Gompertz Linear Units: Leveraging Asymmetry for Enhanced Learning Dynamics

TL;DR

The paper introduces Gompertz Linear Unit (GoLU), a novel activation function leveraging asymmetry to improve training dynamics and performance across various deep learning tasks.

Contribution

It proposes GoLU, a new self-gated activation function based on the Gompertz function, demonstrating improved variance reduction and gradient flow over existing functions.

Findings

GoLU outperforms GELU and Swish in multiple tasks.

GoLU reduces variance in latent space effectively.

Experiments cover diverse applications like image and language tasks.

Abstract

Activation functions are fundamental elements of deep learning architectures as they significantly influence training dynamics. ReLU, while widely used, is prone to the dying neuron problem, which has been mitigated by variants such as LeakyReLU, PReLU, and ELU that better handle negative neuron outputs. Recently, self-gated activations like GELU and Swish have emerged as state-of-the-art alternatives, leveraging their smoothness to ensure stable gradient flow and prevent neuron inactivity. In this work, we introduce the Gompertz Linear Unit (GoLU), a novel self-gated activation function defined as $\mathrm{GoLU}(x) = x \, \mathrm{Gompertz}(x)$, where $\mathrm{Gompertz}(x) = e^{-e^{-x}}$. The GoLU activation leverages the right-skewed asymmetry in the Gompertz function to reduce variance in the latent space more effectively compared to GELU and Swish, while preserving robust gradient flow. Extensive experiments across diverse tasks, including Image Classification, Language Modeling, Semantic Segmentation, Object Detection, Instance Segmentation, and Diffusion, highlight GoLU's superior performance relative to state-of-the-art activation functions, establishing GoLU as a robust alternative to existing activation functions.