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Hao Shen

Publications and source records attributed to Hao Shen.

At least 109 records · Page 6Linked to original sources
arXiv2021

Stochastic Ricci Flow on Compact Surfaces

In this paper we introduce the stochastic Ricci flow (SRF) in two spatial dimensions. The flow is symmetric with respect to a measure induced by Liouville Conformal Field Theory. Using the theory of Dirichlet forms, we construct a weak solution to the associated equation of the area measure on a flat torus, in the full "$L^1$ regime" $σ< σ_{L^1}=2\sqrtπ$ where $σ$ is the noise strength. We also describe the main necessary modifications needed for the SRF on general compact surfaces, and list some open questions.

math.PR↗
arXiv2021

Large $N$ Limit of the $O(N)$ Linear Sigma Model via Stochastic Quantization

This article studies large $N$ limits of a coupled system of $N$ interacting $Φ^4$ equations posed over $\mathbb{T}^{d}$ for $d=2$, known as the $O(N)$ linear sigma model. Uniform in $N$ bounds on the dynamics are established, allowing us to show convergence to a mean-field singular SPDE, also proved to be globally well-posed. Moreover, we show tightness of the invariant measures in the large $N$ limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique invariant measure of the mean-field dynamics, at a rate of order $1/\sqrt{N}$ with respect to the Wasserstein distance. We also consider fluctuations and obtain tightness results for certain $O(N)$ invariant observables, along with an exact description of the limiting correlations.

math.PR↗
arXiv2020

Knowledge as Invariance -- History and Perspectives of Knowledge-augmented Machine Learning

Research in machine learning is at a turning point. While supervised deep learning has conquered the field at a breathtaking pace and demonstrated the ability to solve inference problems with unprecedented accuracy, it still does not quite live up to its name if we think of learning as the process of acquiring knowledge about a subject or problem. Major weaknesses of present-day deep learning models are, for instance, their lack of adaptability to changes of environment or their incapability to perform other kinds of tasks than the one they were trained for. While it is still unclear how to overcome these limitations, one can observe a paradigm shift within the machine learning community, with research interests shifting away from increasing the performance of highly parameterized models to exceedingly specific tasks, and towards employing machine learning algorithms in highly diverse domains. This research question can be approached from different angles. For instance, the field of Informed AI investigates the problem of infusing domain knowledge into a machine learning model, by using techniques such as regularization, data augmentation or post-processing. On the other hand, a remarkable number of works in the recent years has focused on developing models that by themselves guarantee a certain degree of versatility and invariance with respect to the domain or problem at hand. Thus, rather than investigating how to provide domain-specific knowledge to machine learning models, these works explore methods that equip the models with the capability of acquiring the knowledge by themselves. This white paper provides an introduction and discussion of this emerging field in machine learning research. To this end, it reviews the role of knowledge in machine learning, and discusses its relation to the concept of invariance, before providing a literature review of the field.

cs.LG↗
arXiv2020

Attentional Separation-and-Aggregation Network for Self-supervised Depth-Pose Learning in Dynamic Scenes

Learning depth and ego-motion from unlabeled videos via self-supervision from epipolar projection can improve the robustness and accuracy of the 3D perception and localization of vision-based robots. However, the rigid projection computed by ego-motion cannot represent all scene points, such as points on moving objects, leading to false guidance in these regions. To address this problem, we propose an Attentional Separation-and-Aggregation Network (ASANet), which can learn to distinguish and extract the scene's static and dynamic characteristics via the attention mechanism. We further propose a novel MotionNet with an ASANet as the encoder, followed by two separate decoders, to estimate the camera's ego-motion and the scene's dynamic motion field. Then, we introduce an auto-selecting approach to detect the moving objects for dynamic-aware learning automatically. Empirical experiments demonstrate that our method can achieve the state-of-the-art performance on the KITTI benchmark.

cs.CV↗
arXiv2020

3D Scene Geometry-Aware Constraint for Camera Localization with Deep Learning

Camera localization is a fundamental and key component of autonomous driving vehicles and mobile robots to localize themselves globally for further environment perception, path planning and motion control. Recently end-to-end approaches based on convolutional neural network have been much studied to achieve or even exceed 3D-geometry based traditional methods. In this work, we propose a compact network for absolute camera pose regression. Inspired from those traditional methods, a 3D scene geometry-aware constraint is also introduced by exploiting all available information including motion, depth and image contents. We add this constraint as a regularization term to our proposed network by defining a pixel-level photometric loss and an image-level structural similarity loss. To benchmark our method, different challenging scenes including indoor and outdoor environment are tested with our proposed approach and state-of-the-arts. And the experimental results demonstrate significant performance improvement of our method on both prediction accuracy and convergence efficiency.

cs.CV↗
arXiv2020

CenterMask: single shot instance segmentation with point representation

In this paper, we propose a single-shot instance segmentation method, which is simple, fast and accurate. There are two main challenges for one-stage instance segmentation: object instances differentiation and pixel-wise feature alignment. Accordingly, we decompose the instance segmentation into two parallel subtasks: Local Shape prediction that separates instances even in overlapping conditions, and Global Saliency generation that segments the whole image in a pixel-to-pixel manner. The outputs of the two branches are assembled to form the final instance masks. To realize that, the local shape information is adopted from the representation of object center points. Totally trained from scratch and without any bells and whistles, the proposed CenterMask achieves 34.5 mask AP with a speed of 12.3 fps, using a single-model with single-scale training/testing on the challenging COCO dataset. The accuracy is higher than all other one-stage instance segmentation methods except the 5 times slower TensorMask, which shows the effectiveness of CenterMask. Besides, our method can be easily embedded to other one-stage object detectors such as FCOS and performs well, showing the generalization of CenterMask.

cs.CV↗
arXiv2020

Dynamic Variational Autoencoders for Visual Process Modeling

This work studies the problem of modeling visual processes by leveraging deep generative architectures for learning linear, Gaussian representations from observed sequences. We propose a joint learning framework, combining a vector autoregressive model and Variational Autoencoders. This results in an architecture that allows Variational Autoencoders to simultaneously learn a non-linear observation as well as a linear state model from sequences of frames. We validate our approach on artificial sequences and dynamic textures.

cs.NE↗
arXiv2019

Interactive Image Restoration

Machine learning and many of its applications are considered hard to approach due to their complexity and lack of transparency. One mission of human-centric machine learning is to improve algorithm transparency and user satisfaction while ensuring an acceptable task accuracy. In this work, we present an interactive image restoration framework, which exploits both image prior and human painting knowledge in an iterative manner such that they can boost on each other. Additionally, in this system users can repeatedly get feedback of their interactions from the restoration progress. This informs the users about their impact on the restoration results, which leads to better sense of control, which can lead to greater trust and approachability. The positive results of both objective and subjective evaluation indicate that, our interactive approach positively contributes to the approachability of restoration algorithms in terms of algorithm performance and user experience.

cs.HC↗
arXiv2019

Grand Challenge of 106-Point Facial Landmark Localization

Facial landmark localization is a very crucial step in numerous face related applications, such as face recognition, facial pose estimation, face image synthesis, etc. However, previous competitions on facial landmark localization (i.e., the 300-W, 300-VW and Menpo challenges) aim to predict 68-point landmarks, which are incompetent to depict the structure of facial components. In order to overcome this problem, we construct a challenging dataset, named JD-landmark. Each image is manually annotated with 106-point landmarks. This dataset covers large variations on pose and expression, which brings a lot of difficulties to predict accurate landmarks. We hold a 106-point facial landmark localization competition1 on this dataset in conjunction with IEEE International Conference on Multimedia and Expo (ICME) 2019. The purpose of this competition is to discover effective and robust facial landmark localization approaches.

cs.CV↗
arXiv2019

Stochastic quantization of an Abelian gauge theory

We study the Langevin dynamics of a U(1) lattice gauge theory on the torus, and prove that they converge for short time in a suitable gauge to a system of stochastic PDEs driven by space-time white noises. This also yields convergence of some gauge invariant observables on a short time interval. We fix gauge via a DeTurck trick, and prove a version of Ward identity which results in cancellation of renormalization constants that would otherwise break gauge symmetry. The proof relies on a discrete version of the theory of regularity structures.

math.PR↗
arXiv2019

A High-Efficiency Framework for Constructing Large-Scale Face Parsing Benchmark

Face parsing, which is to assign a semantic label to each pixel in face images, has recently attracted increasing interest due to its huge application potentials. Although many face related fields (e.g., face recognition and face detection) have been well studied for many years, the existing datasets for face parsing are still severely limited in terms of the scale and quality, e.g., the widely used Helen dataset only contains 2,330 images. This is mainly because pixel-level annotation is a high cost and time-consuming work, especially for the facial parts without clear boundaries. The lack of accurate annotated datasets becomes a major obstacle in the progress of face parsing task. It is a feasible way to utilize dense facial landmarks to guide the parsing annotation. However, annotating dense landmarks on human face encounters the same issues as the parsing annotation. To overcome the above problems, in this paper, we develop a high-efficiency framework for face parsing annotation, which considerably simplifies and speeds up the parsing annotation by two consecutive modules. Benefit from the proposed framework, we construct a new Dense Landmark Guided Face Parsing (LaPa) benchmark. It consists of 22,000 face images with large variations in expression, pose, occlusion, etc. Each image is provided with accurate annotation of a 11-category pixel-level label map along with coordinates of 106-point landmarks. To the best of our knowledge, it is currently the largest public dataset for face parsing. To make full use of our LaPa dataset with abundant face shape and boundary priors, we propose a simple yet effective Boundary-Sensitive Parsing Network (BSPNet). Our network is taken as a baseline model on the proposed LaPa dataset, and meanwhile, it achieves the state-of-the-art performance on the Helen dataset without resorting to extra face alignment.

cs.CV↗
arXiv2019

A Generative Map for Image-based Camera Localization

In image-based camera localization systems, information about the environment is usually stored in some representation, which can be referred to as a map. Conventionally, most maps are built upon hand-crafted features. Recently, neural networks have attracted attention as a data-driven map representation, and have shown promising results in visual localization. However, these neural network maps are generally hard to interpret by human. A readable map is not only accessible to humans, but also provides a way to be verified when the ground truth pose is unavailable. To tackle this problem, we propose Generative Map, a new framework for learning human-readable neural network maps, by combining a generative model with the Kalman filter, which also allows it to incorporate additional sensor information such as stereo visual odometry. For evaluation, we use real world images from the 7-Scenes and Oxford RobotCar datasets. We demonstrate that our Generative Map can be queried with a pose of interest from the test sequence to predict an image, which closely resembles the true scene. For localization, we show that Generative Map achieves comparable performance with current regression models. Moreover, our framework is trained completely from scratch, unlike regression models which rely on large ImageNet pretrained networks.

cs.CV↗
arXiv2019

Some recent progress in singular stochastic PDEs

Stochastic PDEs are ubiquitous in mathematical modeling. Yet, many such equations are too singular to admit classical treatment. In this article we review some recent progress in defining, approximating and studying the properties of a few examples of such equations. We focus mainly on the dynamical Phi4 equation, KPZ equation and Parabolic Anderson Model, as well as touch on a few other equations which arise mainly in physics.

math.PR↗
arXiv2019

Stochastic PDE Limit of the Six Vertex Model

We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $Δ\to 1^+$ so as to zoom into the ferroelectric/disordered phase critical point) its height function fluctuations converge to the solution to the KPZ equation. We also prove that the one-dimensional family of stochastic Gibbs states for the symmetric six vertex model converge under the same scaling to the stationary solution to the stochastic Burgers equation. Our proofs rely upon the Markov (self) duality of our model. The starting point is an exact microscopic Hopf-Cole transform for the stochastic six vertex model which follows from the model's known one-particle Markov self-duality. Given this transform, the crucial step is to establish self-averaging for specific quadratic function of the transformed height function. We use the model's two-particle self-duality to produce explicit expressions (as Bethe ansatz contour integrals) for conditional expectations from which we extract time-decorrelation and hence self-averaging in time. The crux of our Markov duality method is that the entire convergence result reduces to precise estimates on the one-particle and two-particle transition probabilities. Previous to our work, Markov dualities had only been used to prove convergence of particle systems to linear Gaussian SPDEs (e.g. the stochastic heat equation with additive noise).

math.PR↗
arXiv2019

Local solution to the multi-layer KPZ equation

In this article we prove local well-posedness of the system of equations $\partial_t h_{i}= \sum_{j=1}^{i}\partial_x^2 h_{i}+ (\partial_x h_{i})^2 + ξ$ on the circle where $1\leq i\leq N$ and $ξ$ is a space-time white noise. We attempt to generalize the renormalization procedure which gives the Hopf-Cole solution for the single layer equation and our $h_1$ (solution to the first layer) coincides with this solution. However, we observe that cancellation of logarithmic divergences that occurs at the first layer does not hold at higher layers and develop explicit combinatorial formulae for them.

math.PR↗
arXiv2018

A Differential Topological View of Challenges in Learning with Feedforward Neural Networks

Among many unsolved puzzles in theories of Deep Neural Networks (DNNs), there are three most fundamental challenges that highly demand solutions, namely, expressibility, optimisability, and generalisability. Although there have been significant progresses in seeking answers using various theories, e.g. information bottleneck theory, sparse representation, statistical inference, Riemannian geometry, etc., so far there is no single theory that is able to provide solutions to all these challenges. In this work, we propose to engage the theory of differential topology to address the three problems. By modelling the dataset of interest as a smooth manifold, DNNs can be considered as compositions of smooth maps between smooth manifolds. Specifically, our work offers a differential topological view of loss landscape of DNNs, interplay between width and depth in expressibility, and regularisations for generalisability. Finally, in the setting of deep representation learning, we further apply the quotient topology to investigate the architecture of DNNs, which enables to capture nuisance factors in data with respect to a specific learning task.

cs.LG↗
arXiv2018

Trace Quotient with Sparsity Priors for Learning Low Dimensional Image Representations

This work studies the problem of learning appropriate low dimensional image representations. We propose a generic algorithmic framework, which leverages two classic representation learning paradigms, i.e., sparse representation and the trace quotient criterion. The former is a well-known powerful tool to identify underlying self-explanatory factors of data, while the latter is known for disentangling underlying low dimensional discriminative factors in data. Our developed solutions disentangle sparse representations of images by employing the trace quotient criterion. We construct a unified cost function, coined as the SPARse LOW dimensional representation (SparLow) function, for jointly learning both a sparsifying dictionary and a dimensionality reduction transformation. The SparLow function is widely applicable for developing various algorithms in three classic machine learning scenarios, namely, unsupervised, supervised, and semi-supervised learning. In order to develop efficient joint learning algorithms for maximizing the SparLow function, we deploy a framework of sparse coding with appropriate convex priors to ensure the sparse representations to be locally differentiable. Moreover, we develop an efficient geometric conjugate gradient algorithm to maximize the SparLow function on its underlying Riemannian manifold. Performance of the proposed SparLow algorithmic framework is investigated on several image processing tasks, such as 3D data visualization, face/digit recognition, and object/scene categorization.

cs.CV↗