mlsanityData to 14 Oct 2026

Orthogonium : A Unified, Efficient Library of Orthogonal and 1-Lipschitz Building Blocks

arXiv 2601.13776 ↗First posted 20 Jan 2026cs.LG stat.MLcited by 0

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Abstract (arXiv)

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.

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References · 32

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20 more
  1. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
  2. 2018The Singular Values of Convolutional Layerscited by 95
  3. 2019Preventing Gradient Attenuation in Lipschitz Constrained Convolutional Networkscited by 87
  4. 2021Skew Orthogonal Convolutionscited by 67
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  6. 2023Direct Parameterization of Lipschitz-Bounded Deep Networkscited by 51
  7. 2020Deep Isometric Learning for Visual Recognitioncited by 39
  8. 2022Almost-Orthogonal Layers for Efficient General-Purpose Lipschitz Networkscited by 39
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  19. 2024Tight and Efficient Upper Bound on Spectral Norm of Convolutional Layerscited by 7
  20. 2024Spectral Norm of Convolutional Layers with Circular and Zero Paddingscited by 4

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