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In this paper, we consider a highly general image recognition setting wherein, given a labelled and unlabelled set of images, the task is to categorize all images in the unlabelled set. Here, the unlabelled images may come from labelled classes or from novel ones. Existing recognition methods are not able to deal with this setting, because they make several restrictive assumptions, such as the unlabelled instances only coming from known - or unknown - classes and the number of unknown classes being known a-priori. We address the more unconstrained setting, naming it 'Generalized Category Discovery', and challenge all these assumptions. We first establish strong baselines by taking state-of-the-art algorithms from novel category discovery and adapting them for this task. Next, we propose the use of vision transformers with contrastive representation learning for this open world setting. We then introduce a simple yet effective semi-supervised $k$-means method to cluster the unlabelled data into seen and unseen classes automatically, substantially outperforming the baselines. Finally, we also propose a new approach to estimate the number of classes in the unlabelled data. We thoroughly evaluate our approach on public datasets for generic object classification including CIFAR10, CIFAR100 and ImageNet-100, and for fine-grained visual recognition including CUB, Stanford Cars and Herbarium19, benchmarking on this new setting to foster future research.

This paper focuses on stochastic saddle point problems with decision-dependent distributions in both the static and time-varying settings. These are problems whose objective is the expected value of a stochastic payoff function, where random variables are drawn from a distribution induced by a distributional map. For general distributional maps, the problem of finding saddle points is in general computationally burdensome, even if the distribution is known. To enable a tractable solution approach, we introduce the notion of equilibrium points -- which are saddle points for the stationary stochastic minimax problem that they induce -- and provide conditions for their existence and uniqueness. We demonstrate that the distance between the two classes of solutions is bounded provided that the objective has a strongly-convex-strongly-concave payoff and Lipschitz continuous distributional map. We develop deterministic and stochastic primal-dual algorithms and demonstrate their convergence to the equilibrium point. In particular, by modeling errors emerging from a stochastic gradient estimator as sub-Weibull random variables, we provide error bounds in expectation and in high probability that hold for each iteration; moreover, we show convergence to a neighborhood in expectation and almost surely. Finally, we investigate a condition on the distributional map -- which we call opposing mixture dominance -- that ensures the objective is strongly-convex-strongly-concave. Under this assumption, we show that primal-dual algorithms converge to the saddle points in a similar fashion.

The Fr\'{e}chet distance is a well-studied similarity measure between curves that is widely used throughout computer science. Motivated by applications where curves stem from paths and walks on an underlying graph (such as a road network), we define and study the Fr\'{e}chet distance for paths and walks on graphs. When provided with a distance oracle of $G$ with $O(1)$ query time, the classical quadratic-time dynamic program can compute the Fr\'{e}chet distance between two walks $P$ and $Q$ in a graph $G$ in $O(|P| \cdot |Q|)$ time. We show that there are situations where the graph structure helps with computing Fr\'{e}chet distance: when the graph $G$ is planar, we apply existing (approximate) distance oracles to compute a $(1+\varepsilon)$-approximation of the Fr\'{e}chet distance between any shortest path $P$ and any walk $Q$ in $O(|G| \log |G| / \sqrt{\varepsilon} + |P| + \frac{|Q|}{\varepsilon } )$ time. We generalise this result to near-shortest paths, i.e. $\kappa$-straight paths, as we show how to compute a $(1+\varepsilon)$-approximation between a $\kappa$-straight path $P$ and any walk $Q$ in $O(|G| \log |G| / \sqrt{\varepsilon} + |P| + \frac{\kappa|Q|}{\varepsilon } )$ time. Our algorithmic results hold for both the strong and the weak discrete Fr\'{e}chet distance over the shortest path metric in $G$. Finally, we show that additional assumptions on the input, such as our assumption on path straightness, are indeed necessary to obtain truly subquadratic running time. We provide a conditional lower bound showing that the Fr\'{e}chet distance, or even its $1.01$-approximation, between arbitrary \emph{paths} in a weighted planar graph cannot be computed in $O((|P|\cdot|Q|)^{1-\delta})$ time for any $\delta > 0$ unless the Orthogonal Vector Hypothesis fails. For walks, this lower bound holds even when $G$ is planar, unit-weight and has $O(1)$ vertices.

Continual learning in environments with shifting data distributions is a challenging problem with several real-world applications. In this paper we consider settings in which the data distribution(task) shifts abruptly and the timing of these shifts are not known. Furthermore, we consider a semi-supervised task-agnostic setting in which the learning algorithm has access to both task-segmented and unsegmented data for offline training. We propose a novel approach called mixture of Basismodels (MoB) for addressing this problem setting. The core idea is to learn a small set of basis models and to construct a dynamic, task-dependent mixture of the models to predict for the current task. We also propose a new methodology to detect observations that are out-of-distribution with respect to the existing basis models and to instantiate new models as needed. We test our approach in multiple domains and show that it attains better prediction error than existing methods in most cases while using fewer models than other multiple model approaches. Moreover, we analyze the latent task representations learned by MoB and show that similar tasks tend to cluster in the latent space and that the latent representation shifts at the task boundaries when tasks are dissimilar.

For the general class of residual distribution (RD) schemes, including many finite element (such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach to construct entropy conservative/ dissipative semidiscretizations by adding suitable correction terms has been proposed by Abgrall (J.~Comp.~Phys. 372: pp. 640--666, 2018). In this work, the correction terms are characterized as solutions of certain optimization problems and are adapted to the SBP-SAT framework, focusing on discontinuous Galerkin methods. Novel generalizations to entropy inequalities, multiple constraints, and kinetic energy preservation for the Euler equations are developed and tested in numerical experiments. For all of these optimization problems, explicit solutions are provided. Additionally, the correction approach is applied for the first time to obtain a fully discrete entropy conservative/dissipative RD scheme. Here, the application of the deferred correction (DeC) method for the time integration is essential. This paper can be seen as describing a systematic method to construct structure preserving discretization, at least for the considered example.

We propose a general and scalable approximate sampling strategy for probabilistic models with discrete variables. Our approach uses gradients of the likelihood function with respect to its discrete inputs to propose updates in a Metropolis-Hastings sampler. We show empirically that this approach outperforms generic samplers in a number of difficult settings including Ising models, Potts models, restricted Boltzmann machines, and factorial hidden Markov models. We also demonstrate the use of our improved sampler for training deep energy-based models on high dimensional discrete data. This approach outperforms variational auto-encoders and existing energy-based models. Finally, we give bounds showing that our approach is near-optimal in the class of samplers which propose local updates.

In recent years, knowledge distillation has been proved to be an effective solution for model compression. This approach can make lightweight student models acquire the knowledge extracted from cumbersome teacher models. However, previous distillation methods of detection have weak generalization for different detection frameworks and rely heavily on ground truth (GT), ignoring the valuable relation information between instances. Thus, we propose a novel distillation method for detection tasks based on discriminative instances without considering the positive or negative distinguished by GT, which is called general instance distillation (GID). Our approach contains a general instance selection module (GISM) to make full use of feature-based, relation-based and response-based knowledge for distillation. Extensive results demonstrate that the student model achieves significant AP improvement and even outperforms the teacher in various detection frameworks. Specifically, RetinaNet with ResNet-50 achieves 39.1% in mAP with GID on COCO dataset, which surpasses the baseline 36.2% by 2.9%, and even better than the ResNet-101 based teacher model with 38.1% AP.

Object detectors tend to perform poorly in new or open domains, and require exhaustive yet costly annotations from fully labeled datasets. We aim at benefiting from several datasets with different categories but without additional labelling, not only to increase the number of categories detected, but also to take advantage from transfer learning and to enhance domain independence. Our dataset merging procedure starts with training several initial Faster R-CNN on the different datasets while considering the complementary datasets' images for domain adaptation. Similarly to self-training methods, the predictions of these initial detectors mitigate the missing annotations on the complementary datasets. The final OMNIA Faster R-CNN is trained with all categories on the union of the datasets enriched by predictions. The joint training handles unsafe targets with a new classification loss called SoftSig in a softly supervised way. Experimental results show that in the case of fashion detection for images in the wild, merging Modanet with COCO increases the final performance from 45.5% to 57.4%. Applying our soft distillation to the task of detection with domain shift on Cityscapes enables to beat the state-of-the-art by 5.3 points. We hope that our methodology could unlock object detection for real-world applications without immense datasets.

In this paper, we propose an efficient and fast object detector which can process hundreds of frames per second. To achieve this goal we investigate three main aspects of the object detection framework: network architecture, loss function and training data (labeled and unlabeled). In order to obtain compact network architecture, we introduce various improvements, based on recent work, to develop an architecture which is computationally light-weight and achieves a reasonable performance. To further improve the performance, while keeping the complexity same, we utilize distillation loss function. Using distillation loss we transfer the knowledge of a more accurate teacher network to proposed light-weight student network. We propose various innovations to make distillation efficient for the proposed one stage detector pipeline: objectness scaled distillation loss, feature map non-maximal suppression and a single unified distillation loss function for detection. Finally, building upon the distillation loss, we explore how much can we push the performance by utilizing the unlabeled data. We train our model with unlabeled data using the soft labels of the teacher network. Our final network consists of 10x fewer parameters than the VGG based object detection network and it achieves a speed of more than 200 FPS and proposed changes improve the detection accuracy by 14 mAP over the baseline on Pascal dataset.

Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well without careful hyperparameter tuning and proper initialization. We investigate whether turning the adversarial min-max problem into an optimization problem by replacing the maximization part with its dual improves the quality of the resulting alignment and explore its connections to Maximum Mean Discrepancy. Our empirical results suggest that using the dual formulation for the restricted family of linear discriminators results in a more stable convergence to a desirable solution when compared with the performance of a primal min-max GAN-like objective and an MMD objective under the same restrictions. We test our hypothesis on the problem of aligning two synthetic point clouds on a plane and on a real-image domain adaptation problem on digits. In both cases, the dual formulation yields an iterative procedure that gives more stable and monotonic improvement over time.