![]() ![]() And the motivation of these selected activation functions is confusing and unclear in theory. Although there is a minuscule amount of pioneering work to simply explore several alternatives (e.g., Leaky ReLU, Softplus) for verifying some specific issues, such as invertibility and stiff systems, ReLU is always utilized in Neural ODEs by default. Contrary to the extensive utilization of various activation functions in conventional neural networks, the family of Neural ODEs has not made substantial progress on these functions. However, Neural ODEs still have some limitations. Due to remarkable properties, such as constant memory cost, adaptive computation and rich theory, ,, , there has been a range of work to study Neural ODEs. Neural Ordinary Differential Equations (Neural ODEs), which use an ODE solver to perform forward propagation, make a huge breakthrough by removing the trouble of choosing the number of layers for convolutional neural networks. To be specific, ResNets can be regarded as an Euler discretization of continuous dynamical systems described in terms of ODEs with the variable that changes over time,. Fortunately, the relationship between ResNets and ordinary differential equations (ODEs) has been studied extensively in recent years. Despite numerous successes, they still lack theoretical support and guidelines on understanding and designing deep neural networks. Residual networks (ResNets), by introducing identity shortcut connections, have developed into an extremely deep architecture with high accuracy and wide applications in a variety of tasks. ![]() Meanwhile, our work theoretically provides a prospective framework to choose appropriate activation functions to match neural differential equations. Experiments show that our model consistently outperforms Neural ODEs with basic activation functions on robustness both against stochastic noise images and adversarial examples across Fashion-MNIST, CIFAR-10, and CIFAR-100 datasets, which strongly validates the applicability of half-Swish and suggests that half-Swish function plays a positive role in regularizing the dynamic behavior to enhance stability. Besides, we explore the effect of evolution time and batch size on Neural ODEs, respectively. Motivated by a family of weight functions used to enhance the stability of dynamical systems, we introduce a new activation function named half-Swish to match Neural ODEs. Fortunately, existing studies have shown that activation functions are essential for Neural ODEs in governing intrinsic dynamics. Moreover, the dynamical behavior existing in them becomes more unclear and complicated as training progresses. However, they have not made substantial progress on activation functions, and ReLU is always utilized by default. Neural Ordinary Differential Equations (Neural ODEs), as a family of novel deep models, delicately link conventional neural networks and dynamical systems, which bridges the gap between theory and practice.
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