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Regularized Optimal Transport Layers for Generalized Global Pooling Operations.

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    This study introduces a generalized global pooling framework using optimal transport, improving machine learning performance. The novel regularized optimal transport pooling (ROTP) layers offer better data representation and reduce design complexity.

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    Area of Science:

    • Machine Learning
    • Optimal Transport Theory
    • Data Representation

    Background:

    • Global pooling is crucial for machine learning but often lacks mathematical rigor, leading to suboptimal performance.
    • Existing pooling methods rely on empirical mechanisms rather than solid theoretical foundations.

    Purpose of the Study:

    • To develop a novel, generalized global pooling framework grounded in optimal transport theory.
    • To provide an interpretable and mathematically sound approach to information fusion and structured data representation.

    Main Methods:

    • Developed a generalized global pooling framework using optimal transport, interpretable via expectation-maximization.
    • Demonstrated existing pooling methods as special cases of regularized optimal transport (ROT).
    • Introduced learnable regularized optimal transport pooling (ROTP) layers implemented as deep implicit layers.

    Main Results:

    • Showcased ROTP layers' ability to imitate existing methods or create new, data-fitting pooling layers.
    • Experimental validation across multi-instance learning, graph classification, graph set representation, and image classification.
    • ROTP layers simplify the design and selection of global pooling operations.

    Conclusions:

    • The proposed optimal transport-based framework offers a mathematically robust foundation for global pooling.
    • ROTP layers provide a versatile and effective solution for various set-level machine learning tasks.
    • This approach enhances performance and reduces complexity in global pooling implementation.