories

Northeastern University(东北大学);Khoury College of Computer Sciences(库里计算机学院);The Australian National University(澳大利亚国立大学);School of Computing(计算学院)

Eli Sennesh, Tom Xu, Yoshihiro Maruyama

摘要:

应用范畴论最近开发了用于在有趣的范畴中使用态射进行计算的库,而机器学习开发了学习有趣语言的程序的方法。基于范畴与语言的类比,本文定义了自由monoidal范畴中态射在领域特定生成对象和态射上的概率生成模型。本文展示了如何非循环有向接线图可以模型规范的态射,该模型可以用来生成态射。生成模型中的摊销变分推理然后使得能够学习参数(通过最大似然)和推断潜变量(通过贝叶斯反演)。实验结果表明,自由类别先验在Omniglot数据集上具有较好的重建性能。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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