Learnable Fourier Features for Multi-Dimensional Spatial Positional Encoding
This addresses the need for effective positional encoding in deep learning models for sequences or images, offering a novel approach that is particularly beneficial for capturing spatial relationships, though it is incremental in nature.
The paper tackles the problem of positional encoding for attention-based models like Transformers by proposing a learnable Fourier feature method that represents multi-dimensional positions as trainable encodings, which improves accuracy and enables faster convergence on several benchmark tasks.
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.