Polynomial Composition Activations: Unleashing the Dynamics of Large Language Models

TL;DR

This paper introduces Polynomial Composition Activations (PolyCom), a novel activation function for transformers that enhances expressivity and efficiency, leading to improved performance in large language models through theoretical analysis and empirical validation.

Contribution

The paper proposes PolyCom, a new activation function with proven optimal approximation capabilities, and demonstrates its effectiveness in large language model pre-training.

Findings

PolyCom achieves the optimal approximation rate.

LLMs with PolyCom outperform those with traditional activations.

PolyCom improves accuracy and convergence in large language models.

Abstract

Transformers have found extensive applications across various domains due to the powerful fitting capabilities. This success can be partially attributed to their inherent nonlinearity. Thus, in addition to the ReLU function employed in the original transformer architecture, researchers have explored alternative modules such as GeLU and SwishGLU to enhance nonlinearity and thereby augment representational capacity. In this paper, we propose a novel category of polynomial composition activations (PolyCom), designed to optimize the dynamics of transformers. Theoretically, we provide a comprehensive mathematical analysis of PolyCom, highlighting its enhanced expressivity and efficacy relative to other activation functions. Notably, we demonstrate that networks incorporating PolyCom achieve the $\textbf{optimal approximation rate}$, indicating that PolyCom networks require minimal parameters to approximate general smooth functions in Sobolev spaces. We conduct empirical experiments on the pre-training configurations of large language models (LLMs), including both dense and sparse architectures. By substituting conventional activation functions with PolyCom, we enable LLMs to capture higher-order interactions within the data, thus improving performance metrics in terms of accuracy and convergence rates. Extensive experimental results demonstrate the effectiveness of our method, showing substantial improvements over other activation functions. Code is available at https://github.com/BryceZhuo/PolyCom.