Transformers have achieved remarkable success in a wide range of natural language processing and computer vision applications. However, the representation capacity of a deep transformer model is degraded due to the over-smoothing issue in which the token representations become identical when the model's depth grows. In this work, we show that self-attention layers in transformers minimize a functional which promotes smoothness, thereby causing token uniformity. We then propose a novel regularizer that penalizes the norm of the difference between the smooth output tokens from self-attention and the input tokens to preserve the fidelity of the tokens. Minimizing the resulting regularized energy functional, we derive the Neural Transformer with a Regularized Nonlocal Functional (NeuTRENO), a novel class of transformer models that can mitigate the over-smoothing issue. We empirically demonstrate the advantages of NeuTRENO over the baseline transformers and state-of-the-art methods in reducing the over-smoothing of token representations on various practical tasks, including object classification, image segmentation, and language modeling.

Unfortunately, different attributes possess diverse characteristics. In this paper, the network homophily rate defined with respect to the node labels is extended to attribute homophily rate by taking the attributes as weak labels.

Several attempts have been made to tackle the issue by bringing linked node pairs close and unlinked pairs distinct. However, they often ignore the intrinsic community structures and would result in sub-optimal performance.

Transformers have achieved remarkable success in a wide range of natural language processing and computer vision applications. However, the representation capacity of a deep transformer model is degraded due to the over-smoothing issue in which the token representations become identical when the model's depth grows. In this work, we show that self-attention layers in transformers minimize a functional which promotes smoothness, thereby causing token uniformity. We then propose a novel regularizer that penalizes the norm of the difference between the smooth output tokens from self-attention and the input tokens to preserve the fidelity of the tokens. Minimizing the resulting regularized energy functional, we derive the Neural Transformer with a Regularized Nonlocal Functional (NeuTRENO), a novel class of transformer models that can mitigate the over-smoothing issue. We empirically demonstrate the advantages of NeuTRENO over the baseline transformers and state-of-the-art methods in reducing the over-smoothing of token representations on various practical tasks, including object classification, image segmentation, and language modeling.