Learning Functors using Gradient Descent

Bruno Gavranovic
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引用次数: 4

Abstract

Neural networks are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this paper we build a category-theoretic formalism around a neural network system called CycleGAN. CycleGAN is a general approach to unpaired image-to-image translation that has been getting attention in the recent years. Inspired by categorical database systems, we show that CycleGAN is a "schema", i.e. a specific category presented by generators and relations, whose specific parameter instantiations are just set-valued functors on this schema. We show that enforcing cycle-consistencies amounts to enforcing composition invariants in this category. We generalize the learning procedure to arbitrary such categories and show a special class of functors, rather than functions, can be learned using gradient descent. Using this framework we design a novel neural network system capable of learning to insert and delete objects from images without paired data. We qualitatively evaluate the system on the CelebA dataset and obtain promising results.
使用梯度下降学习函子
神经网络是可微优化的一般框架,它包括许多其他机器学习方法作为特殊情况。在本文中,我们围绕一个叫做CycleGAN的神经网络系统建立了一个范畴论的形式化系统。CycleGAN是近年来备受关注的一种通用的非配对图像到图像翻译方法。受分类数据库系统的启发,我们证明了CycleGAN是一个“模式”,即由生成器和关系表示的特定类别,其特定参数实例化只是该模式上的集值函子。我们证明,在这个范畴中,强制循环一致性等同于强制组合不变量。我们将学习过程推广到任意这样的类别,并展示了一类特殊的函子,而不是函数,可以使用梯度下降来学习。利用这个框架,我们设计了一个新的神经网络系统,能够在没有配对数据的情况下学习从图像中插入和删除对象。我们在CelebA数据集上对系统进行了定性评估,并获得了令人满意的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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