Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform

Strictly enforcing orthonormality constraints on parameter matrices has been shown advantageous in deep learning. This amounts to Riemannian optimization on the Stiefel manifold, which, however, is computationally expensive. To address this challenge, we present two main contributions: (1) A new efficient retraction map based on an iterative Cayley transform for optimization updates, and (2) An implicit vector transport mechanism based on the combination of a projection of the momentum and the Cayley transform on the Stiefel manifold. We specify two new optimization algorithms: Cayley SGD with momentum, and Cayley ADAM on the Stiefel manifold. Convergence of Cayley SGD is theoretically analyzed. Our experiments for CNN training demonstrate that both algorithms: (a) Use less running time per iteration relative to existing approaches that enforce orthonormality of CNN parameters; and (b) Achieve faster convergence rates than the baseline SGD and ADAM algorithms without compromising the performance of the CNN. Cayley SGD and Cayley ADAM are also shown to reduce the training time for optimizing the unitary transition matrices in RNNs.

PointPWC-Net: A Coarse-to-Fine Network for Supervised and Self-Supervised Scene Flow Estimation on 3D Point Clouds

We propose a novel end-to-end deep scene flow model, called PointPWC-Net, on 3D point clouds in a coarse-to-fine fashion. Flow computed at the coarse level is upsampled and warped to a finer level, enabling the algorithm to accommodate for large motion without a prohibitive search space. We introduce novel cost volume, upsampling, and warping layers to efficiently handle 3D point cloud data. Unlike traditional cost volumes that require exhaustively computing all the cost values on a high-dimensional grid, our point-based formulation discretizes the cost volume onto input 3D points, and a PointConv operation efficiently computes convolutions on the cost volume. Experiment results on FlyingThings3D outperform the state-of-the-art by a large margin. We further explore novel self-supervised losses to train our model and achieve comparable results to state-of-the-art trained with supervised loss. Without any fine-tuning, our method also shows great generalization ability on KITTI Scene Flow 2015 dataset, outperforming all previous methods.

Visualizing Point Cloud Classifiers by Curvature Smoothing

Recently, several networks that operate directly on point clouds have been proposed. There is significant utility in understanding them better, so that humans can understand more about the mechanisms how those networks classify point clouds, potentially helping diagnosing them and designing better architectures and data augmentation pipelines. In this paper, we propose a novel approach to visualize important features used in classification decisions of point cloud networks. Following ideas in visualizing 2-D convolutional networks, our approach is based on gradually smoothing parts of the point cloud. However, different from the 2-D case, we smooth the curvature of the point cloud to remove sharp shape features. The resulting point cloud is then evaluated on the original point cloud network to see whether the performance has dropped or remained the same, from which parts that are important to the point cloud classification are identified. A technical contribution of the paper is an approximated curvature smoothing algorithm, which can smoothly transition from the original point cloud to one of constant curvature, such as a uniform sphere. With this smoothing algorithm, we propose PCI-GOS, a 3-D extension of the Integrated-Gradients Optimized Saliency (I-GOS) algorithm, as a perturbation-based visualization technique realized on 3-D shapes. Experiment results revealed insights into these classifiers.

Implicit Generative Modeling for Efficient Exploration

Efficient exploration remains a challenging problem in reinforcement learning, especially for those tasks where rewards from environments are sparse. A commonly used approach for exploring such environments is to introduce some "intrinsic" reward. In this work, we focus on model uncertainty estimation as an intrinsic reward for efficient exploration. In particular, we introduce an implicit generative modeling approach to estimate a Bayesian uncertainty of the agent's belief of the environment dynamics. Each random draw from our generative model is a neural network that instantiates the dynamic function, hence multiple draws would approximate the posterior, and the variance in the future prediction based on this posterior is used as an intrinsic reward for exploration. We design a training algorithm for our generative model based on the amortized Stein Variational Gradient Descent. In experiments, we compare our implementation with state-of-the-art intrinsic reward-based exploration approaches, including two recent approaches based on an ensemble of dynamic models. In challenging exploration tasks, our implicit generative model consistently outperforms competing approaches regarding data efficiency in exploration.

Topology-Preserving Deep Image Segmentation

Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss function that enforces a segmentation to have the same topology as the ground truth, i.e., having the same Betti number. The proposed topology-preserving loss function is differentiable and we incorporate it into end-to-end training of a deep neural network. Our method achieves much better performance on the Betti number error, which directly accounts for the topological correctness. It also performs superiorly on other topology-relevant metrics, e.g., the Adjusted Rand Index and the Variation of Information. We illustrate the effectiveness of the proposed method on a broad spectrum of natural and biomedical datasets.

Visualizing Deep Networks by Optimizing with Integrated Gradients

Understanding and interpreting the decisions made by deep learning models is valuable in many domains. In computer vision, computing heatmaps from a deep network is a popular approach for visualizing and understanding deep networks. However, heatmaps that do not correlate with the network may mislead human, hence the performance of heatmaps in providing a faithful explanation to the underlying deep network is crucial. In this paper, we propose I-GOS, which optimizes for a heatmap so that the classification scores on the masked image would maximally decrease. The main novelty of the approach is to compute descent directions based on the integrated gradients instead of the normal gradient, which avoids local optima and speeds up convergence. Compared with previous approaches, our method can flexibly compute heatmaps at any resolution for different user needs. Extensive experiments on several benchmark datasets show that the heatmaps produced by our approach are more correlated with the decision of the underlying deep network, in comparison with other state-of-the-art approaches.

Adaptive Wing Loss for Robust Face Alignment via Heatmap Regression

Heatmap regression has became one of the mainstream approaches to localize facial landmarks. As Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN) are becoming popular in solving computer vision tasks, extensive research has been done on these architectures. However, the loss function for heatmap regression is rarely studied. In this paper, we analyze the ideal loss function properties for heatmap regression in face alignment problems. Then we propose a novel loss function, named Adaptive Wing loss, that is able to adapt its shape to different types of ground truth heatmap pixels. This adaptability decreases the loss to zero on foreground pixels while leaving some loss on background pixels. To address the imbalance between foreground and background pixels, we also propose Weighted Loss Map, which assigns high weights on foreground and difficult background pixels to help training process focus more on pixels that are crucial to landmark localization. To further improve face alignment accuracy, we introduce boundary prediction and CoordConv with boundary coordinates. Extensive experiments on different benchmarks, including COFW, 300W and WFLW, show our approach outperforms the state-of-the-art by a significant margin on various evaluation metrics. Besides, the Adaptive Wing loss also helps other heatmap regression tasks. Code will be made publicly available.

HyperGAN: A Generative Model for Diverse, Performant Neural Networks

We introduce HyperGAN, a generative network that learns to generate all the weights within a deep neural network. HyperGAN employs a novel mixer to transform independent Gaussian noise into a latent space where dimensions are correlated, which is then transformed to generate weights in each layer of a deep neural network. We utilize an architecture that bears resemblance to generative adversarial networks, but we evaluate the likelihood of samples with a classification loss. This is equivalent to minimizing the KL-divergence between the generated network parameter distribution and an unknown true parameter distribution. We apply HyperGAN to classification, showing that HyperGAN can learn to generate parameters which solve the MNIST and CIFAR-10 datasets with competitive performance to fully supervised learning, while learning a rich distribution of effective parameters. We also show that HyperGAN can also provide better uncertainty than standard ensembles. This is evaluated by the ability of HyperGAN generated ensembles to detect out of distribution data as well as adversarial examples. We see that in addition to being highly accurate on inlier data, HyperGAN can provide reasonable uncertainty estimates.

PointConv: Deep Convolutional Networks on 3D Point Clouds

Unlike images which are represented in regular dense grids, 3D point clouds are irregular and unordered, hence applying convolution on them can be difficult. In this paper, we extend the dynamic filter to a new convolution operation, named PointConv. PointConv can be applied on point clouds to build deep convolutional networks. We treat convolution kernels as nonlinear functions of the local coordinates of 3D points comprised of weight and density functions. With respect to a given point, the weight functions are learned with multi-layer perceptron networks and the density functions through kernel density estimation. A novel reformulation is proposed for efficiently computing the weight functions, which allowed us to dramatically scale up the network and significantly improve its performance. The learned convolution kernel can be used to compute translation-invariant and permutation-invariant convolution on any point set in the 3D space. Besides, PointConv can also be used as deconvolution operators to propagate features from a subsampled point cloud back to its original resolution. Experiments on ModelNet40, ShapeNet, and ScanNet show that deep convolutional neural networks built on PointConv are able to achieve state-of-the-art on challenging semantic segmentation benchmarks on 3D point clouds. Besides, our experiments converting CIFAR-10 into a point cloud showed that networks built on PointConv can match the performance of convolutional networks in 2D images of a similar structure.