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<p>Deep learning-based classification relies on decision boundaries, but existing Euclidean space decision theory can only provide a narrow explanation for how some classifiers work and cannot explain why random low-dimensional features outperform high-dimensional features in image classification (for example, ResNet18 achieved an accuracy of 78.77% on the CUB-200-2011 dataset with a feature masking rate of 35%, surpassing the accuracy of 78.31% achieved by the full-dimensional model). To explain this phenomenon, we propose a general decision boundary theory in non-Euclidean manifold space, proving that feature representations exist on closed surfaces rather than linear vectors. This theory deeply analyzes the essential characteristics of decision boundary classification and elucidates the nature of model classification errors. Based on this, the proposed Randomized Hub for Boundary Correction(RHC) algorithm fine-tunes the model using permanent masked neurons, reducing the parameters of the ResNet18 linear layer from 0.103M to 0.067M (a 35% reduction) while improving accuracy by 0.46%. RHC can to some extent correct the inevitable errors of classifiers in Euclidean space. Through visualization and performance experiments, we demonstrate the validity of our theory in non-Euclidean space and show that RHC can effectively work in most models. Codes are available at: <a href="https://github.com/GZU-SAMLab/RHC">https://github.com/GZU-SAMLab/RHC</a></p>

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A generalized CNN decision boundary theory based on non-Euclidean space

  • 期刊论文

  • 发表日期：

    2025年11月3日

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  • Yongjun Zhou,
  • Qinglei Li,
  • Chenyang Wu,
  • Yuanyuan Xiao,
  • Yuquan Li,
  • Qi Wang

摘要

Deep learning-based classification relies on decision boundaries, but existing Euclidean space decision theory can only provide a narrow explanation for how some classifiers work and cannot explain why random low-dimensional features outperform high-dimensional features in image classification (for example, ResNet18 achieved an accuracy of 78.77% on the CUB-200-2011 dataset with a feature masking rate of 35%, surpassing the accuracy of 78.31% achieved by the full-dimensional model). To explain this phenomenon, we propose a general decision boundary theory in non-Euclidean manifold space, proving that feature representations exist on closed surfaces rather than linear vectors. This theory deeply analyzes the essential characteristics of decision boundary classification and elucidates the nature of model classification errors. Based on this, the proposed Randomized Hub for Boundary Correction(RHC) algorithm fine-tunes the model using permanent masked neurons, reducing the parameters of the ResNet18 linear layer from 0.103M to 0.067M (a 35% reduction) while improving accuracy by 0.46%. RHC can to some extent correct the inevitable errors of classifiers in Euclidean space. Through visualization and performance experiments, we demonstrate the validity of our theory in non-Euclidean space and show that RHC can effectively work in most models. Codes are available at: https://github.com/GZU-SAMLab/RHC