arXiv subjects

Liu Liu

Publications and source records attributed to Liu Liu.

At least 253 records · Page 14Linked to original sources

arXiv2020

Iterative roots of exclusive multifunctions

In this paper we investigate iterative roots of strictly monotone upper semi-continuous multifunctions having finitely many jumps. Known results are concerning roots of order 2 for multifunctions of exact one jump. For the general investigation, we introduce a concept `intensity' to formulate the growth of jumps under iteration and find a class of strictly monotone and upper semi-continuous multifunctions of intensity 1, called exclusive multifunctions, each of which has an absorbing interval. Then we use the absorbing interval to construct iterative roots of order $n$ for those exclusive multifunctions.

math.DS↗

arXiv2020

Toward Trainability of Quantum Neural Networks

Quantum Neural Networks (QNNs) have been recently proposed as generalizations of classical neural networks to achieve the quantum speed-up. Despite the potential to outperform classical models, serious bottlenecks exist for training QNNs; namely, QNNs with random structures have poor trainability due to the vanishing gradient with rate exponential to the input qubit number. The vanishing gradient could seriously influence the applications of large-size QNNs. In this work, we provide a viable solution with theoretical guarantees. Specifically, we prove that QNNs with tree tensor and step controlled architectures have gradients that vanish at most polynomially with the qubit number. We numerically demonstrate QNNs with tree tensor and step controlled structures for the application of binary classification. Simulations show faster convergent rates and better accuracy compared to QNNs with random structures.

quant-ph↗

arXiv2020

PlueckerNet: Learn to Register 3D Line Reconstructions

Aligning two partially-overlapped 3D line reconstructions in Euclidean space is challenging, as we need to simultaneously solve correspondences and relative pose between line reconstructions. This paper proposes a neural network based method and it has three modules connected in sequence: (i) a Multilayer Perceptron (MLP) based network takes Pluecker representations of lines as inputs, to extract discriminative line-wise features and matchabilities (how likely each line is going to have a match), (ii) an Optimal Transport (OT) layer takes two-view line-wise features and matchabilities as inputs to estimate a 2D joint probability matrix, with each item describes the matchness of a line pair, and (iii) line pairs with Top-K matching probabilities are fed to a 2-line minimal solver in a RANSAC framework to estimate a six Degree-of-Freedom (6-DoF) rigid transformation. Experiments on both indoor and outdoor datasets show that the registration (rotation and translation) precision of our method outperforms baselines significantly.

cs.CV↗

arXiv2020

DoveNet: Deep Image Harmonization via Domain Verification

Image composition is an important operation in image processing, but the inconsistency between foreground and background significantly degrades the quality of composite image. Image harmonization, aiming to make the foreground compatible with the background, is a promising yet challenging task. However, the lack of high-quality publicly available dataset for image harmonization greatly hinders the development of image harmonization techniques. In this work, we contribute an image harmonization dataset iHarmony4 by generating synthesized composite images based on COCO (resp., Adobe5k, Flickr, day2night) dataset, leading to our HCOCO (resp., HAdobe5k, HFlickr, Hday2night) sub-dataset. Moreover, we propose a new deep image harmonization method DoveNet using a novel domain verification discriminator, with the insight that the foreground needs to be translated to the same domain as background. Extensive experiments on our constructed dataset demonstrate the effectiveness of our proposed method. Our dataset and code are available at https://github.com/bcmi/Image_Harmonization_Datasets.

cs.CV↗

arXiv2020

On the Guaranteed Almost Equivalence between Imitation Learning from Observation and Demonstration

Imitation learning from observation (LfO) is more preferable than imitation learning from demonstration (LfD) due to the nonnecessity of expert actions when reconstructing the expert policy from the expert data. However, previous studies imply that the performance of LfO is inferior to LfD by a tremendous gap, which makes it challenging to employ LfO in practice. By contrast, this paper proves that LfO is almost equivalent to LfD in the deterministic robot environment, and more generally even in the robot environment with bounded randomness. In the deterministic robot environment, from the perspective of the control theory, we show that the inverse dynamics disagreement between LfO and LfD approaches zero, meaning that LfO is almost equivalent to LfD. To further relax the deterministic constraint and better adapt to the practical environment, we consider bounded randomness in the robot environment and prove that the optimizing targets for both LfD and LfO remain almost same in the more generalized setting. Extensive experiments for multiple robot tasks are conducted to empirically demonstrate that LfO achieves comparable performance to LfD. In fact, most common robot systems in reality are the robot environment with bounded randomness (i.e., the environment this paper considered). Hence, our findings greatly extend the potential of LfO and suggest that we can safely apply LfO without sacrificing the performance compared to LfD in practice.

cs.RO↗

arXiv2020

Solving the Blind Perspective-n-Point Problem End-To-End With Robust Differentiable Geometric Optimization

Blind Perspective-n-Point (PnP) is the problem of estimating the position and orientation of a camera relative to a scene, given 2D image points and 3D scene points, without prior knowledge of the 2D-3D correspondences. Solving for pose and correspondences simultaneously is extremely challenging since the search space is very large. Fortunately it is a coupled problem: the pose can be found easily given the correspondences and vice versa. Existing approaches assume that noisy correspondences are provided, that a good pose prior is available, or that the problem size is small. We instead propose the first fully end-to-end trainable network for solving the blind PnP problem efficiently and globally, that is, without the need for pose priors. We make use of recent results in differentiating optimization problems to incorporate geometric model fitting into an end-to-end learning framework, including Sinkhorn, RANSAC and PnP algorithms. Our proposed approach significantly outperforms other methods on synthetic and real data.

cs.CV↗

arXiv2020

Robust Structured Statistical Estimation via Conditional Gradient Type Methods

Structured statistical estimation problems are often solved by Conditional Gradient (CG) type methods to avoid the computationally expensive projection operation. However, the existing CG type methods are not robust to data corruption. To address this, we propose to robustify CG type methods against Huber's corruption model and heavy-tailed data. First, we show that the two Pairwise CG methods are stable, i.e., do not accumulate error. Combined with robust mean gradient estimation techniques, we can therefore guarantee robustness to a wide class of problems, but now in a projection-free algorithmic framework. Next, we consider high dimensional problems. Robust mean estimation based approaches may have an unacceptably high sample complexity. When the constraint set is a $\ell_0$ norm ball, Iterative-Hard-Thresholding-based methods have been developed recently. Yet extension is non-trivial even for general sets with $O(d)$ extreme points. For setting where the feasible set has $O(\text{poly}(d))$ extreme points, we develop a novel robustness method, based on a new condition we call the Robust Atom Selection Condition (RASC). When RASC is satisfied, our method converges linearly with a corresponding statistical error, with sample complexity that scales correctly in the sparsity of the problem, rather than the ambient dimension as would be required by any approach based on robust mean estimation.

cs.LG↗

arXiv2020

Channel Attention based Iterative Residual Learning for Depth Map Super-Resolution

Despite the remarkable progresses made in deep-learning based depth map super-resolution (DSR), how to tackle real-world degradation in low-resolution (LR) depth maps remains a major challenge. Existing DSR model is generally trained and tested on synthetic dataset, which is very different from what would get from a real depth sensor. In this paper, we argue that DSR models trained under this setting are restrictive and not effective in dealing with real-world DSR tasks. We make two contributions in tackling real-world degradation of different depth sensors. First, we propose to classify the generation of LR depth maps into two types: non-linear downsampling with noise and interval downsampling, for which DSR models are learned correspondingly. Second, we propose a new framework for real-world DSR, which consists of four modules : 1) An iterative residual learning module with deep supervision to learn effective high-frequency components of depth maps in a coarse-to-fine manner; 2) A channel attention strategy to enhance channels with abundant high-frequency components; 3) A multi-stage fusion module to effectively re-exploit the results in the coarse-to-fine process; and 4) A depth refinement module to improve the depth map by TGV regularization and input loss. Extensive experiments on benchmarking datasets demonstrate the superiority of our method over current state-of-the-art DSR methods.

cs.CV↗

arXiv2020

Computation on Sparse Neural Networks: an Inspiration for Future Hardware

Neural network models are widely used in solving many challenging problems, such as computer vision, personalized recommendation, and natural language processing. Those models are very computationally intensive and reach the hardware limit of the existing server and IoT devices. Thus, finding better model architectures with much less amount of computation while maximally preserving the accuracy is a popular research topic. Among various mechanisms that aim to reduce the computation complexity, identifying the zero values in the model weights and in the activations to avoid computing them is a promising direction. In this paper, we summarize the current status of the research on the computation of sparse neural networks, from the perspective of the sparse algorithms, the software frameworks, and the hardware accelerations. We observe that the search for the sparse structure can be a general methodology for high-quality model explorations, in addition to a strategy for high-efficiency model execution. We discuss the model accuracy influenced by the number of weight parameters and the structure of the model. The corresponding models are called to be located in the weight dominated and structure dominated regions, respectively. We show that for practically complicated problems, it is more beneficial to search large and sparse models in the weight dominated region. In order to achieve the goal, new approaches are required to search for proper sparse structures, and new sparse training hardware needs to be developed to facilitate fast iterations of sparse models.

cs.LG↗

arXiv2020

Cost-effectiveness Analysis of Antiepidemic Policies and Global Situation Assessment of COVID-19

With a two-layer contact-dispersion model and data in China, we analyze the cost-effectiveness of three types of antiepidemic measures for COVID-19: regular epidemiological control, local social interaction control, and inter-city travel restriction. We find that: 1) intercity travel restriction has minimal or even negative effect compared to the other two at the national level; 2) the time of reaching turning point is independent of the current number of cases, and only related to the enforcement stringency of epidemiological control and social interaction control measures; 3) strong enforcement at the early stage is the only opportunity to maximize both antiepidemic effectiveness and cost-effectiveness; 4) mediocre stringency of social interaction measures is the worst choice. Subsequently, we cluster countries/regions into four groups based on their control measures and provide situation assessment and policy suggestions for each group.

physics.soc-ph↗

arXiv2020

Image Harmonization Dataset iHarmony4: HCOCO, HAdobe5k, HFlickr, and Hday2night

Image composition is an important operation in image processing, but the inconsistency between foreground and background significantly degrades the quality of composite image. Image harmonization, which aims to make the foreground compatible with the background, is a promising yet challenging task. However, the lack of high-quality public dataset for image harmonization, which significantly hinders the development of image harmonization techniques. Therefore, we contribute an image harmonization dataset iHarmony4 by generating synthesized composite images based on existing COCO (resp., Adobe5k, day2night) dataset, leading to our HCOCO (resp., HAdobe5k, Hday2night) sub-dataset. To enrich the diversity of our dataset, we also generate synthesized composite images based on our collected Flick images, leading to our HFlickr sub-dataset. The image harmonization dataset iHarmony4 is released at https://github.com/bcmi/Image_Harmonization_Datasets.

cs.CV↗

arXiv2020

Learning 2D-3D Correspondences To Solve The Blind Perspective-n-Point Problem

Conventional absolute camera pose via a Perspective-n-Point (PnP) solver often assumes that the correspondences between 2D image pixels and 3D points are given. When the correspondences between 2D and 3D points are not known a priori, the task becomes the much more challenging blind PnP problem. This paper proposes a deep CNN model which simultaneously solves for both the 6-DoF absolute camera pose and 2D--3D correspondences. Our model comprises three neural modules connected in sequence. First, a two-stream PointNet-inspired network is applied directly to both the 2D image keypoints and the 3D scene points in order to extract discriminative point-wise features harnessing both local and contextual information. Second, a global feature matching module is employed to estimate a matchability matrix among all 2D--3D pairs. Third, the obtained matchability matrix is fed into a classification module to disambiguate inlier matches. The entire network is trained end-to-end, followed by a robust model fitting (P3P-RANSAC) at test time only to recover the 6-DoF camera pose. Extensive tests on both real and simulated data have shown that our method substantially outperforms existing approaches, and is capable of processing thousands of points a second with the state-of-the-art accuracy.

cs.CV↗

arXiv2020

Hodge and Podge: Hybrid Supervised Sound Event Detection with Multi-Hot MixMatch and Composition Consistence Training

In this paper, we propose a method called Hodge and Podge for sound event detection. We demonstrate Hodge and Podge on the dataset of Detection and Classification of Acoustic Scenes and Events (DCASE) 2019 Challenge Task 4. This task aims to predict the presence or absence and the onset and offset times of sound events in home environments. Sound event detection is challenging due to the lack of large scale real strongly labeled data. Recently deep semi-supervised learning (SSL) has proven to be effective in modeling with weakly labeled and unlabeled data. This work explores how to extend deep SSL to result in a new, state-of-the-art sound event detection method called Hodge and Podge. With convolutional recurrent neural networks (CRNN) as the backbone network, first, a multi-scale squeeze-excitation mechanism is introduced and added to generate a pyramid squeeze-excitation CRNN. The pyramid squeeze-excitation layer can pay attention to the issue that different sound events have different durations, and to adaptively recalibrate channel-wise spectrogram responses. Further, in order to remedy the lack of real strongly labeled data problem, we propose multi-hot MixMatch and composition consistency training with temporal-frequency augmentation. Our experiments with the public DCASE2019 challenge task 4 validation data resulted in an event-based F-score of 43.4\%, and is about absolutely 1.6\% better than state-of-the-art methods in the challenge. While the F-score of the official baseline is 25.8\%.

cs.SD↗

arXiv2020

Hypocoercivity for a BGK model for gas mixtures

We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continuous phase space. By constructing an entropy functional, we can prove exponential relaxation to equilibrium with explicit rates. Our strategy is based on the entropy and spectral methods adapting Lyapunov's direct method as presented in [Achleitner-Arnold-Carlen, 2016] for the one species linearized BGK model. In comparison to the one species case, we start with two partial differential equations, one for each species. These equations are coupled due to interspecies interactions, which requires additional estimates on these interspecies terms.

math.AP↗

arXiv2019

Optimal Feature Transport for Cross-View Image Geo-Localization

This paper addresses the problem of cross-view image geo-localization, where the geographic location of a ground-level street-view query image is estimated by matching it against a large scale aerial map (e.g., a high-resolution satellite image). State-of-the-art deep-learning based methods tackle this problem as deep metric learning which aims to learn global feature representations of the scene seen by the two different views. Despite promising results are obtained by such deep metric learning methods, they, however, fail to exploit a crucial cue relevant for localization, namely, the spatial layout of local features. Moreover, little attention is paid to the obvious domain gap (between aerial view and ground view) in the context of cross-view localization. This paper proposes a novel Cross-View Feature Transport (CVFT) technique to explicitly establish cross-view domain transfer that facilitates feature alignment between ground and aerial images. Specifically, we implement the CVFT as network layers, which transports features from one domain to the other, leading to more meaningful feature similarity comparison. Our model is differentiable and can be learned end-to-end. Experiments on large-scale datasets have demonstrated that our method has remarkably boosted the state-of-the-art cross-view localization performance, e.g., on the CVUSA dataset, with significant improvements for top-1 recall from 40.79% to 61.43%, and for top-10 from 76.36% to 90.49%. We expect the key insight of the paper (i.e., explicitly handling domain difference via domain transport) will prove to be useful for other similar problems in computer vision as well.

cs.CV↗

arXiv2019

Gaussian wave packet transform based numerical scheme for the semi-classical Schrödinger equation with random inputs

In this work, we study the semi-classical limit of the Schrödinger equation with random inputs, and show that the semi-classical Schrödinger equation produces $O(\varepsilon)$ oscillations in the random variable space. With the Gaussian wave packet transform, the original Schrödinger equation is mapped to an ODE system for the wave packet parameters coupled with a PDE for the quantity $w$ in rescaled variables. Further, we show that the $w$ equation does not produce $\varepsilon$ dependent oscillations, and thus it is more amenable for numerical simulations. We propose multi-level sampling strategy in implementing the Gaussian wave packet transform, where in the most costly part, i.e. simulating the $w$ equation, it is sufficient to use $\varepsilon$ independent samples. We also provide extensive numerical tests as well as meaningful numerical experiments to justify the properties of the numerical algorithm, and hopefully shed light on possible future directions.

math.NA↗

arXiv2019

Encoding Selection for Solving Hamiltonian Cycle Problems with ASP

It is common for search and optimization problems to have alternative equivalent encodings in ASP. Typically none of them is uniformly better than others when evaluated on broad classes of problem instances. We claim that one can improve the solving ability of ASP by using machine learning techniques to select encodings likely to perform well on a given instance. We substantiate this claim by studying the hamiltonian cycle problem. We propose several equivalent encodings of the problem and several classes of hard instances. We build models to predict the behavior of each encoding, and then show that selecting encodings for a given instance using the learned performance predictors leads to significant performance gains.

cs.AI↗

arXiv2019

Quantum algorithm for finding the negative curvature direction in non-convex optimization

We present an efficient quantum algorithm aiming to find the negative curvature direction for escaping the saddle point, which is the critical subroutine for many second-order non-convex optimization algorithms. We prove that our algorithm could produce the target state corresponding to the negative curvature direction with query complexity O(polylog(d) /ε), where d is the dimension of the optimization function. The quantum negative curvature finding algorithm is exponentially faster than any known classical method which takes time at least O(d /\sqrtε). Moreover, we propose an efficient quantum algorithm to achieve the classical read-out of the target state. Our classical read-out algorithm runs exponentially faster on the degree of d than existing counterparts.

quant-ph↗