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.

翻译：基于Lipschitz的认证方法能提供高效、确定性的鲁棒性保证，但在模型规模、训练效率和ImageNet性能方面一直难以扩展。我们提出了LipNeXt——首个用于认证鲁棒性的无约束且无卷积的1-Lipschitz架构。LipNeXt基于两项技术构建：(1) 直接在正交流形上更新参数的流形优化过程；(2) 用于建模空间模式的无卷积空间移位模块。整个网络采用正交投影、空间移位、简单的1-Lipschitz $β$-Abs非线性函数以及$L_2$空间池化，在保持严格Lipschitz控制的同时实现了富有表现力的特征融合。在CIFAR-10/100和Tiny-ImageNet数据集上，LipNeXt在干净准确率和认证鲁棒准确率（CRA）方面均达到最先进水平；在ImageNet上，该架构可扩展至10-20亿参数的大型模型，在保持高效稳定的低精度训练的同时，其CRA较先前Lipschitz模型有显著提升（例如在$\varepsilon{=}1$时最高提升$+8\%$）。这些结果表明，基于Lipschitz的认证方法能够受益于现代扩展趋势，且无需牺牲确定性或效率。