arXiv subjects
Publications and source records attributed to Jun Yu.
In this paper we show that for a connected compact Lie group to be acceptable it is necessary and sufficient that its derived subgroup is isomorphic to a direct product of the groups $\SU(n)$, $\Sp(n)$, $\SO(2n+1)$, $\G_2$, $\SO(4)$. We show that there are invariant functions on $\SO_{4}(\mathbb{C})^{2}$ which are not generated by 1-argument invariants, though the group $\SO_{4}(\mathbb{C})$ is acceptable.
In this paper, we obtain explicit branching laws for all irreducible unitary representations of $\Spin(N,1)$ restricted to a parabolic subgroup $P$. The restriction turns out to be a finite direct sum of irreducible unitary representations of $P$. We also verify Duflo's conjecture for the branching law of tempered representations of $\Spin(N,1)$ with respect to a parabolic subgroup $P$. That is to show: in the framework of the orbit method, the branching law of a tempered representation is determined by the behavior of the moment map from the corresponding coadjoint orbit. A few key tools used in this work include: Fourier transform, Knapp-Stein intertwining operator, Casselman-Wallach globalization, Zuckerman translation principle, du Cloux's results for smooth representations of semi-algebraic groups.
Let $G$ be a real linear reductive group and $K$ be a maximal compact subgroup. Let $P$ be a minimal parabolic subgroup of $G$ with complexified Lie algebra $\mathfrak{p}$, and $\mathfrak{n}$ be its nilradical. In this paper we show that: for any admissible finitely generated moderate growth smooth Fréchet representation $V$ of $G$, the inclusion $V_{K}\subset V$ induces isomorphisms $H_{i}(\mathfrak{n},V_{K})\cong H_{i}(\mathfrak{n},V)$ ($i\geq 0$), where $V_{K}$ denotes the $(\mathfrak{g},K)$ module of $K$ finite vectors in $V$. This is called Casselman's comparison theorem. As a consequence, we show that: for any $k\geq 1$, $\mathfrak{n}^{k}V$ is a closed subspace of $V$ and the inclusion $V_{K}\subset V$ induces an isomorphism $V_{K}/\mathfrak{n}^{k}V_{K}= V/\mathfrak{n}^{k}V$. This strengthens Casselman's automatic continuity theorem.
Vision-and-language pretraining (VLP) aims to learn generic multimodal representations from massive image-text pairs. While various successful attempts have been proposed, learning fine-grained semantic alignments between image-text pairs plays a key role in their approaches. Nevertheless, most existing VLP approaches have not fully utilized the intrinsic knowledge within the image-text pairs, which limits the effectiveness of the learned alignments and further restricts the performance of their models. To this end, we introduce a new VLP method called ROSITA, which integrates the cross- and intra-modal knowledge in a unified scene graph to enhance the semantic alignments. Specifically, we introduce a novel structural knowledge masking (SKM) strategy to use the scene graph structure as a priori to perform masked language (region) modeling, which enhances the semantic alignments by eliminating the interference information within and across modalities. Extensive ablation studies and comprehensive analysis verifies the effectiveness of ROSITA in semantic alignments. Pretrained with both in-domain and out-of-domain datasets, ROSITA significantly outperforms existing state-of-the-art VLP methods on three typical vision-and-language tasks over six benchmark datasets.
Hashing plays an important role in information retrieval, due to its low storage and high speed of processing. Among the techniques available in the literature, multi-modal hashing, which can encode heterogeneous multi-modal features into compact hash codes, has received particular attention. Most of the existing multi-modal hashing methods adopt the fixed weighting factors to fuse multiple modalities for any query data, which cannot capture the variation of different queries. Besides, many methods introduce hyper-parameters to balance many regularization terms that make the optimization harder. Meanwhile, it is time-consuming and labor-intensive to set proper parameter values. The limitations may significantly hinder their promotion in real applications. In this paper, we propose a simple, yet effective method that is inspired by the Hadamard matrix. The proposed method captures the multi-modal feature information in an adaptive manner and preserves the discriminative semantic information in the hash codes. Our framework is flexible and involves a very few hyper-parameters. Extensive experimental results show the method is effective and achieves superior performance compared to state-of-the-art algorithms.
This study investigated the effect of harsh winter climate on the performance of high speed passenger trains in northern Sweden. Novel approaches based on heterogeneous statistical models were introduced to analyse the train performance in order to take the time-varying risks of train delays into consideration. Specifically, stratified Cox model and heterogeneous Markov chain model were used for modelling primary delays and arrival delays, respectively. Our results showed that the weather variables including temperature, humidity, snow depth, and ice/snow precipitation have significant impact on the train performance.
Semi-supervised Fine-Grained Recognition is a challenge task due to the difficulty of data imbalance, high inter-class similarity and domain mismatch. Recent years, this field has witnessed great progress and many methods has gained great performance. However, these methods can hardly generalize to the large-scale datasets, such as Semi-iNat, as they are prone to suffer from noise in unlabeled data and the incompetence for learning features from imbalanced fine-grained data. In this work, we propose Bilateral-Branch Self-Training Framework (BiSTF), a simple yet effective framework to improve existing semi-supervised learning methods on class-imbalanced and domain-shifted fine-grained data. By adjusting the update frequency through stochastic epoch update, BiSTF iteratively retrains a baseline SSL model with a labeled set expanded by selectively adding pseudo-labeled samples from an unlabeled set, where the distribution of pseudo-labeled samples are the same as the labeled data. We show that BiSTF outperforms the existing state-of-the-art SSL algorithm on Semi-iNat dataset.
Monocular depth estimation (MDE) is a fundamental task in many applications such as scene understanding and reconstruction. However, most of the existing methods rely on accurately labeled datasets. A weakly-supervised framework based on attention nested U-net (ANU) named as ANUW is introduced in this paper for cases with wrong labels. The ANUW is trained end-to-end to convert an input single RGB image into a depth image. It consists of a dense residual network structure, an adaptive weight channel attention (AWCA) module, a patch second non-local (PSNL) module and a soft label generation method. The dense residual network is the main body of the network to encode and decode the input. The AWCA module can adaptively adjust the channel weights to extract important features. The PSNL module implements the spatial attention mechanism through a second-order non-local method. The proposed soft label generation method uses the prior knowledge of the dataset to produce soft labels to replace false ones. The proposed ANUW is trained on a defective monocular depth dataset and the trained model is tested on three public datasets, and the results demonstrate the superiority of ANUW in comparison with the state-of-the-art MDE methods.
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the data volume is so large that nonuniform subsampling probabilities cannot be calculated all at once, then subsampling with replacement is infeasible to implement. This paper solves this problem using Poisson subsampling. We first derive optimal Poisson subsampling probabilities in the context of quasi-likelihood estimation under the A- and L-optimality criteria. For a practically implementable algorithm with approximated optimal subsampling probabilities, we establish the consistency and asymptotic normality of the resultant estimators. To deal with the situation that the full data are stored in different blocks or at multiple locations, we develop a distributed subsampling framework, in which statistics are computed simultaneously on smaller partitions of the full data. Asymptotic properties of the resultant aggregated estimator are investigated. We illustrate and evaluate the proposed strategies through numerical experiments on simulated and real data sets.
We propose a novel method on refining cross-person gaze prediction task with eye/face images only by explicitly modelling the person-specific differences. Specifically, we first assume that we can obtain some initial gaze prediction results with existing method, which we refer to as InitNet, and then introduce three modules, the Validity Module (VM), Self-Calibration (SC) and Person-specific Transform (PT)) Module. By predicting the reliability of current eye/face images, our VM is able to identify invalid samples, e.g. eye blinking images, and reduce their effects in our modelling process. Our SC and PT module then learn to compensate for the differences on valid samples only. The former models the translation offsets by bridging the gap between initial predictions and dataset-wise distribution. And the later learns more general person-specific transformation by incorporating the information from existing initial predictions of the same person. We validate our ideas on three publicly available datasets, EVE, XGaze and MPIIGaze and demonstrate that our proposed method outperforms the SOTA methods significantly on all of them, e.g. respectively 21.7%, 36.0% and 32.9% relative performance improvements. We won the GAZE 2021 Competition on the EVE dataset. Our code can be found here https://github.com/bjj9/EVE_SCPT.
Explicitly using the block structure of the unknown signal can achieve better reconstruction performance in compressive sensing. Theoretically, an unknown signal with block structure can be accurately recovered from a few number of under-determined linear measurements provided that it is sufficiently block sparse. From the practical point of view, a severe concern is that the block sparse level appears often unknown. In this paper, we introduce a soft measure of block sparsity $k_α(\mathbf{x})=\left(\lVert\mathbf{x}\rVert_{2,α}/\lVert\mathbf{x}\rVert_{2,1}\right)^{\fracα{1-α}}$ with $α\in[0,\infty]$, and propose an estimation procedure by using multivariate centered isotropic symmetric $α$-stable random projections. The limiting distribution of the estimator is established. Simulations are conducted to illustrate our theoretical results.
In learning with noisy labels, the sample selection approach is very popular, which regards small-loss data as correctly labeled during training. However, losses are generated on-the-fly based on the model being trained with noisy labels, and thus large-loss data are likely but not certainly to be incorrect. There are actually two possibilities of a large-loss data point: (a) it is mislabeled, and then its loss decreases slower than other data, since deep neural networks "learn patterns first"; (b) it belongs to an underrepresented group of data and has not been selected yet. In this paper, we incorporate the uncertainty of losses by adopting interval estimation instead of point estimation of losses, where lower bounds of the confidence intervals of losses derived from distribution-free concentration inequalities, but not losses themselves, are used for sample selection. In this way, we also give large-loss but less selected data a try; then, we can better distinguish between the cases (a) and (b) by seeing if the losses effectively decrease with the uncertainty after the try. As a result, we can better explore underrepresented data that are correctly labeled but seem to be mislabeled at first glance. Experiments demonstrate that the proposed method is superior to baselines and robust to a broad range of label noise types.
The problem of open-set noisy labels denotes that part of training data have a different label space that does not contain the true class. Lots of approaches, e.g., loss correction and label correction, cannot handle such open-set noisy labels well, since they need training data and test data to share the same label space, which does not hold for learning with open-set noisy labels. The state-of-the-art methods thus employ the sample selection approach to handle open-set noisy labels, which tries to select clean data from noisy data for network parameters updates. The discarded data are seen to be mislabeled and do not participate in training. Such an approach is intuitive and reasonable at first glance. However, a natural question could be raised "can such data only be discarded during training?". In this paper, we show that the answer is no. Specifically, we discuss that the instances of discarded data could consist of some meaningful information for generalization. For this reason, we do not abandon such data, but use instance correction to modify the instances of the discarded data, which makes the predictions for the discarded data consistent with given labels. Instance correction are performed by targeted adversarial attacks. The corrected data are then exploited for training to help generalization. In addition to the analytical results, a series of empirical evidences are provided to justify our claims.
This paper proposes an approach to Dense Video Captioning (DVC) without pairwise event-sentence annotation. First, we adopt the knowledge distilled from relevant and well solved tasks to generate high-quality event proposals. Then we incorporate contrastive loss and cycle-consistency loss typically applied to cross-modal retrieval tasks to build semantic matching between the proposals and sentences, which are eventually used to train the caption generation module. In addition, the parameters of matching module are initialized via pre-training based on annotated images to improve the matching performance. Extensive experiments on ActivityNet-Caption dataset reveal the significance of distillation-based event proposal generation and cross-modal retrieval-based semantic matching to weakly supervised DVC, and demonstrate the superiority of our method to existing state-of-the-art methods.
Deep neural networks (DNNs) are vulnerable to adversarial noise. Preprocessing based defenses could largely remove adversarial noise by processing inputs. However, they are typically affected by the error amplification effect, especially in the front of continuously evolving attacks. To solve this problem, in this paper, we propose to remove adversarial noise by implementing a self-supervised adversarial training mechanism in a class activation feature space. To be specific, we first maximize the disruptions to class activation features of natural examples to craft adversarial examples. Then, we train a denoising model to minimize the distances between the adversarial examples and the natural examples in the class activation feature space. Empirical evaluations demonstrate that our method could significantly enhance adversarial robustness in comparison to previous state-of-the-art approaches, especially against unseen adversarial attacks and adaptive attacks.
The fog radio access network (Fog-RAN) has been considered a promising wireless access architecture to help shorten the communication delay and relieve the large data delivery burden over the backhaul links. However, limited by conventional inflexible communication design, Fog-RAN cannot be used in some complex communication scenarios. In this study, we focus on investigating a more intelligent Fog-RAN to assist the communication in a high-speed railway environment. Due to the train's continuously moving, the communication should be designed intelligently to adapt to channel variation. Specifically, we dynamically optimize the power allocation in the remote radio heads (RRHs) to minimize the total network power cost considering multiple quality-of-service (QoS) requirements and channel variation. The impact of caching on the power allocation is considered. The dynamic power optimization is analyzed to obtain a closed-form solution in certain cases. The inherent tradeoff among the total network cost, delay and delivery content size is further discussed. To evaluate the performance of the proposed dynamic power allocation, we present an invariant power allocation counterpart as a performance comparison benchmark. The result of our simulation reveals that dynamic power allocation can significantly outperform the invariant power allocation scheme, especially with a random caching strategy or limited caching resources at the RRHs.
We classify abelian subgroups of the automorphism group of any compact simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup. This leads to a classification of the maximal abelian subgroups of compact simple groups of adjoint type and a classification of the fine group gradings of complex simple Lie algebras.
In this paper we show three new results concerning dimension datum. Firstly, for two subgroups $H_{1}$($\cong U(2n+1)$) and $H_{2}$($\cong Sp(n)\times SO(2n+2)$) of $SU(4n+2)$, we find a family of pairs of irreducible representations $(τ_1,τ_2)\in\hat{H_{1}}\times\hat{H_{2}}$ such that $\mathscr{D}_{H_1,τ_1}=\mathscr{D}_{H_2,τ_2}$. With this we construct examples of isospectral hermitian vector bundles. Secondly, we show that: $τ$-dimension data of one-dimensional representations of a connected compact Lie group $H$ determine the image of homomorphism from $H$ to a given compact Lie group $G$. Lastly, we improve a compactness result for an isospectral set of normal homogeneous spaces $(G/H,m)$ by allowing the Riemannian metric $m$ vary, but posing a constraint that $G$ is semisimple.