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    We introduce deep declarative networks, a novel class of end-to-end learnable models. These networks implicitly define functions via optimization, enabling gradient backpropagation for enhanced deep learning capabilities.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Deep Learning

    Background:

    • Current deep learning models rely on explicitly defined forward functions.
    • Implicitly defined functions offer a more flexible and powerful modeling paradigm.
    • Integrating declarative approaches into deep learning can enhance model expressiveness.

    Purpose of the Study:

    • To introduce and define deep declarative networks (DDNs).
    • To demonstrate that DDNs encompass existing deep learning models.
    • To show how DDNs enable end-to-end learning through gradient backpropagation.

    Main Methods:

    • Defining data processing nodes via mathematical optimization problems.
    • Utilizing the implicit function theorem for gradient computation.
    • Implementing declarative nodes within the PyTorch deep learning framework.

    Main Results:

    • Deep declarative networks subsume current deep learning architectures.
    • Gradients can be effectively back-propagated through declaratively defined nodes.
    • Declarative and imperative nodes can coexist within hybrid networks.

    Conclusions:

    • Deep declarative networks offer a powerful new paradigm for end-to-end learning.
    • This approach enhances model flexibility and expressiveness in deep learning.
    • DDNs show promise for applications in image and point cloud classification.