Deep Declarative Networks: A New Hope
This proposes a foundational shift in how neural networks are designed, potentially affecting all of ML/AI by offering a more flexible framework for model construction.
The paper introduces deep declarative networks, a new class of models where network layers are defined implicitly as solutions to optimization problems, and shows they subsume existing deep learning models while enabling end-to-end learning via gradient backpropagation.
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.