We provide URL to our code release in abstract.

We introduce a general method for achieving robust group-invariance in groupequivariant convolutional neural networks (G-CNNs), which we call the G-triplecorrelation (G-TC) layer. The approach leverages the theory of the triple-correlation on groups, which is the unique, lowest-degree polynomial invariant map that is also complete. Many commonly used invariant maps--such as the max--are incomplete: they remove both group and signal structure. A complete invariant, by contrast, removes only the variation due to the actions of the group, while preserving all information about the structure of the signal. The completeness of the triple correlation endows the G-TC layer with strong robustness, which can be observed in its resistance to invariance-based adversarial attacks. In addition, we observe that it yields measurable improvements in classification accuracy over standard Max G-Pooling in G-CNN architectures. We provide a general and efficient implementation of the method for any discretized group, which requires only a table defining the group's product structure.

We present a novel approach to the generation of static and articulated 3D assets that has a 3D autodecoder at its core. The 3D autodecoder framework embeds properties learned from the target dataset in the latent space, which can then be decoded into a volumetric representation for rendering view-consistent appearance and geometry. We then identify the appropriate intermediate volumetric latent space, and introduce robust normalization and de-normalization operations to learn a 3D diffusion from 2D images or monocular videos of rigid or articulated objects. Our approach is flexible enough to use either existing camera supervision or no camera information at all - instead efficiently learning it during training. Our evaluations demonstrate that our generation results outperform state-of-theart alternatives on various benchmark datasets and metrics, including multi-view image datasets of synthetic objects, real in-the-wild videos of moving people, and a large-scale, real video dataset of static objects.

A wide array of modern machine learning applications - from adversarial models to multi-agent reinforcement learning - can be formulated as non-cooperative games whose Nash equilibria represent the system's desired operational states. Despite having a highly non-convex loss landscape, many cases of interest possess a latent convex structure that could potentially be leveraged to yield convergence to an equilibrium. Driven by this observation, our paper proposes a flexible first-order method that successfully exploits such "hidden structures" and achieves convergence under minimal assumptions for the transformation connecting the players' control variables to the game's latent, convex-structured layer. The proposed method - which we call preconditioned hidden gradient descent (PHGD) - hinges on a judiciously chosen gradient preconditioning scheme related to natural gradient methods. Importantly, we make no separability assumptions for the game's hidden structure, and we provide explicit convergence rate guarantees for both deterministic and stochastic environments.