LipNeXt: Scaling up Lipschitz-based Certified Robustness to Billion-parameter Models
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| Format: | Preprint |
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2026
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| author | Hu, Kai Hu, Haoqi Fredrikson, Matt |
| author_facet | Hu, Kai Hu, Haoqi Fredrikson, Matt |
| contents | Lipschitz-based certification offers efficient, deterministic robustness guarantees but has struggled to scale in model size, training efficiency, and ImageNet performance. We introduce \emph{LipNeXt}, the first \emph{constraint-free} and \emph{convolution-free} 1-Lipschitz architecture for certified robustness. LipNeXt is built using two techniques: (1) a manifold optimization procedure that updates parameters directly on the orthogonal manifold and (2) a \emph{Spatial Shift Module} to model spatial pattern without convolutions. The full network uses orthogonal projections, spatial shifts, a simple 1-Lipschitz $β$-Abs nonlinearity, and $L_2$ spatial pooling to maintain tight Lipschitz control while enabling expressive feature mixing. Across CIFAR-10/100 and Tiny-ImageNet, LipNeXt achieves state-of-the-art clean and certified robust accuracy (CRA), and on ImageNet it scales to 1-2B large models, improving CRA over prior Lipschitz models (e.g., up to $+8\%$ at $\varepsilon{=}1$) while retaining efficient, stable low-precision training. These results demonstrate that Lipschitz-based certification can benefit from modern scaling trends without sacrificing determinism or efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18513 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | LipNeXt: Scaling up Lipschitz-based Certified Robustness to Billion-parameter Models Hu, Kai Hu, Haoqi Fredrikson, Matt Machine Learning Lipschitz-based certification offers efficient, deterministic robustness guarantees but has struggled to scale in model size, training efficiency, and ImageNet performance. We introduce \emph{LipNeXt}, the first \emph{constraint-free} and \emph{convolution-free} 1-Lipschitz architecture for certified robustness. LipNeXt is built using two techniques: (1) a manifold optimization procedure that updates parameters directly on the orthogonal manifold and (2) a \emph{Spatial Shift Module} to model spatial pattern without convolutions. The full network uses orthogonal projections, spatial shifts, a simple 1-Lipschitz $β$-Abs nonlinearity, and $L_2$ spatial pooling to maintain tight Lipschitz control while enabling expressive feature mixing. Across CIFAR-10/100 and Tiny-ImageNet, LipNeXt achieves state-of-the-art clean and certified robust accuracy (CRA), and on ImageNet it scales to 1-2B large models, improving CRA over prior Lipschitz models (e.g., up to $+8\%$ at $\varepsilon{=}1$) while retaining efficient, stable low-precision training. These results demonstrate that Lipschitz-based certification can benefit from modern scaling trends without sacrificing determinism or efficiency. |
| title | LipNeXt: Scaling up Lipschitz-based Certified Robustness to Billion-parameter Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.18513 |