Adaptive Parametric Activation

Konstantinos Panagiotis Alexandridis1, Jiankang Deng1, Anh Nguyen2, Shan Luo3,

1 Huawei Noah's Ark Lab, 2 University of Liverpool, 3 King's College London

APA activation
Figure 1: APA unifies most activation functions under the same formula.

Abstract

The activation function plays a crucial role in model optimisation, yet the optimal choice remains unclear. For example, the Sigmoid activation is the de-facto activation in balanced classification tasks, however, in imbalanced classification, it proves inappropriate due to bias towards frequent classes. In this work, we delve deeper in this phenomenon by performing a comprehensive statistical analysis in the classification and intermediate layers of both balanced and imbalanced networks and we empirically show that aligning the activation function with the data distribution, enhances the performance in both balanced and imbalanced tasks. To this end, we propose the Adaptive Parametric Activation (APA) function, a novel and versatile activation function that unifies most common activation functions under a single formula. APA can be applied in both intermediate layers and attention layers, significantly outperforming the state-of-the-art on several imbalanced benchmarks such as ImageNet-LT, iNaturalist2018, Places-LT, CIFAR100-LT and LVIS and balanced benchmarks such as ImageNet1K, COCO and V3DET.

The arxiv link is here

Definition

The Adaptive Parametric Activation APA is defined as: APA(z,λ,κ)=(λexp(−κz)+1)1−λAPA(z,λ,κ) = (λ exp(−κz) + 1) ^{\frac{1}{−λ}}. APA unifies most activation functions under the same formula as shwon in Figure 1.

APA can be used insed the intermediate layers using Adaptive Generalised Linear Unit (AGLU): AGLU(z,λ,κ)=zAPA(z,λ,κ)AGLU(z,λ,κ) = z APA(z,λ,κ). The derivatives of AGLU with respect to κ (top), λ (middle) and z (bottom) are shown in Figure 2:

AGLU derivatives
Figure 2: The derivatives of AGLU with respect to κ (top), λ (middle) and z (bottom).

Simple Code implementation 

class Unified(nn.Module):
    """Unified activation function module."""

    def __init__(self, device=None, dtype=None) -> None:
        """Initialize the Unified activation function."""
        factory_kwargs = {"device": device, "dtype": dtype}
        super().__init__()
        lambda_param = torch.nn.init.uniform_(torch.empty(1, **factory_kwargs))
        kappa_param = torch.nn.init.uniform_(torch.empty(1, **factory_kwargs))
        self.softplus = nn.Softplus(beta=-1.0)
        self.lambda_param = nn.Parameter(lambda_param)
        self.kappa_param = nn.Parameter(kappa_param)

    def forward(self, input: torch.Tensor) -> torch.Tensor:
        """Compute the forward pass of the Unified activation function."""
        l = torch.clamp(self.lambda_param, min=0.0001)
        p = torch.exp((1 / l) * self.softplus((self.kappa_param * input) - torch.log(l)))
        return p  # for AGLU simply return p*input

BibTeX 

@inproceedings{alexandridis2024adaptive,
  title={Adaptive Parametric Activation},
  author={Alexandridis, Konstantinos Panagiotis and Deng, Jiankang and Nguyen, Anh and Luo, Shan},
  booktitle={European Conference on Computer Vision},
  pages={455--476},
  year={2024},
  organization={Springer}
}