p-Laplacian Transformer

• URL: http://arxiv.org/abs/2311.03235v1
• Date: Mon, 6 Nov 2023 16:25:56 GMT
• Title: p-Laplacian Transformer
• Authors: Tuan Nguyen, Tam Nguyen, Vinh Nguyen, Tan M. Nguyen
• Abstract summary: $p$-Laplacian regularization, rooted in graph and image signal processing, introduces a parameter $p$ to control the regularization effect on these data. We first show that the self-attention mechanism obtains the minimal Laplacian regularization. We then propose a novel class of transformers, namely the $p$-Laplacian Transformer (p-LaT)
• Score: 7.2541371193810384
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: $p$-Laplacian regularization, rooted in graph and image signal processing, introduces a parameter $p$ to control the regularization effect on these data. Smaller values of $p$ promote sparsity and interpretability, while larger values encourage smoother solutions. In this paper, we first show that the self-attention mechanism obtains the minimal Laplacian regularization ($p=2$) and encourages the smoothness in the architecture. However, the smoothness is not suitable for the heterophilic structure of self-attention in transformers where attention weights between tokens that are in close proximity and non-close ones are assigned indistinguishably. From that insight, we then propose a novel class of transformers, namely the $p$-Laplacian Transformer (p-LaT), which leverages $p$-Laplacian regularization framework to harness the heterophilic features within self-attention layers. In particular, low $p$ values will effectively assign higher attention weights to tokens that are in close proximity to the current token being processed. We empirically demonstrate the advantages of p-LaT over the baseline transformers on a wide range of benchmark datasets.

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