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We investigate the generalization and optimization properties of shallow neural-network classifiers trained by gradient descent in the interpolating regime. Specifically, in a realizable scenario where model weights can achieve arbitrarily small training error $\epsilon$ and their distance from initialization is $g(\epsilon)$, we demonstrate that gradient descent with $n$ training data achieves training error $O(g(1/T)^2 /T)$ and generalization error $O(g(1/T)^2 /n)$ at iteration $T$, provided there are at least $m=\Omega(g(1/T)^4)$ hidden neurons. We then show that our realizable setting encompasses a special case where data are separable by the model's neural tangent kernel. For this and logistic-loss minimization, we prove the training loss decays at a rate of $\tilde O(1/ T)$ given polylogarithmic number of neurons $m=\Omega(\log^4 (T))$. Moreover, with $m=\Omega(\log^{4} (n))$ neurons and $T\approx n$ iterations, we bound the test loss by $\tilde{O}(1/n)$. Our results differ from existing generalization outcomes using the algorithmic-stability framework, which necessitate polynomial width and yield suboptimal generalization rates. Central to our analysis is the use of a new self-bounded weak-convexity property, which leads to a generalized local quasi-convexity property for sufficiently parameterized neural-network classifiers. Eventually, despite the objective's non-convexity, this leads to convergence and generalization-gap bounds that resemble those found in the convex setting of linear logistic regression.

Deep learning surrogate models are being increasingly used in accelerating scientific simulations as a replacement for costly conventional numerical techniques. However, their use remains a significant challenge when dealing with real-world complex examples. In this work, we demonstrate three types of neural network architectures for efficient learning of highly non-linear deformations of solid bodies. The first two architectures are based on the recently proposed CNN U-NET and MAgNET (graph U-NET) frameworks which have shown promising performance for learning on mesh-based data. The third architecture is Perceiver IO, a very recent architecture that belongs to the family of attention-based neural networks--a class that has revolutionised diverse engineering fields and is still unexplored in computational mechanics. We study and compare the performance of all three networks on two benchmark examples, and show their capabilities to accurately predict the non-linear mechanical responses of soft bodies.

Deep neural networks (DNNs) have greatly impacted numerous fields over the past decade. Yet despite exhibiting superb performance over many problems, their black-box nature still poses a significant challenge with respect to explainability. Indeed, explainable artificial intelligence (XAI) is crucial in several fields, wherein the answer alone -- sans a reasoning of how said answer was derived -- is of little value. This paper uncovers a troubling property of explanation methods for image-based DNNs: by making small visual changes to the input image -- hardly influencing the network's output -- we demonstrate how explanations may be arbitrarily manipulated through the use of evolution strategies. Our novel algorithm, AttaXAI, a model-agnostic, adversarial attack on XAI algorithms, only requires access to the output logits of a classifier and to the explanation map; these weak assumptions render our approach highly useful where real-world models and data are concerned. We compare our method's performance on two benchmark datasets -- CIFAR100 and ImageNet -- using four different pretrained deep-learning models: VGG16-CIFAR100, VGG16-ImageNet, MobileNet-CIFAR100, and Inception-v3-ImageNet. We find that the XAI methods can be manipulated without the use of gradients or other model internals. Our novel algorithm is successfully able to manipulate an image in a manner imperceptible to the human eye, such that the XAI method outputs a specific explanation map. To our knowledge, this is the first such method in a black-box setting, and we believe it has significant value where explainability is desired, required, or legally mandatory.

Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still suffer from two deficiencies: (1) they cannot flexibly explore all possible meta-paths and extract the most useful ones for a target object, which hinders both effectiveness and interpretability; (2) they often need to generate intermediate meta-path based dense graphs, which leads to high computational complexity. To address the above issues, we propose an interpretable and efficient Heterogeneous Graph Convolutional Network (ie-HGCN) to learn the representations of objects in HINs. It is designed as a hierarchical aggregation architecture, i.e., object-level aggregation first, followed by type-level aggregation. The novel architecture can automatically extract useful meta-paths for each object from all possible meta-paths (within a length limit), which brings good model interpretability. It can also reduce the computational cost by avoiding intermediate HIN transformation and neighborhood attention. We provide theoretical analysis about the proposed ie-HGCN in terms of evaluating the usefulness of all possible meta-paths, its connection to the spectral graph convolution on HINs, and its quasi-linear time complexity. Extensive experiments on three real network datasets demonstrate the superiority of ie-HGCN over the state-of-the-art methods.

Sequential recommendation (SR) is to accurately recommend a list of items for a user based on her current accessed ones. While new-coming users continuously arrive in the real world, one crucial task is to have inductive SR that can produce embeddings of users and items without re-training. Given user-item interactions can be extremely sparse, another critical task is to have transferable SR that can transfer the knowledge derived from one domain with rich data to another domain. In this work, we aim to present the holistic SR that simultaneously accommodates conventional, inductive, and transferable settings. We propose a novel deep learning-based model, Relational Temporal Attentive Graph Neural Networks (RetaGNN), for holistic SR. The main idea of RetaGNN is three-fold. First, to have inductive and transferable capabilities, we train a relational attentive GNN on the local subgraph extracted from a user-item pair, in which the learnable weight matrices are on various relations among users, items, and attributes, rather than nodes or edges. Second, long-term and short-term temporal patterns of user preferences are encoded by a proposed sequential self-attention mechanism. Third, a relation-aware regularization term is devised for better training of RetaGNN. Experiments conducted on MovieLens, Instagram, and Book-Crossing datasets exhibit that RetaGNN can outperform state-of-the-art methods under conventional, inductive, and transferable settings. The derived attention weights also bring model explainability.

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.

Conventionally, spatiotemporal modeling network and its complexity are the two most concentrated research topics in video action recognition. Existing state-of-the-art methods have achieved excellent accuracy regardless of the complexity meanwhile efficient spatiotemporal modeling solutions are slightly inferior in performance. In this paper, we attempt to acquire both efficiency and effectiveness simultaneously. First of all, besides traditionally treating H x W x T video frames as space-time signal (viewing from the Height-Width spatial plane), we propose to also model video from the other two Height-Time and Width-Time planes, to capture the dynamics of video thoroughly. Secondly, our model is designed based on 2D CNN backbones and model complexity is well kept in mind by design. Specifically, we introduce a novel multi-view fusion (MVF) module to exploit video dynamics using separable convolution for efficiency. It is a plug-and-play module and can be inserted into off-the-shelf 2D CNNs to form a simple yet effective model called MVFNet. Moreover, MVFNet can be thought of as a generalized video modeling framework and it can specialize to be existing methods such as C2D, SlowOnly, and TSM under different settings. Extensive experiments are conducted on popular benchmarks (i.e., Something-Something V1 & V2, Kinetics, UCF-101, and HMDB-51) to show its superiority. The proposed MVFNet can achieve state-of-the-art performance with 2D CNN's complexity.

This paper proposes a generic method to learn interpretable convolutional filters in a deep convolutional neural network (CNN) for object classification, where each interpretable filter encodes features of a specific object part. Our method does not require additional annotations of object parts or textures for supervision. Instead, we use the same training data as traditional CNNs. Our method automatically assigns each interpretable filter in a high conv-layer with an object part of a certain category during the learning process. Such explicit knowledge representations in conv-layers of CNN help people clarify the logic encoded in the CNN, i.e., answering what patterns the CNN extracts from an input image and uses for prediction. We have tested our method using different benchmark CNNs with various structures to demonstrate the broad applicability of our method. Experiments have shown that our interpretable filters are much more semantically meaningful than traditional filters.

The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.

Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive features than deep, multi-layer models -- which potentially limits performance. In this work, we introduce ConvE, a multi-layer convolutional network model for link prediction, and report state-of-the-art results for several established datasets. We also show that the model is highly parameter efficient, yielding the same performance as DistMult and R-GCN with 8x and 17x fewer parameters. Analysis of our model suggests that it is particularly effective at modelling nodes with high indegree -- which are common in highly-connected, complex knowledge graphs such as Freebase and YAGO3. In addition, it has been noted that the WN18 and FB15k datasets suffer from test set leakage, due to inverse relations from the training set being present in the test set -- however, the extent of this issue has so far not been quantified. We find this problem to be severe: a simple rule-based model can achieve state-of-the-art results on both WN18 and FB15k. To ensure that models are evaluated on datasets where simply exploiting inverse relations cannot yield competitive results, we investigate and validate several commonly used datasets -- deriving robust variants where necessary. We then perform experiments on these robust datasets for our own and several previously proposed models, and find that ConvE achieves state-of-the-art Mean Reciprocal Rank across all datasets.