Linearized Relative Positional Encoding

• URL: http://arxiv.org/abs/2307.09270v1
• Date: Tue, 18 Jul 2023 13:56:43 GMT
• Title: Linearized Relative Positional Encoding
• Authors: Zhen Qin, Weixuan Sun, Kaiyue Lu, Hui Deng, Dongxu Li, Xiaodong Han, Yuchao Dai, Lingpeng Kong, Yiran Zhong
• Abstract summary: Relative positional encoding is widely used in vanilla and linear transformers to represent positional information. We put together a variety of existing linear relative positional encoding approaches under a canonical form. We further propose a family of linear relative positional encoding algorithms via unitary transformation.
• Score: 43.898057545832366
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Relative positional encoding is widely used in vanilla and linear transformers to represent positional information. However, existing encoding methods of a vanilla transformer are not always directly applicable to a linear transformer, because the latter requires a decomposition of the query and key representations into separate kernel functions. Nevertheless, principles for designing encoding methods suitable for linear transformers remain understudied. In this work, we put together a variety of existing linear relative positional encoding approaches under a canonical form and further propose a family of linear relative positional encoding algorithms via unitary transformation. Our formulation leads to a principled framework that can be used to develop new relative positional encoding methods that preserve linear space-time complexity. Equipped with different models, the proposed linearized relative positional encoding (LRPE) family derives effective encoding for various applications. Experiments show that compared with existing methods, LRPE achieves state-of-the-art performance in language modeling, text classification, and image classification. Meanwhile, it emphasizes a general paradigm for designing broadly more relative positional encoding methods that are applicable to linear transformers. The code is available at https://github.com/OpenNLPLab/Lrpe.

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