Breathing life into activation functions: the SWIn framework for sustained nonlinearity

Activation functions serve as the primary mechanism for introducing nonlinearity into deep learning models, playing an indispensable role in both model training and inference. By incorporating nonlinear transformations, they significantly enhance the representational capacity of neural networks, thereby improving overall model performance, particularly for complex tasks - such as Computer Vision (CV) and Natural Language Processing (NLP). However, most mainstream activation functions suffer from a common limitation: they tend to degenerate into linear-like behaviors when inputs assume extremely large or small values, consequently impairing their ability to model complex, nonlinear relationships across all non-saturated input domains. To address this limitation, this paper proposes a novel Sinusoidal Wave Integration (SWIn) framework. The core innovation lies in superimposing adjusted sinusoidal wave onto the activation function, which ensures that the composite function preserves the original monotonicity and global trend of the base activation function while guaranteeing persistent nonlinear characteristics within all non-plateau regions of the continuous base activation functions. We conducted extensive evaluations comparing standard activation functions with their SWIn-enhanced counterparts on image classification (CIFAR-100 and ImageNet-1K), machine translation (WMT14 DE-EN, CS-EN, RU-EN) tasks. Experimental results demonstrate that the SWIn framework yields significant performance improvements for continuous activation functions such as SiLU, Mish, and GELU. This is attributed to the enriched function representation and improved gradient propagation introduced by the controlled oscillations. In contrast, for inherently non-smooth functions like PReLU and SELU, the SWIn transformation tends to amplify existing gradient discontinuities, resulting in marginal or no performance gains.