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<p>Activation functions play a crucial role in the dynamics, convergence speed, and overall performance of deep convolutional neural networks (CNNs). In this work, we first propose P-SiLU, an activation function based on trigonometric functions, which integrates trigonometric properties with controller design principles. P-SiLU is designed to address challenges in CNN optimization, thereby enhancing learning efficiency and generalization capability. We evaluate P-SiLU on three widely used architectures—VGG16, ResNet50, and DenseNet121—across five standard benchmark datasets: CIFAR10, CIFAR100, MNIST, Fashion MNIST, and TinyImageNet. Experimental results show that P-SiLU significantly improves network performance, achieving higher accuracy in image classification tasks compared with ReLU and its variants. Specifically, on CIFAR10 with VGG16, P-SiLU attains an average accuracy of 85.31%, exceeding other activation functions by at least 1.02%. Building on this finding, we further demonstrate that combining SiLU with trigonometric functions can enhance classification accuracy. Inspired by P-SiLU, we propose two additional activation functions—R-SiLU and L-SiLU—which achieve average accuracies of 88.97% and 88.57% on CIFAR10 with VGG16, respectively. Moreover, we introduce a multidimensional space projection technique to visualize network weights, thereby providing insights into the decision-making process and revealing the impact of activation functions on network behavior.</p>

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P-SiLU: a trigonometric-based activation function for enhanced convolutional neural networks

  • 期刊论文

  • 发表日期：

    2025年9月19日

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  • Yinlei Cheng,
  • Naidong Zhao

摘要

Activation functions play a crucial role in the dynamics, convergence speed, and overall performance of deep convolutional neural networks (CNNs). In this work, we first propose P-SiLU, an activation function based on trigonometric functions, which integrates trigonometric properties with controller design principles. P-SiLU is designed to address challenges in CNN optimization, thereby enhancing learning efficiency and generalization capability. We evaluate P-SiLU on three widely used architectures—VGG16, ResNet50, and DenseNet121—across five standard benchmark datasets: CIFAR10, CIFAR100, MNIST, Fashion MNIST, and TinyImageNet. Experimental results show that P-SiLU significantly improves network performance, achieving higher accuracy in image classification tasks compared with ReLU and its variants. Specifically, on CIFAR10 with VGG16, P-SiLU attains an average accuracy of 85.31%, exceeding other activation functions by at least 1.02%. Building on this finding, we further demonstrate that combining SiLU with trigonometric functions can enhance classification accuracy. Inspired by P-SiLU, we propose two additional activation functions—R-SiLU and L-SiLU—which achieve average accuracies of 88.97% and 88.57% on CIFAR10 with VGG16, respectively. Moreover, we introduce a multidimensional space projection technique to visualize network weights, thereby providing insights into the decision-making process and revealing the impact of activation functions on network behavior.