A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks

In this paper, we derive generalization bounds for the two primary classes of graph neural networks (GNNs), namely graph convolutional networks (GCNs) and message passing GNNs (MPGNNs), via a PAC-Bayesian approach. Our result reveals that the maximum node degree and spectral norm of the weights govern the generalization bounds of both models. We also show that our bound for GCNs is a natural generalization of the results developed in arXiv:1707.09564v2 [cs.LG] for fully-connected and convolutional neural networks. For message passing GNNs, our PAC-Bayes bound improves over the Rademacher complexity based bound in arXiv:2002.06157v1 [cs.LG], showing a tighter dependency on the maximum node degree and the maximum hidden dimension. The key ingredients of our proofs are a perturbation analysis of GNNs and the generalization of PAC-Bayes analysis to non-homogeneous GNNs. We perform an empirical study on several real-world graph datasets and verify that our PAC-Bayes bound is tighter than others.

GeoNet++: Iterative Geometric Neural Network with Edge-Aware Refinement for Joint Depth and Surface Normal Estimation

In this paper, we propose a geometric neural network with edge-aware refinement (GeoNet++) to jointly predict both depth and surface normal maps from a single image. Building on top of two-stream CNNs, GeoNet++ captures the geometric relationships between depth and surface normals with the proposed depth-to-normal and normal-to-depth modules. In particular, the "depth-to-normal" module exploits the least square solution of estimating surface normals from depth to improve their quality, while the "normal-to-depth" module refines the depth map based on the constraints on surface normals through kernel regression. Boundary information is exploited via an edge-aware refinement module. GeoNet++ effectively predicts depth and surface normals with strong 3D consistency and sharp boundaries resulting in better reconstructed 3D scenes. Note that GeoNet++ is generic and can be used in other depth/normal prediction frameworks to improve the quality of 3D reconstruction and pixel-wise accuracy of depth and surface normals. Furthermore, we propose a new 3D geometric metric (3DGM) for evaluating depth prediction in 3D. In contrast to current metrics that focus on evaluating pixel-wise error/accuracy, 3DGM measures whether the predicted depth can reconstruct high-quality 3D surface normals. This is a more natural metric for many 3D application domains. Our experiments on NYUD-V2 and KITTI datasets verify that GeoNet++ produces fine boundary details, and the predicted depth can be used to reconstruct high-quality 3D surfaces. Code has been made publicly available.

DSDNet: Deep Structured self-Driving Network

In this paper, we propose the Deep Structured self-Driving Network (DSDNet), which performs object detection, motion prediction, and motion planning with a single neural network. Towards this goal, we develop a deep structured energy based model which considers the interactions between actors and produces socially consistent multimodal future predictions. Furthermore, DSDNet explicitly exploits the predicted future distributions of actors to plan a safe maneuver by using a structured planning cost. Our sample-based formulation allows us to overcome the difficulty in probabilistic inference of continuous random variables. Experiments on a number of large-scale self driving datasets demonstrate that our model significantly outperforms the state-of-the-art.

Testing the Safety of Self-driving Vehicles by Simulating Perception and Prediction

We present a novel method for testing the safety of self-driving vehicles in simulation. We propose an alternative to sensor simulation, as sensor simulation is expensive and has large domain gaps. Instead, we directly simulate the outputs of the self-driving vehicle's perception and prediction system, enabling realistic motion planning testing. Specifically, we use paired data in the form of ground truth labels and real perception and prediction outputs to train a model that predicts what the online system will produce. Importantly, the inputs to our system consists of high definition maps, bounding boxes, and trajectories, which can be easily sketched by a test engineer in a matter of minutes. This makes our approach a much more scalable solution. Quantitative results on two large-scale datasets demonstrate that we can realistically test motion planning using our simulations.

Learning Lane Graph Representations for Motion Forecasting

We propose a motion forecasting model that exploits a novel structured map representation as well as actor-map interactions. Instead of encoding vectorized maps as raster images, we construct a lane graph from raw map data to explicitly preserve the map structure. To capture the complex topology and long range dependencies of the lane graph, we propose LaneGCN which extends graph convolutions with multiple adjacency matrices and along-lane dilation. To capture the complex interactions between actors and maps, we exploit a fusion network consisting of four types of interactions, actor-to-lane, lane-to-lane, lane-to-actor and actor-to-actor. Powered by LaneGCN and actor-map interactions, our model is able to predict accurate and realistic multi-modal trajectories. Our approach significantly outperforms the state-of-the-art on the large scale Argoverse motion forecasting benchmark.

Implicit Latent Variable Model for Scene-Consistent Motion Forecasting

In order to plan a safe maneuver an autonomous vehicle must accurately perceive its environment, and understand the interactions among traffic participants. In this paper, we aim to learn scene-consistent motion forecasts of complex urban traffic directly from sensor data. In particular, we propose to characterize the joint distribution over future trajectories via an implicit latent variable model. We model the scene as an interaction graph and employ powerful graph neural networks to learn a distributed latent representation of the scene. Coupled with a deterministic decoder, we obtain trajectory samples that are consistent across traffic participants, achieving state-of-the-art results in motion forecasting and interaction understanding. Last but not least, we demonstrate that our motion forecasts result in safer and more comfortable motion planning.

Fast and Accurate: Structure Coherence Component for Face Alignment

In this paper, we propose a fast and accurate coordinate regression method for face alignment. Unlike most existing facial landmark regression methods which usually employ fully connected layers to convert feature maps into landmark coordinate, we present a structure coherence component to explicitly take the relation among facial landmarks into account. Due to the geometric structure of human face, structure coherence between different facial parts provides important cues for effectively localizing facial landmarks. However, the dense connection in the fully connected layers overuses such coherence, making the important cues unable to be distinguished from all connections. Instead, our structure coherence component leverages a dynamic sparse graph structure to passing features among the most related landmarks. Furthermore, we propose a novel objective function, named Soft Wing loss, to improve the accuracy. Extensive experiments on three popular benchmarks, including WFLW, COFW and 300W, demonstrate the effectiveness of the proposed method, achieving state-of-the-art performance with fast speed. Our approach is especially robust to challenging cases resulting in impressively low failure rate (0% and 2.88%) in COFW and WFLW datasets.

Latent Variable Modelling with Hyperbolic Normalizing Flows

The choice of approximate posterior distributions plays a central role in stochastic variational inference (SVI). One effective solution is the use of normalizing flows \cut{defined on Euclidean spaces} to construct flexible posterior distributions. However, one key limitation of existing normalizing flows is that they are restricted to the Euclidean space and are ill-equipped to model data with an underlying hierarchical structure. To address this fundamental limitation, we present the first extension of normalizing flows to hyperbolic spaces. We first elevate normalizing flows to hyperbolic spaces using coupling transforms defined on the tangent bundle, termed Tangent Coupling ($\mathcal{TC}$). We further introduce Wrapped Hyperboloid Coupling ($\mathcal{W}\mathbb{H}C$), a fully invertible and learnable transformation that explicitly utilizes the geometric structure of hyperbolic spaces, allowing for expressive posteriors while being efficient to sample from. We demonstrate the efficacy of our novel normalizing flow over hyperbolic VAEs and Euclidean normalizing flows. Our approach achieves improved performance on density estimation, as well as reconstruction of real-world graph data, which exhibit a hierarchical structure. Finally, we show that our approach can be used to power a generative model over hierarchical data using hyperbolic latent variables.

Nonlinear Equation Solving: A Faster Alternative to Feedforward Computation

Feedforward computations, such as evaluating a neural network or sampling from an autoregressive model, are ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and cannot be easily accelerated with parallel computing. To enable parrallelization, we frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point iteration method, as well as hybrid methods of both. Crucially, Jacobi updates operate independently on each equation and can be executed in parallel. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallel iterations. Experimentally, we demonstrate the effectiveness of our approach in accelerating 1) the evaluation of DenseNets on ImageNet and 2) autoregressive sampling of MADE and PixelCNN. We are able to achieve between 1.2 and 33 speedup factors under various conditions and computation models.

Spatially-Aware Graph Neural Networks for Relational Behavior Forecasting from Sensor Data

In this paper, we tackle the problem of relational behavior forecasting from sensor data. Towards this goal, we propose a novel spatially-aware graph neural network (SpAGNN) that models the interactions between agents in the scene. Specifically, we exploit a convolutional neural network to detect the actors and compute their initial states. A graph neural network then iteratively updates the actor states via a message passing process. Inspired by Gaussian belief propagation, we design the messages to be spatially-transformed parameters of the output distributions from neighboring agents. Our model is fully differentiable, thus enabling end-to-end training. Importantly, our probabilistic predictions can model uncertainty at the trajectory level. We demonstrate the effectiveness of our approach by achieving significant improvements over the state-of-the-art on two real-world self-driving datasets: ATG4D and nuScenes.