Mitigating Over-smoothing in Transformers via Regularized Nonlocal Functionals

Tam Nguyen, Tan M. Nguyen, R. Baraniuk
2/12/2026

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Abstract

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.

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@article{nguyen2026mitigating,
  title  = {Mitigating Over-smoothing in Transformers via Regularized Nonlocal Functionals},
  author = {Tam Nguyen and Tan M. Nguyen and R. Baraniuk},
  year   = {2026},
  eprint = {2312.00751},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/2312.00751},
  journal = {NEURIPS 2023 2023}
}

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