Deep Declarative Networks: A New Hope

TL;DR

Deep declarative networks define data processing layers via optimization problems, enabling flexible, end-to-end learnable models that unify declarative and imperative programming within deep learning frameworks.

Contribution

This paper introduces deep declarative networks, a novel class of models where layers are defined by optimization problems, expanding the expressiveness of deep learning architectures.

Findings

Declarative nodes can be integrated into PyTorch.

Gradients can be computed via the implicit function theorem.

Applications demonstrated on image and point cloud classification.

Abstract

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.