Noise Stability of Transformer Models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912889916358656 |
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| author | Haris, Themistoklis Zhang, Zihan Yoshida, Yuichi |
| author_facet | Haris, Themistoklis Zhang, Zihan Yoshida, Yuichi |
| contents | Understanding simplicity biases in deep learning offers a promising path toward developing reliable AI. A common metric for this, inspired by Boolean function analysis, is average sensitivity, which captures a model's robustness to single-token perturbations. We argue that average sensitivity has two key limitations: it lacks a natural generalization to real-valued domains and fails to explain the "junta-like" input dependence we empirically observe in modern LLMs. To address these limitations, we propose noise stability as a more comprehensive simplicity metric. Noise stability expresses a model's robustness to correlated noise applied to all input coordinates simultaneously. We provide a theoretical analysis of noise stability for single-layer attention and ReLU MLP layers and tackle the multi-layer propagation problem with a covariance interval propagation approach. Building on this theory, we develop a practical noise stability regularization method. Experiments on algorithmic and next-token-prediction tasks show that our regularizer consistently catalyzes grokking and accelerates training by approximately $35\%$ and $75\%$ respectively. Our results sculpt a new connection between signal propagation in neural networks and interpretability, with noise stability emerging as a powerful tool for understanding and improving modern Transformers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_08287 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Noise Stability of Transformer Models Haris, Themistoklis Zhang, Zihan Yoshida, Yuichi Machine Learning Artificial Intelligence Understanding simplicity biases in deep learning offers a promising path toward developing reliable AI. A common metric for this, inspired by Boolean function analysis, is average sensitivity, which captures a model's robustness to single-token perturbations. We argue that average sensitivity has two key limitations: it lacks a natural generalization to real-valued domains and fails to explain the "junta-like" input dependence we empirically observe in modern LLMs. To address these limitations, we propose noise stability as a more comprehensive simplicity metric. Noise stability expresses a model's robustness to correlated noise applied to all input coordinates simultaneously. We provide a theoretical analysis of noise stability for single-layer attention and ReLU MLP layers and tackle the multi-layer propagation problem with a covariance interval propagation approach. Building on this theory, we develop a practical noise stability regularization method. Experiments on algorithmic and next-token-prediction tasks show that our regularizer consistently catalyzes grokking and accelerates training by approximately $35\%$ and $75\%$ respectively. Our results sculpt a new connection between signal propagation in neural networks and interpretability, with noise stability emerging as a powerful tool for understanding and improving modern Transformers. |
| title | Noise Stability of Transformer Models |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.08287 |