Hyper-flexible Convolutional Neural Networks based on Generalized Lehmer and Power Means

Area of Science:

• Computer Science
• Artificial Intelligence
• Machine Learning

Background:

• Convolutional Neural Networks (CNNs) are widely used for image classification but suffer from poor reusability due to data-specific tuning.
• Traditional CNNs rely on fixed mathematical operations, limiting their adaptability to new problems.

Purpose of the Study:

• To enhance the reusability and robustness of Convolutional Neural Networks.
• To introduce trainable parameters into mathematical functions within CNN architectures.

Main Methods:

• Replaced fixed operations (e.g., arithmetic mean) with flexible mathematical functions (Generalized Lehmer Mean, Generalized Power Mean) with trainable parameters.
• Developed a novel architecture named hyper-flexible convolutional neural network.
• Provided mathematical justification for the new components.

Main Results:

• The proposed hyper-flexible CNN architecture demonstrated superior performance compared to traditional CNNs.
• The new architecture exhibited improved robustness against adversarial perturbations in testing data.
• Trainable parameters in mathematical functions allow for distinguishing task-specific and capability-specific parameters.

Conclusions:

• Hyper-flexible CNNs offer a promising direction for creating more adaptable and resilient deep learning models.
• The integration of trainable mathematical functions enhances CNNs' generalization capabilities.
• This approach addresses the limitations of fixed computations in traditional neural networks.