Lightlike Neuromanifolds, Occam's Razor and Deep Learning

Why do deep neural networks generalize with a very high dimensional parameter space? We took an information theoretic approach. We find that the dimensionality of the parameter space can be studied by singular semi-Riemannian geometry and is upper-bounded by the sample size. We adapt Fisher information to this singular neuromanifold. We use random matrix theory to derive a minimum description length of a deep learning model, where the spectrum of the Fisher information matrix plays a key role to improve generalisation.

High-Resolution Representations for Labeling Pixels and Regions

High-resolution representation learning plays an essential role in many vision problems, e.g., pose estimation and semantic segmentation. The high-resolution network (HRNet)~\cite{SunXLW19}, recently developed for human pose estimation, maintains high-resolution representations through the whole process by connecting high-to-low resolution convolutions in \emph{parallel} and produces strong high-resolution representations by repeatedly conducting fusions across parallel convolutions. In this paper, we conduct a further study on high-resolution representations by introducing a simple yet effective modification and apply it to a wide range of vision tasks. We augment the high-resolution representation by aggregating the (upsampled) representations from all the parallel convolutions rather than only the representation from the high-resolution convolution as done in~\cite{SunXLW19}. This simple modification leads to stronger representations, evidenced by superior results. We show top results in semantic segmentation on Cityscapes, LIP, and PASCAL Context, and facial landmark detection on AFLW, COFW, $300$W, and WFLW. In addition, we build a multi-level representation from the high-resolution representation and apply it to the Faster R-CNN object detection framework and the extended frameworks. The proposed approach achieves superior results to existing single-model networks on COCO object detection. The code and models have been publicly available at \url{https://github.com/HRNet}.

Fisher-Bures Adversary Graph Convolutional Networks

In a graph convolutional network, we assume that the graph $G$ is generated with respect to some observation noise. We make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum information geometry, we can have quantitative measurements on the scale of $\Delta{}G$. We try to maximize the intrinsic scale of the permutation with a small budget while minimizing the loss based on the perturbed $G+\Delta{G}$. Our proposed model can consistently improve graph convolutional networks on semi-supervised node classification tasks with reasonable computational overhead. We present two different types of geometry on the manifold of graphs: one is for measuring the intrinsic change of a graph; the other is for measuring how such changes can affect externally a graph neural network. These new analytical tools will be useful in developing a good understanding of graph neural networks and fostering new techniques.

Virtual Adversarial Training on Graph Convolutional Networks in Node Classification

The effectiveness of Graph Convolutional Networks (GCNs) has been demonstrated in a wide range of graph-based machine learning tasks. However, the update of parameters in GCNs is only from labeled nodes, lacking the utilization of unlabeled data. In this paper, we apply Virtual Adversarial Training (VAT), an adversarial regularization method based on both labeled and unlabeled data, on the supervised loss of GCN to enhance its generalization performance. By imposing virtually adversarial smoothness on the posterior distribution in semi-supervised learning, VAT yields improvement on the Symmetrical Laplacian Smoothness of GCNs. In addition, due to the difference of property in features, we perturb virtual adversarial perturbations on sparse and dense features, resulting in GCN Sparse VAT (GCNSVAT) and GCN Dense VAT (GCNDVAT) algorithms, respectively. Extensive experiments verify the effectiveness of our two methods across different training sizes. Our work paves the way towards better understanding the direction of improvement on GCNs in the future.

Multi-Stage Self-Supervised Learning for Graph Convolutional Networks

Graph Convolutional Networks(GCNs) play a crucial role in graph learning tasks, however, learning graph embedding with few supervised signals is still a difficult problem. In this paper, we propose a novel training algorithm for Graph Convolutional Network, called Multi-Stage Self-Supervised(M3S) Training Algorithm, combined with self-supervised learning approach, focusing on improving the generalization performance of GCNs on graphs with few labeled nodes. Firstly, a Multi-Stage Training Framework is provided as the basis of M3S training method. Then we leverage DeepCluster technique, a popular form of self-supervised learning, and design corresponding aligning mechanism on the embedding space to refine the Multi-Stage Training Framework, resulting in M3S Training Algorithm. Finally, extensive experimental results verify the superior performance of our algorithm on graphs with few labeled nodes under different label rates compared with other state-of-the-art approaches.

Enhancing the Robustness of Deep Neural Networks by Boundary Conditional GAN

Deep neural networks have been widely deployed in various machine learning tasks. However, recent works have demonstrated that they are vulnerable to adversarial examples: carefully crafted small perturbations to cause misclassification by the network. In this work, we propose a novel defense mechanism called Boundary Conditional GAN to enhance the robustness of deep neural networks against adversarial examples. Boundary Conditional GAN, a modified version of Conditional GAN, can generate boundary samples with true labels near the decision boundary of a pre-trained classifier. These boundary samples are fed to the pre-trained classifier as data augmentation to make the decision boundary more robust. We empirically show that the model improved by our approach consistently defenses against various types of adversarial attacks successfully. Further quantitative investigations about the improvement of robustness and visualization of decision boundaries are also provided to justify the effectiveness of our strategy. This new defense mechanism that uses boundary samples to enhance the robustness of networks opens up a new way to defense adversarial attacks consistently.

Towards Understanding Adversarial Examples Systematically: Exploring Data Size, Task and Model Factors

Most previous works usually explained adversarial examples from several specific perspectives, lacking relatively integral comprehension about this problem. In this paper, we present a systematic study on adversarial examples from three aspects: the amount of training data, task-dependent and model-specific factors. Particularly, we show that adversarial generalization (i.e. test accuracy on adversarial examples) for standard training requires more data than standard generalization (i.e. test accuracy on clean examples); and uncover the global relationship between generalization and robustness with respect to the data size especially when data is augmented by generative models. This reveals the trade-off correlation between standard generalization and robustness in limited training data regime and their consistency when data size is large enough. Furthermore, we explore how different task-dependent and model-specific factors influence the vulnerability of deep neural networks by extensive empirical analysis. Relevant recommendations on defense against adversarial attacks are provided as well. Our results outline a potential path towards the luminous and systematic understanding of adversarial examples.

Deep High-Resolution Representation Learning for Human Pose Estimation

This is an official pytorch implementation of Deep High-Resolution Representation Learning for Human Pose Estimation. In this work, we are interested in the human pose estimation problem with a focus on learning reliable high-resolution representations. Most existing methods recover high-resolution representations from low-resolution representations produced by a high-to-low resolution network. Instead, our proposed network maintains high-resolution representations through the whole process. We start from a high-resolution subnetwork as the first stage, gradually add high-to-low resolution subnetworks one by one to form more stages, and connect the mutli-resolution subnetworks in parallel. We conduct repeated multi-scale fusions such that each of the high-to-low resolution representations receives information from other parallel representations over and over, leading to rich high-resolution representations. As a result, the predicted keypoint heatmap is potentially more accurate and spatially more precise. We empirically demonstrate the effectiveness of our network through the superior pose estimation results over two benchmark datasets: the COCO keypoint detection dataset and the MPII Human Pose dataset. The code and models have been publicly available at \url{https://github.com/leoxiaobin/deep-high-resolution-net.pytorch}.

Relative Geometry-Aware Siamese Neural Network for 6DOF Camera Relocalization

6DOF camera relocalization is an important component of autonomous driving and navigation. Deep learning has recently emerged as a promising technique to tackle this problem. In this paper, we present a novel relative geometry-aware Siamese neural network to enhance the performance of deep learning-based methods through explicitly exploiting the relative geometry constraints between images. We perform multi-task learning and predict the absolute and relative poses simultaneously. We regularize the shared-weight twin networks in both the pose and feature domains to ensure that the estimated poses are globally as well as locally correct. We employ metric learning and design a novel adaptive metric distance loss to learn a feature that is capable of distinguishing poses of visually similar images from different locations. We evaluate the proposed method on public indoor and outdoor benchmarks and the experimental results demonstrate that our method can significantly improve localization performance. Furthermore, extensive ablation evaluations are conducted to demonstrate the effectiveness of different terms of the loss function.

On The Chain Rule Optimal Transport Distance

We define a novel class of distances between statistical multivariate distributions by solving an optimal transportation problem on their marginal densities with respect to a ground distance defined on their conditional densities. By using the chain rule factorization of probabilities, we show how to perform optimal transport on a ground space being an information-geometric manifold of conditional probabilities. We prove that this new distance is a metric whenever the chosen ground distance is a metric. Our distance generalizes both the Wasserstein distances between point sets and a recently introduced metric distance between statistical mixtures. As a first application of this Chain Rule Optimal Transport (CROT) distance, we show that the ground distance between statistical mixtures is upper bounded by this optimal transport distance, whenever the ground distance is joint convex. We report on our experiments which quantify the tightness of the CROT distance for the total variation distance and a square root generalization of the Jensen-Shannon divergence between mixtures.