Learnable Fourier Features for Multi-Dimensional Spatial Positional Encoding

TL;DR

This paper introduces a learnable Fourier feature-based positional encoding for attention models, enhancing spatial understanding and outperforming existing methods in accuracy and convergence speed.

Contribution

It proposes a novel trainable positional encoding method using learnable Fourier features for multi-dimensional spatial data in attention models.

Findings

Outperforms existing positional encoding methods in benchmarks.

Improves accuracy in spatial tasks.

Enables faster convergence during training.

Abstract

Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this paper, we propose a novel positional encoding method based on learnable Fourier features. Instead of hard-coding each position as a token or a vector, we represent each position, which can be multi-dimensional, as a trainable encoding based on learnable Fourier feature mapping, modulated with a multi-layer perceptron. The representation is particularly advantageous for a spatial multi-dimensional position, e.g., pixel positions on an image, where $L_2$ distances or more complex positional relationships need to be captured. Our experiments based on several public benchmark tasks show that our learnable Fourier feature representation for multi-dimensional positional encoding outperforms existing methods by both improving the accuracy and allowing faster convergence.