An Adaptive Orthogonal Convolution Scheme for Efficient and Flexible CNN Architectures

Orthogonal convolutional layers are the workhorse of multiple areas in machine learning, such as adversarial robustness, normalizing flows, GANs, and Lipschitzconstrained models. Their ability to preserve norms and ensure stable gradient propagation makes them valuable for a large range of problems. Despite their promise, the deployment of orthogonal convolution in large-scale applications is a significant challenge due to computational overhead and limited support for modern features like strides, dilations, group convolutions, and transposed convolutions.In this paper, we introduce AOC (Adaptative Orthogonal Convolution), a scalable method for constructing orthogonal convolutions, effectively overcoming these limitations. This advancement unlocks the construction of architectures that were previously considered impractical. We demonstrate through our experiments that our method produces expressive models that become increasingly efficient as they scale. To foster further advancement, we provide an open-source library implementing this method, available at https://github.com/thib-s/orthogonium.

DP-SGD Without Clipping: The Lipschitz Neural Network Way

State-of-the-art approaches for training Differentially Private (DP) Deep Neural Networks (DNN) faces difficulties to estimate tight bounds on the sensitivity of the network's layers, and instead rely on a process of per-sample gradient clipping. This clipping process not only biases the direction of gradients but also proves costly both in memory consumption and in computation. To provide sensitivity bounds and bypass the drawbacks of the clipping process, our theoretical analysis of Lipschitz constrained networks reveals an unexplored link between the Lipschitz constant with respect to their input and the one with respect to their parameters. By bounding the Lipschitz constant of each layer with respect to its parameters we guarantee DP training of these networks. This analysis not only allows the computation of the aforementioned sensitivities at scale but also provides leads on to how maximize the gradient-to-noise ratio for fixed privacy guarantees. To facilitate the application of Lipschitz networks and foster robust and certifiable learning under privacy guarantees, we provide a Python package that implements building blocks allowing the construction and private training of such networks.