Graph Neural Networks (GNNs) have emerged as a powerful and flexible framework for representation learning on irregular data. As they generalize the operations of classical CNNs on grids to arbitrary topologies, GNNs also bring much of the implementation challenges of their Euclidean counterparts. Model size, memory footprint, and energy consumption are common concerns for many real-world applications. Network binarization allocates a single bit to parameters and activations, thus dramatically reducing the memory requirements (up to 32x compared to single-precision floating-point numbers) and maximizing the benefits of fast SIMD instructions on modern hardware for measurable speedups. However, in spite of the large body of work on binarization for classical CNNs, this area remains largely unexplored in geometric deep learning. In this paper, we present and evaluate different strategies for the binarization of graph neural networks. We show that through careful design of the models, and control of the training process, binary graph neural networks can be trained at only a moderate cost in accuracy on challenging benchmarks. In particular, we present the first dynamic graph neural network in Hamming space, able to leverage efficient k-NN search on binary vectors to speed-up the construction of the dynamic graph. We further verify that the binary models offer significant savings on embedded devices. Our code is publicly available on Github1.

Abstract Standard registration algorithms need to be independently applied to each surface to register, following careful pre-processing and hand-tuning. Recently, learning-based approaches have emerged that reduce the registration of new scans to running inference with a previously-trained model. The potential benefits are multifold: inference is typically orders of magnitude faster than solving a new instance of a difficult optimization problem, deep learning models can be made robust to noise and corruption, and the trained model may be re-used for other tasks, e.g. through transfer learning. In this paper, we cast the registration task as a surface-to-surface translation problem, and design a model to reliably capture the latent geometric information directly from raw 3D face scans. We introduce Shape-My-Face (SMF), a powerful encoder-decoder architecture based on an improved point cloud encoder, a novel visual attention mechanism, graph convolutional decoders with skip connections, and a specialized mouth model that we smoothly integrate with the mesh convolutions. Compared to the previous state-of-the-art learning algorithms for non-rigid registration of face scans, SMF only requires the raw data to be rigidly aligned (with scaling) with a pre-defined face template. Additionally, our model provides topologically-sound meshes with minimal supervision, offers faster training time, has orders of magnitude fewer trainable parameters, is more robust to noise, and can generalize to previously unseen datasets. We extensively evaluate the quality of our registrations on diverse data. We demonstrate the robustness and generalizability of our model with in-the-wild face scans across different modalities, sensor types, and resolutions. Finally, we show that, by learning to register scans, SMF produces a hybrid linear and non-linear morphable model. Manipulation of the latent space of SMF allows for shape generation, and morphing applications such as expression transfer in-the-wild. We train SMF on a dataset of human faces comprising 9 large-scale databases on commodity hardware.

Graph convolution operators bring the advantages of deep learning to a variety of graph and mesh processing tasks previously deemed out of reach. With their continued success comes the desire to design more powerful architectures, often by adapting existing deep learning techniques to non-Euclidean data. In this paper, we argue geometry should remain the primary driving force behind innovation in the emerging field of geometric deep learning. We relate graph neural networks to widely successful computer graphics and data approximation models: radial basis functions (RBFs). We conjecture that, like RBFs, graph convolution layers would benefit from the addition of simple functions to the powerful convolution kernels. We introduce affine skip connections, a novel building block formed by combining a fully connected layer with any graph convolution operator. We experimentally demonstrate the effectiveness of our technique, and show the improved performance is the consequence of more than the increased number of parameters. Operators equipped with the affine skip connection markedly outperform their base performance on every task we evaluated, i.e., shape reconstruction, dense shape correspondence, and graph classification. We hope our simple and effective approach will serve as a solid baseline and help ease future research in graph neural networks.

Dictionary learning and component analysis models are fundamental for learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by means of specific structure, such as sparsity, low-rankness, or nonnegativity. Unfortunately, approaches like K-SVD - that learn dictionaries for sparse coding via Singular Value Decomposition (SVD) - are hard to scale to high-volume and high-dimensional visual data, and fragile in the presence of outliers. Conversely, robust component analysis methods such as the Robust Principal Component Analysis (RPCA) are able to recover low-complexity (e.g., low-rank) representations from data corrupted with noise of unknown magnitude and support, but do not provide a dictionary that respects the structure of the data (e.g., images), and also involve expensive computations. In this paper, we propose a novel Kronecker-decomposable component analysis model, coined as Robust Kronecker Component Analysis (RKCA), that combines ideas from sparse dictionary learning and robust component analysis. RKCA has several appealing properties, including robustness to gross corruption; it can be used for low-rank modeling, and leverages separability to solve significantly smaller problems. We design an efficient learning algorithm by drawing links with a restricted form of tensor factorization, and analyze its optimality and low-rankness properties. The effectiveness of the proposed approach is demonstrated on real-world applications, namely background subtraction and image denoising and completion, by performing a thorough comparison with the current state of the art.