We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

翻译：我们阐述了关于构建通用框架以描述和研究深度学习架构这一棘手问题的立场。我们认为，目前的关键尝试在模型必须满足的约束条件与模型实现规范之间缺乏连贯的桥梁。为搭建这一桥梁，我们提出应用范畴论——具体而言，是参数化映射的2-范畴中取值的单子泛代数——作为统一优雅地涵盖这两种神经网络设计风格的理论。为支撑这一立场，我们展示了该理论如何重获几何深度学习所诱导的约束，以及如何实现来自多样化神经网络领域（如RNN）的众多架构。我们还阐述了该理论如何自然地编码计算机科学和自动机理论中的许多标准构造。