Mathieu Serrurier

Orthogonal and 1-Lipschitz neural network layers are essential building blocks in robust deep learning architectures, crucial for certified adversarial robustness, stable generative models, and reliable recurrent networks. Despite significant advancements, existing implementations remain fragmented, limited, and computationally demanding. To address these issues, we introduce Orthogonium , a unified, efficient, and comprehensive PyTorch library providing orthogonal and 1-Lipschitz layers. Orthogonium provides access to standard convolution features-including support for strides, dilation, grouping, and transposed-while maintaining strict mathematical guarantees. Its optimized implementations reduce overhead on large scale benchmarks such as ImageNet. Moreover, rigorous testing within the library has uncovered critical errors in existing implementations, emphasizing the importance of standardized and reliable tools. Orthogonium thus significantly lowers adoption barriers, enabling scalable experimentation and integration across diverse applications requiring orthogonality and robust Lipschitz constraints. Orthogonium is available at https://github.com/deel-ai/orthogonium.

Deep Neural Networks are vulnerable to small perturbations that can drastically alter their predictions for perceptually unchanged inputs. The literature on adversarially robust Deep Learning attempts to either enhance the robustness of neural networks (e.g, via adversarial training) or to certify their decisions up to a given robustness level (e.g, by using randomized smoothing, formal methods or Lipschitz bounds). These studies mostly focus on classification tasks and few efficient certification procedures currently exist for semantic segmentation. In this work, we introduce a new class of certifiably robust Semantic Segmentation networks with built-in Lipschitz constraints that are efficiently trainable and achieve competitive pixel accuracy on challenging datasets such as Cityscapes. Additionally, we provide a novel framework that generalizes robustness certificates for semantic segmentation tasks, where we showcase the flexibility and computational efficiency of using Lipschitz networks. Our approach unlocks real-time compatible certifiably robust semantic segmentation for the first time. Moreover, it allows the computation of worst-case performance under $\ell_2$ attacks of radius $ε$ across a wide range of performance measures. Crucially, we benchmark the runtime of our certification process and find our approach to be around 600 times faster than randomized smoothing methods at inference with comparable certificates on an NVIDIA A100 GPU. Finally, we evaluate the tightness of our worstcase certificates against state-of-the-art adversarial attacks to further validate the performance of our method.