We explore a new class of end-to-end learnable models wherein data processing
nodes (or network layers) are defined in terms of desired behavior rather than
an explicit forward function. Specifically, the forward function is implicitly
defined as the solution to a mathematical optimization problem. Consistent with
nomenclature in the programming languages community, we name these models deep
declarative networks. Importantly, we show that the class of deep declarative
networks subsumes current deep learning models. Moreover, invoking the implicit
function theorem, we show how gradients can be back-propagated through many
declaratively defined data processing nodes thereby enabling end-to-end
learning. We show how these declarative processing nodes can be implemented in
the popular PyTorch deep learning software library allowing declarative and
imperative nodes to co-exist within the same network. We also provide numerous
insights and illustrative examples of declarative nodes and demonstrate their
application for image and point cloud classification tasks.

本研究探索了一类新的端到端可学习模型，其中数据处理节点是根据预期行为而不是显式的前向函数定义的，并且演示了这些模型如何超越当前的深度学习模型，如何通过隐式函数定理进行反向传播导致端到端学习，以及如何在常见的 PyTorch 深度学习软件库中实现这些声明性处理节点。