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An interpretive constrained linear model for ResNet and MgNet.

Juncai He1, Jinchao Xu2, Lian Zhang3

  • 1Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia.

Neural Networks : the Official Journal of the International Neural Network Society
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Summary

We introduce a constrained linear model for interpretable image classification with convolutional neural networks (CNNs). This approach yields modified ResNet models with fewer parameters and higher accuracy, validating our data-feature mapping assumption.

Keywords:
Convolutional neural networksData-feature mappingMgNetMultigrid iterative methodsResNet

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Machine Learning

Background:

  • Convolutional Neural Networks (CNNs) are pivotal in image classification.
  • Existing models like ResNet and MgNet offer powerful architectures but lack interpretability.
  • Understanding the mathematical underpinnings of CNNs can lead to improved model design.

Purpose of the Study:

  • To propose a constrained linear data-feature mapping model for interpretable CNN-based image classification.
  • To establish connections between traditional iterative schemes and CNN architectures (ResNet, MgNet).
  • To develop novel, efficient, and accurate image classification models.

Main Methods:

  • Formulated a constrained linear data-feature mapping model.
  • Established mathematical links between iterative linear system solvers and ResNet/MgNet architectures.
  • Developed modified ResNet models with reduced parameters and enhanced accuracy.
  • Proposed a general data-feature iterative scheme to rationalize MgNet.

Main Results:

  • Modified ResNet models demonstrated superior performance (fewer parameters, higher accuracy) compared to original versions.
  • The constrained learning data-feature mapping assumption was validated.
  • MgNet, based on the proposed iterative scheme, showed significant advantages in image classification.
  • Numerical studies confirmed MgNet's success against established networks.

Conclusions:

  • The constrained linear data-feature mapping model provides an interpretable framework for CNNs.
  • Architectural modifications inspired by iterative schemes can yield more efficient and accurate models.
  • MgNet presents a promising, rationalized approach for advanced image classification tasks.