Learnable Fourier Features for Multi-dimensional Spatial Positional Encoding

Yang Li, Si Si, Gang Li, Cho-Jui Hsieh, Samy Bengio

Keywords: Positional encoding, Transformer, Fourier features, multi-dimensional spatial tasks, image classification, image generation, object detection, widget captioning, UI modeling

TL;DR: The work presents a method for encoding multi-dimensional positions using learnable Fourier features for Transformer models.

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.

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Community Implementations: [ 4 code implementations](https://www.catalyzex.com/paper/learnable-fourier-features-for-multi/code)