Classical Embedding Research Articles

Zero-shot Cross-modal Retrieval by Assembling AutoEncoder and Generative Adversarial Network

Conventional cross-modal retrieval models mainly assume the same scope of the classes for both the training set and the testing set. This assumption limits their extensibility on zero-shot cross-modal retrieval (ZS-CMR), where the testing set consists of unseen classes that are disjoint with seen classes in the training set. The ZS-CMR task is more challenging due to the heterogeneous distributions of different modalities and the semantic inconsistency between seen and unseen classes. A few of recently proposed approaches are inspired by zero-shot learning to estimate the distribution underlying multimodal data by generative models and make the knowledge transfer from seen classes to unseen classes by leveraging class embeddings. However, directly borrowing the idea from zero-shot learning (ZSL) is not fully adaptive to the retrieval task, since the core of the retrieval task is learning the common space. To address the above issues, we propose a novel approach named Assembling AutoEncoder and Generative Adversarial Network (AAEGAN), which combines the strength of AutoEncoder (AE) and Generative Adversarial Network (GAN), to jointly incorporate common latent space learning, knowledge transfer, and feature synthesis for ZS-CMR. Besides, instead of utilizing class embeddings as common space, the AAEGAN approach maps all multimodal data into a learned latent space with the distribution alignment via three coupled AEs. We empirically show the remarkable improvement for ZS-CMR task and establish the state-of-the-art or competitive performance on four image-text retrieval datasets.

Charged Wormholes in Spacetimes of Embedding Class One

The existence of charged black holes has suggested that wormholes may also be charged. The purpose of this paper is to construct a general model of a charged wormhole that proves to be a natural extension of the original Morris-Thorne wormhole. This goal is achieved by means of the classical embedding theory that has played a major role in the general theory of relativity.

Generalized Zero-Shot Learning With Multiple Graph Adaptive Generative Networks.

Generative adversarial networks (GANs) for (generalized) zero-shot learning (ZSL) aim to generate unseen image features when conditioned on unseen class embeddings, each of which corresponds to one unique category. Most existing works on GANs for ZSL generate features by merely feeding the seen image feature/class embedding (combined with random Gaussian noise) pairs into the generator/discriminator for a two-player minimax game. However, the structure consistency of the distributions among the real/fake image features, which may shift the generated features away from their real distribution to some extent, is seldom considered. In this paper, to align the weights of the generator for better structure consistency between real/fake features, we propose a novel multigraph adaptive GAN (MGA-GAN). Specifically, a Wasserstein GAN equipped with a classification loss is trained to generate discriminative features with structure consistency. MGA-GAN leverages the multigraph similarity structures between sliced seen real/fake feature samples to assist in updating the generator weights in the local feature manifold. Moreover, correlation graphs for the whole real/fake features are adopted to guarantee structure correlation in the global feature manifold. Extensive evaluations on four benchmarks demonstrate well the superiority of MGA-GAN over its state-of-the-art counterparts.

Embeddings of non-simply-connected 4-manifolds in 7-space. II. On the smooth classification

We work in the smooth category. Let $N$ be a closed connected orientable 4-manifold with torsion free $H_1$, where $H_q := H_q(N; {\mathbb Z} )$. Our main result is a readily calculable classification of embeddings$N \to {\mathbb R}^7$up to isotopy, with an indeterminacy. Such a classification was only known before for $H_1=0$ by our earlier work from 2008. Our classification is complete when $H_2=0$ or when the signature of $N$ is divisible neither by 64 nor by 9.The group of knots $S^4\to {\mathbb R}^7$ acts on the set of embeddings $N\to {\mathbb R}^7$ up to isotopy by embedded connected sum. In Part I we classified the quotient of this action. The main novelty of this paper is the description of this action for $H_1 \ne 0$, with an indeterminacy.Besides the invariants of Part I, detecting the action of knots involves a refinement of the Kreck invariant from our work of 2008.For $N=S^1\times S^3$ we give a geometrically defined 1–1 correspondence between the set of isotopy classes of embeddings and a certain explicitly defined quotient of the set ${\mathbb Z} \oplus {\mathbb Z} \oplus {\mathbb Z} _{12}$.

НЕРАВЕНСТВА, УТОЧНЯЮЩИЕ СВЯЗИ МЕЖДУ СМЕШАННЫМИ МОДУЛЯМИ ГЛАДКОСТИ В МЕТРИКАХ $L_p$ и $L_{\infty}$

The problem of estimating the moduli of smoothness of functions from Lq in terms of their moduli of smoothness from Lp is well known. The first stage in the estimation of moduli of smoothness was the study of the properties of functions from the Lipschitz classes and obtaining the corresponding embeddings in the works of Titchmarsh, Hardy, Littlewood, Nikol’skii. The classical Hardy-Littlewood embedding for Lipschitz spaces can be obtained as a consequence of the Ulyanov’s inequality for the moduli of continuity of a function of one variable. In the works of Ulyanov, the modulus of smoothness of natural order was considered. The introduction of fractional moduli of smoothness made it possible in the works of Potapov, Simonov, Tikhonov to strengthen the Ulyanov’s inequality. Later, the same authors were able to generalize Ulyanov’s inequality to functions of two variables, obtaining estimates for mixed moduli of smoothness. The sharpness of these inequalities was proved in the case when 1 < 𝑝 < 𝑞 < ∞ or 1 = 𝑝 < 𝑞 = ∞. In this article, we study mixed moduli of smoothness of fractional orders of a function of two variables. Inequalities are obtained that refine the previously known estimates of the Ulyanov type inequalities between mixed moduli of smoothness in the metrics Lp and Lq for values 1 < 𝑝 < 𝑞 = ∞. The accuracy of the obtained estimates is investigated. The relationship between these and previously known estimates has been studied.

Deep Neural Network-based Fusion and Natural Language Processing in Additive Manufacturing for Customer Satisfaction

Modern Machine learning fusion approaches tend to extract features depending on two techniques (hand-crafted feature and representation learning). Hand-crafted features can waste time and are not sufficient for downstream tasks. Unlike representation learning, we automatically learn features with minimum time and effort and are suitable for downstream tasks. In our paper, we provide work on graph neural network methods with details on classical graph embedding approaches and the different methods in neural graph networks such as graph filtering, graph pooling, and the learning parameter for graph following each technique with a general framework or mathematical proof for customer satisfaction. To satisfy customer's feel, this research employs NLP techniques. We describe the adversarial attacks and defenses on graph representation approaches. Also, advanced application of neural graph networks is reviewed, such as combinational optimization, learning program representation, physical system modeling, and natural language processing. Finally, the challenges in geometric neural networks and future research work have been introduced.

A Path Growing Approach to Optical Virtual Network Embedding in SLICE Networks

Network virtualization (NV) is considered to be a promising solution to address the ossification of the current Internet infrastructure. With the recent advancements in optical virtualization, network virtualization can be further extended to virtualization-enabled optical substrate networks that supply connectivity-as-a-service. This integration of NV and optical virtualization is referred to as optical-based network virtualization in this work, which warrants a future-proof Internet that is not only technology-friendly (i.e, due to the service and hardware decoupling in NV) but also bandwidth-abundant (i.e., with optical networking). In optical-based network virtualization, it remains to resolve the classic virtual network embedding (VNE) problem (i.e., a NP-Complete problem) with the extra dimension of complexity from physical characteristics of the specific type of optical network (e.g., WDM or SLICE). In this work, we study this variant of the VNE problem, namely Optical Virtual Network Embedding (OVNE), in SLICE-based network virtualization. We avoid addressing the OVNE problem with simple add-on constraints to VNE but address it with two strategies: first, exploring the OVNE problem structure at different granular of network elements (e.g., path-channel and channel graph) to mitigate the complexity; second, designing a path growing process that solves the OVNE model with substantially reduced variables. The proposed approach is evaluated and compared to other representative path-based schemes with demonstrated improvements. The proposed approach can also obtain near-optimal solution to the OVNE problem with guaranteed closeness to the optimal solution.

A Coverage-Aware Resource Provisioning Method for Network Slicing

With network slicing in 5G networks, Mobile Network Operators can create various slices for Service Providers (SPs) to accommodate customized services. Usually, the various Service Function Chains (SFCs) belonging to a slice are deployed on a best-effort basis. Nothing ensures that the Infrastructure Provider (InP) will be able to allocate enough resources to cope with the increasing demands of some SP. Moreover, in many situations, slices have to be deployed over some geographical area: coverage as well as minimum per-user rate constraints have then to be taken into account. This paper takes the InP perspective and proposes a slice resource provisioning approach to cope with multiple slice demands in terms of computing, storage, coverage, and rate constraints. The resource requirements of the various SFCs within a slice are aggregated within a graph of Slice Resource Demands (SRD). Infrastructure nodes and links have then to be provisioned so as to satisfy all SRDs. This problem leads to a Mixed Integer Linear Programming formulation. A two-step approach is considered, with several variants, depending on whether the constraints of each slice to be provisioned are taken into account sequentially or jointly. Once provisioning has been performed, any slice deployment strategy may be considered on the reduced-size infrastructure graph on which resources have been provisioned. Simulation results demonstrate the effectiveness of the proposed approach compared to a more classical direct slice embedding approach.

RANK-TO-RANK EMBEDDINGS AND STEEL’S CONJECTURE

AbstractThis paper establishes a conjecture of Steel [7] regarding the structure of elementary embeddings from a level of the cumulative hierarchy into itself. Steel’s question is related to the Mitchell order on these embeddings, studied in [5] and [7]. Although this order is known to be illfounded, Steel conjectured that it has certain large wellfounded suborders, which is what we establish. The proof relies on a simple and general analysis of the much broader class of extender embeddings and a variant of the Mitchell order called the internal relation.

On Ultraproduct Embeddings and Amenability for Tracial von Neumann Algebras

Abstract We define the notion of self-tracial stability for tracial von Neumann algebras and show that a tracial von Neumann algebra satisfying the Connes embedding problem (CEP) is self-tracially stable if and only if it is amenable. We then generalize a result of Jung by showing that a separable tracial von Neumann algebra that satisfies the CEP is amenable if and only if any two embeddings into $R^{\mathcal{U}}$ are ucp-conjugate. Moreover, we show that for a II$_1$ factor $N$ satisfying CEP, the space $\mathbb{H}$om$(N, \prod _{k\to \mathcal{U}}M_k)$ of unitary equivalence classes of embeddings is separable if and only $N$ is hyperfinite. This resolves a question of Popa for Connes embeddable factors. These results hold when we further ask that the pairs of embeddings commute, admitting a nontrivial action of $\textrm{Out}(N\otimes N)$ on ${\mathbb{H}}\textrm{om}(N\otimes N, \prod _{k\to \mathcal{U}}M_k)$ whenever $N$ is non-amenable. We also obtain an analogous result for commuting sofic representations of countable sofic groups.

Susceptible-infected-spreading-based network embedding in static and temporal networks

Link prediction can be used to extract missing information, identify spurious interactions as well as forecast network evolution. Network embedding is a methodology to assign coordinates to nodes in a low-dimensional vector space. By embedding nodes into vectors, the link prediction problem can be converted into a similarity comparison task. Nodes with similar embedding vectors are more likely to be connected. Classic network embedding algorithms are random-walk-based. They sample trajectory paths via random walks and generate node pairs from the trajectory paths. The node pair set is further used as the input for a Skip-Gram model, a representative language model that embeds nodes (which are regarded as words) into vectors. In the present study, we propose to replace random walk processes by a spreading process, namely the susceptible-infected (SI) model, to sample paths. Specifically, we propose two susceptible-infected-spreading-based algorithms, i.e., Susceptible-Infected Network Embedding (SINE) on static networks and Temporal Susceptible-Infected Network Embedding (TSINE) on temporal networks. The performance of our algorithms is evaluated by the missing link prediction task in comparison with state-of-the-art static and temporal network embedding algorithms. Results show that SINE and TSINE outperform the baselines across all six empirical datasets. We further find that the performance of SINE is mostly better than TSINE, suggesting that temporal information does not necessarily improve the embedding for missing link prediction. Moreover, we study the effect of the sampling size, quantified as the total length of the trajectory paths, on the performance of the embedding algorithms. The better performance of SINE and TSINE requires a smaller sampling size in comparison with the baseline algorithms. Hence, SI-spreading-based embedding tends to be more applicable to large-scale networks.

Embedding Schramm spaces into Chanturiya classes

The main theorem of this paper establishes a necessary and sufficient condition for embedding Schramm spaces $$\varPhi BV$$ into Chanturiya classes $$V[\nu ]$$ . This result is new even for the classical spaces in the theory of Fourier series, namely, for the Wiener and the Salem classes. Furthermore, it provides a characterization of the embedding of Waterman classes $$\varLambda BV$$ into $$V[\nu ]$$ . As a by-product of the main result, we establish a convergence criterion for the Fourier series of functions of $$\varPhi BV$$ ; this is an extension of a well-known result due to Salem. An estimate on the magnitude of the Fourier coefficients in the space $$\varPhi BV$$ is also given, and finally it is shown that some of these results can be extended to a more general setting.

Weakly supervised classification model for zero‐shot semantic segmentation

As one of the most fundamental tasks in computer vision, semantic segmentation assigns per pixel prediction of object categories. Training a robust model for semantic segmentation is challenging since pixel-level annotations are expensive to obtain. To alleviate the burden of annotations, the authors propose a weakly-supervised framework for zero-shot semantic segmentation, which can segment images having target classes without any pixel-level labelled instances. Under the assumption that the accessibility to image-level annotations of target classes does not violate the principle of zero pixel-level label in zero-shot semantic segmentation, we utilised image-level annotations to improve the proposed model's ability to extract pixel-level features. Furthermore, unlike existing zero-shot semantic segmentation methods, which use semantic embeddings as class embeddings to transfer knowledge from source classes to target classes, we use image-level features as their class embeddings to transfer knowledge since the distribution of pixel-level features is more similar to the distribution of image-level features rather than the distribution of semantic embeddings. Experimental results on the PASCAL-VOC data set under different data splits demonstrate that the proposed model achieves promising results.

Analysis of Word Embeddings for Semantic Role Labeling of Russian Texts

Currently, there are a huge number of works dedicated to semantic role labeling of English texts [1–3]. However, semantic role labeling of Russian texts was an unexplored area for many years due to the lack of train and test corpora. Semantic role labeling of Russian Texts was widely disseminated after the appearance of the FrameBank corpus [4]. In this approach, we analyzed the influence of the word embedding models on the quality of semantic role labeling of Russian texts. Micro- and macro- F1 scores on word2vec [5], fastText [6], ELMo [7] embedding models were calculated. The set of experiments have shown that fastText models averaged slightly better than word2vec models as applied to Russian FrameBank corpus. The higher micro- and macro- F1 scores were obtained on deep tokenized word representation model ELMo in relation to classical shallow embedding models.

Combinatorial Construction of Seamless Parameter Domains

AbstractThe problem of seamless parametrization of surfaces is of interest in the context of structured quadrilateral mesh generation and spline‐based surface approximation. It has been tackled by a variety of approaches, commonly relying on continuous numerical optimization to ultimately obtain suitable parameter domains. We present a general combinatorial seamless parameter domain construction, free from the potential numerical issues inherent to continuous optimization techniques in practice. The domains are constructed as abstract polygonal complexes which can be embedded in a discrete planar grid space, as unions of unit squares. We ensure that the domain structure matches any prescribed parametrization singularities (cones) and satisfies seamlessness conditions. Surfaces of arbitrary genus are supported. Once a domain suitable for a given surface is constructed, a seamless and locally injective parametrization over this domain can be obtained using existing planar disk mapping techniques, making recourse to Tutte's classical embedding theorem.

A Variational Autoencoder with Deep Embedding Model for Generalized Zero-Shot Learning

Generalized zero-shot learning (GZSL) is a challenging task that aims to recognize not only unseen classes unavailable during training, but also seen classes used at training stage. It is achieved by transferring knowledge from seen classes to unseen classes via a shared semantic space (e.g. attribute space). Most existing GZSL methods usually learn a cross-modal mapping between the visual feature space and the semantic space. However, the mapping model learned only from the seen classes will produce an inherent bias when used in the unseen classes. In order to tackle such a problem, this paper integrates a deep embedding network (DE) and a modified variational autoencoder (VAE) into a novel model (DE-VAE) to learn a latent space shared by both image features and class embeddings. Specifically, the proposed model firstly employs DE to learn the mapping from the semantic space to the visual feature space, and then utilizes VAE to transform both original visual features and the features obtained by the mapping into latent features. Finally, the latent features are used to train a softmax classifier. Extensive experiments on four GZSL benchmark datasets show that the proposed model significantly outperforms the state of the arts.

Algebra and geometry of Sobolev embeddings

We recall the definition of Hölder, Sobolev and Slobodeckii spaces, review some of the classical embeddings, and disprove other statements via scaling arguments. We then provide an algebraic and geometric representation of these results.

Sobolev embeddings with weights in complete Riemannian manifolds

We prove Sobolev embedding Theorems with weights for vector bundles in a complete Riemannian manifold. We also get general Gaffney’s inequality with weights. As a consequence, under a “weak bounded geometry” hypothesis, we improve classical Sobolev embedding Theorems for vector bundles in a complete Riemannian manifold. We also improve known results on Gaffney’s inequality in a complete Riemannian manifold.

Semantic combined network for zero‐shot scene parsing

Recently, image-based scene parsing has attracted increasing attention due to its wide application. However, conventional models can only be valid on images with the same domain of the training set and are typically trained using discrete and meaningless labels. Inspired by the traditional zero-shot learning methods which employ auxiliary side information to bridge the source and target domains, the authors propose a novel framework called semantic combined network (SCN), which aims at learning a scene parsing model only from the images of the seen classes while targeting on the unseen ones. In addition, with the assistance of semantic embeddings of classes, the proposed SCN can further improve the performances of traditional fully supervised scene parsing methods. Extensive experiments are conducted on the data set Cityscapes, and the results show that the proposed SCN can perform well on both zero-shot scene parsing (ZSSP) and generalised ZSSP settings based on several state-of-the-art scenes parsing architectures. Furthermore, the authors test the proposed model under the traditional fully supervised setting and the results show that the proposed SCN can also significantly improve the performances of the original network models.

On the Limit Regularity in Sobolev and Besov Scales Related to Approximation Theory

We study the interrelation between the limit $$L_p(\Omega )$$-Sobolev regularity $$\overline{s}_p$$ of (classes of) functions on bounded Lipschitz domains $$\Omega \subseteq \mathbb {R}^d$$, $$d\ge 2$$, and the limit regularity $$\overline{\alpha }_p$$ within the corresponding adaptivity scale of Besov spaces $$B^\alpha _{\tau ,\tau }(\Omega )$$, where $$1/\tau =\alpha /d+1/p$$ and $$\alpha >0$$ ($$p>1$$ fixed). The former determines the convergence rate of uniform numerical methods, whereas the latter corresponds to the convergence rate of best N-term approximation. We show how additional information on the Besov or Triebel–Lizorkin regularity may be used to deduce upper bounds for $$\overline{\alpha }_p$$ in terms of $$\overline{s}_p$$ simply by means of classical embeddings and the extension of complex interpolation to suitable classes of quasi-Banach spaces due to Kalton et al. (in: De Carli and Milman (ed) Interpolation theory and applications, American Mathematical Society, Providence, 2007). The results are applied to the Poisson equation, to the p-Poisson problem, and to the inhomogeneous stationary Stokes problem. In particular, we show that already established results on the Besov regularity for the Poisson equation are sharp.