Human vision is able to immediately recognize novel visual categories after seeing just one or a few training examples. We describe how to add a similar capability to ConvNet classifiers by directly setting the final layer weights from novel training examples during low-shot learning. We call this process weight imprinting as it directly sets weights for a new category based on an appropriately scaled copy of the embedding layer activations for that training example. The imprinting process provides a valuable complement to training with stochastic gradient descent, as it provides immediate good classification performance and an initialization for any further fine-tuning in the future. We show how this imprinting process is related to proxy-based embeddings. However, it differs in that only a single imprinted weight vector is learned for each novel category, rather than relying on a nearest-neighbor distance to training instances as typically used with embedding methods. Our experiments show that using averaging of imprinted weights provides better generalization than using nearest-neighbor instance embeddings.
Contrastive loss @cite_6 minimizes the distances between inputs with the same label while keeping the distances between inputs with different labels far apart. Rather than minimizing absolute distances, recent approaches formulate objectives focusing on relative distances. FaceNet @cite_10 optimizes a triplet loss and develops an online negative mining strategy to form triplets within a mini-batch. Instead of penalizing violating instance-based triplets independently, alternative loss functions regulate the global structure of the embedding space. Magnet loss @cite_14 optimizes the distribution of different classes by clustering the examples using @math -means and representing classes with centroids. Lifted structured loss @cite_1 incorporates all pair-wise relations within a mini-batch instead of forming triplets. The @math -pair loss @cite_2 requires each batch to have examples from @math categories for improved computational efficiency. All these methods require some online or offline batch generation step to form informative batches to speed up training. Structured clustering loss @cite_18 optimizes a clustering quality metric globally in the embeddings space.
@cite_18 @cite_14 @cite_1 @cite_6 @cite_2 @cite_10
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Deep metric learning has gained much popularity in recent years, following the success of deep learning. However, existing frameworks of deep metric learning based on contrastive loss and triplet loss often suffer from slow convergence, partially because they employ only one negative example while not interacting with the other negative classes in each update. In this paper, we propose to address this problem with a new metric learning objective called multi-class N-pair loss. The proposed objective function firstly generalizes triplet loss by allowing joint comparison among more than one negative examples - more specifically, N-1 negative examples - and secondly reduces the computational burden of evaluating deep embedding vectors via an efficient batch construction strategy using only N pairs of examples, instead of (N+1) x N. We demonstrate the superiority of our proposed loss to the triplet loss as well as other competing loss functions for a variety of tasks on several visual recognition benchmark, including fine-grained object recognition and verification, image clustering and retrieval, and face verification and identification. We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship – an anchor point x is similar to a set of positive points Y , and dissimilar to a set of negative points Z, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15 points, while converging three times as fast as other triplet-based losses. The key point of image-text matching is how to accurately measure the similarity between visual and textual inputs. Despite the great progress of associating the deep cross-modal embeddings with the bi-directional ranking loss, developing the strategies for mining useful triplets and selecting appropriate margins remains a challenge in real applications. In this paper, we propose a cross-modal projection matching (CMPM) loss and a cross-modal projection classification (CMPC) loss for learning discriminative image-text embeddings. The CMPM loss minimizes the KL divergence between the projection compatibility distributions and the normalized matching distributions defined with all the positive and negative samples in a mini-batch. The CMPC loss attempts to categorize the vector projection of representations from one modality onto another with the improved norm-softmax loss, for further enhancing the feature compactness of each class. Extensive analysis and experiments on multiple datasets demonstrate the superiority of the proposed approach. Recently, benefiting from the advances of the deep convolution neural networks (CNNs), significant progress has been made in the field of the face verification and face recognition. Specially, the performance of the FaceNet has overpassed the human level performance in terms of the accuracy on the datasets "Labeled Faces in the Wild (LFW)" and "Youtube Faces in the Wild (YTF)". The triplet loss used in the FaceNet has proved its effectiveness for face verification. However, the number of the possible triplets is explosive when using a large scale dataset to train the model. In this paper, we propose a simple class-wise triplet loss based on the intra inter-class distance metric learning which can largely reduce the number of the possible triplets to be learned. However the simplification of the classic triplet loss function has not degraded the performance of the proposed approach. The experimental evaluations on the most widely used benchmarks LFW and YTF show that the model with the proposed class-wise simple triplet loss can reach the state-of-the-art performance. And the visualization of the distribution of the learned features based on the MNIST dataset has also shown the effectiveness of the proposed method to better separate the classes and make the features more discriminative in comparison with the other state-of-the-art loss function. Deep embeddings answer one simple question: How similar are two images? Learning these embeddings is the bedrock of verification, zero-shot learning, and visual search. The most prominent approaches optimize a deep convolutional network with a suitable loss function, such as contrastive loss or triplet loss. While a rich line of work focuses solely on the loss functions, we show in this paper that selecting training examples plays an equally important role. We propose distance weighted sampling, which selects more informative and stable examples than traditional approaches. In addition, we show that a simple margin based loss is sufficient to outperform all other loss functions. We evaluate our approach on the Stanford Online Products, CAR196, and the CUB200-2011 datasets for image retrieval and clustering, and on the LFW dataset for face verification. Our method achieves state-of-the-art performance on all of them. We present a novel hierarchical triplet loss (HTL) capable of automatically collecting informative training samples (triplets) via a defined hierarchical tree that encodes global context information. This allows us to cope with the main limitation of random sampling in training a conventional triplet loss, which is a central issue for deep metric learning. Our main contributions are two-fold. (i) we construct a hierarchical class-level tree where neighboring classes are merged recursively. The hierarchical structure naturally captures the intrinsic data distribution over the whole dataset. (ii) we formulate the problem of triplet collection by introducing a new violate margin, which is computed dynamically based on the designed hierarchical tree. This allows it to automatically select meaningful hard samples with the guide of global context. It encourages the model to learn more discriminative features from visual similar classes, leading to faster convergence and better performance. Our method is evaluated on the tasks of image retrieval and face recognition, where it outperforms the standard triplet loss substantially by 1 –18 , and achieves new state-of-the-art performance on a number of benchmarks. Learning the distance metric between pairs of examples is of great importance for learning and visual recognition. With the remarkable success from the state of the art convolutional neural networks, recent works have shown promising results on discriminatively training the networks to learn semantic feature embeddings where similar examples are mapped close to each other and dissimilar examples are mapped farther apart. In this paper, we describe an algorithm for taking full advantage of the training batches in the neural network training by lifting the vector of pairwise distances within the batch to the matrix of pairwise distances. This step enables the algorithm to learn the state of the art feature embedding by optimizing a novel structured prediction objective on the lifted problem. Additionally, we collected Online Products dataset: 120k images of 23k classes of online products for metric learning. Our experiments on the CUB-200-2011, CARS196, and Online Products datasets demonstrate significant improvement over existing deep feature embedding methods on all experimented embedding sizes with the GoogLeNet network. The modern image search system requires semantic understanding of image, and a key yet under-addressed problem is to learn a good metric for measuring the similarity between images. While deep metric learning has yielded impressive performance gains by extracting high level abstractions from image data, a proper objective loss function becomes the central issue to boost the performance. In this paper, we propose a novel angular loss, which takes angle relationship into account, for learning better similarity metric. Whereas previous metric learning methods focus on optimizing the similarity (contrastive loss) or relative similarity (triplet loss) of image pairs, our proposed method aims at constraining the angle at the negative point of triplet triangles. Several favorable properties are observed when compared with conventional methods. First, scale invariance is introduced, improving the robustness of objective against feature variance. Second, a third-order geometric constraint is inherently imposed, capturing additional local structure of triplet triangles than contrastive loss or triplet loss. Third, better convergence has been demonstrated by experiments on three publicly available datasets. Learning the distance metric between pairs of examples is of great importance for learning and visual recognition. With the remarkable success from the state of the art convolutional neural networks, recent works [1, 31] have shown promising results on discriminatively training the networks to learn semantic feature embeddings where similar examples are mapped close to each other and dissimilar examples are mapped farther apart. In this paper, we describe an algorithm for taking full advantage of the training batches in the neural network training by lifting the vector of pairwise distances within the batch to the matrix of pairwise distances. This step enables the algorithm to learn the state of the art feature embedding by optimizing a novel structured prediction objective on the lifted problem. Additionally, we collected Stanford Online Products dataset: 120k images of 23k classes of online products for metric learning. Our experiments on the CUB-200-2011 [37], CARS196 [19], and Stanford Online Products datasets demonstrate significant improvement over existing deep feature embedding methods on all experimented embedding sizes with the GoogLeNet [33] network. The source code and the dataset are available at: https: github.com rksltnl Deep-Metric-Learning-CVPR16. Convolutional neural networks have achieved great improvement on face recognition in recent years because of its extraordinary ability in learning discriminative features of people with different identities. To train such a well-designed deep network, tremendous amounts of data is indispensable. Long tail distribution specifically refers to the fact that a small number of generic entities appear frequently while other objects far less existing. Considering the existence of long tail distribution of the real world data, large but uniform distributed data are usually hard to retrieve. Empirical experiences and analysis show that classes with more samples will pose greater impact on the feature learning process and inversely cripple the whole models feature extracting ability on tail part data. Contrary to most of the existing works that alleviate this problem by simply cutting the tailed data for uniform distributions across the classes, this paper proposes a new loss function called range loss to effectively utilize the whole long tailed data in training process. More specifically, range loss is designed to reduce overall intra-personal variations while enlarging inter-personal differences within one mini-batch simultaneously when facing even extremely unbalanced data. The optimization objective of range loss is the @math greatest range's harmonic mean values in one class and the shortest inter-class distance within one batch. Extensive experiments on two famous and challenging face recognition benchmarks (Labeled Faces in the Wild (LFW) and YouTube Faces (YTF) not only demonstrate the effectiveness of the proposed approach in overcoming the long tail effect but also show the good generalization ability of the proposed approach. Deep supervised hashing has emerged as an influential solution to large-scale semantic image retrieval problems in computer vision. In the light of recent progress, convolutional neural network based hashing methods typically seek pair-wise or triplet labels to conduct the similarity preserving learning. However, complex semantic concepts of visual contents are hard to capture by similar dissimilar labels, which limits the retrieval performance. Generally, pair-wise or triplet losses not only suffer from expensive training costs but also lack in extracting sufficient semantic information. In this regard, we propose a novel deep supervised hashing model to learn more compact class-level similarity preserving binary codes. Our deep learning based model is motivated by deep metric learning that directly takes semantic labels as supervised information in training and generates corresponding discriminant hashing code. Specifically, a novel cubic constraint loss function based on Gaussian distribution is proposed, which preserves semantic variations while penalizes the overlap part of different classes in the embedding space. To address the discrete optimization problem introduced by binary codes, a two-step optimization strategy is proposed to provide efficient training and avoid the problem of gradient vanishing. Extensive experiments on four large-scale benchmark databases show that our model can achieve the state-of-the-art retrieval performance. Moreover, when training samples are limited, our method surpasses other supervised deep hashing methods with non-negligible margins. Deep neural networks are commonly trained using stochastic non-convex optimization procedures, which are driven by gradient information estimated on fractions (batches) of the dataset. While it is commonly accepted that batch size is an important parameter for offline tuning, the benefits of online selection of batches remain poorly understood. We investigate online batch selection strategies for two state-of-the-art methods of stochastic gradient-based optimization, AdaDelta and Adam. As the loss function to be minimized for the whole dataset is an aggregation of loss functions of individual datapoints, intuitively, datapoints with the greatest loss should be considered (selected in a batch) more frequently. However, the limitations of this intuition and the proper control of the selection pressure over time are open questions. We propose a simple strategy where all datapoints are ranked w.r.t. their latest known loss value and the probability to be selected decays exponentially as a function of rank. Our experimental results on the MNIST dataset suggest that selecting batches speeds up both AdaDelta and Adam by a factor of about 5. Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been difficult for these to compete with modern classification algorithms in performance and even in feature extraction. In this work, we propose a novel approach explicitly designed to address a number of subtle yet important issues which have stymied earlier DML algorithms. It maintains an explicit model of the distributions of the different classes in representation space. It then employs this knowledge to adaptively assess similarity, and achieve local discrimination by penalizing class distribution overlap. We demonstrate the effectiveness of this idea on several tasks. Our approach achieves state-of-the-art classification results on a number of fine-grained visual recognition datasets, surpassing the standard softmax classifier and outperforming triplet loss by a relative margin of 30-40 . In terms of computational performance, it alleviates training inefficiencies in the traditional triplet loss, reaching the same error in 5-30 times fewer iterations. Beyond classification, we further validate the saliency of the learnt representations via their attribute concentration and hierarchy recovery properties, achieving 10-25 relative gains on the softmax classifier and 25-50 on triplet loss in these tasks. Abstract: Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been difficult for these to compete with modern classification algorithms in performance and even in feature extraction. In this work, we propose a novel approach explicitly designed to address a number of subtle yet important issues which have stymied earlier DML algorithms. It maintains an explicit model of the distributions of the different classes in representation space. It then employs this knowledge to adaptively assess similarity, and achieve local discrimination by penalizing class distribution overlap. We demonstrate the effectiveness of this idea on several tasks. Our approach achieves state-of-the-art classification results on a number of fine-grained visual recognition datasets, surpassing the standard softmax classifier and outperforming triplet loss by a relative margin of 30-40 . In terms of computational performance, it alleviates training inefficiencies in the traditional triplet loss, reaching the same error in 5-30 times fewer iterations. Beyond classification, we further validate the saliency of the learnt representations via their attribute concentration and hierarchy recovery properties, achieving 10-25 relative gains on the softmax classifier and 25-50 on triplet loss in these tasks. Image-language matching tasks have recently attracted a lot of attention in the computer vision field. These tasks include image-sentence matching, i.e., given an image query, retrieving relevant sentences and vice versa, and region-phrase matching or visual grounding, i.e., matching a phrase to relevant regions. This paper investigates two-branch neural networks for learning the similarity between these two data modalities. We propose two network structures that produce different output representations. The first one, referred to as an embedding network, learns an explicit shared latent embedding space with a maximum-margin ranking loss and novel neighborhood constraints. Compared to standard triplet sampling, we perform improved neighborhood sampling that takes neighborhood information into consideration while constructing mini-batches. The second network structure, referred to as a similarity network, fuses the two branches via element-wise product and is trained with regression loss to directly predict a similarity score. Extensive experiments show that our networks achieve high accuracies for phrase localization on the Flickr30K Entities dataset and for bi-directional image-sentence retrieval on Flickr30K and MSCOCO datasets. A metric space X is said to be absolutely Lipschitz extendable if every Lipschitz function f from X into any Banach space Z can be extended to any containing space Y⊇X, where the loss in the Lipschitz constant in the extension is independent of Y,Z, and f. We show that various classes of natural metric spaces are absolutely Lipschitz extendable. To cite this article: J.R. Lee, A. Naor, C. R. Acad. Sci. Paris, Ser. I 338 (2004). Most existing 3D object recognition algorithms focus on leveraging the strong discriminative power of deep learning models with softmax loss for the classification of 3D data, while learning discriminative features with deep metric learning for 3D object retrieval is more or less neglected. In the paper, we study variants of deep metric learning losses for 3D object retrieval, which did not receive enough attention from this area. First , two kinds of representative losses, triplet loss and center loss, are introduced which could learn more discriminative features than traditional classification loss. Then, we propose a novel loss named triplet-center loss, which can further enhance the discriminative power of the features. The proposed triplet-center loss learns a center for each class and requires that the distances between samples and centers from the same class are closer than those from different classes. Extensive experimental results on two popular 3D object retrieval benchmarks and two widely-adopted sketch-based 3D shape retrieval benchmarks consistently demonstrate the effectiveness of our proposed loss, and significant improvements have been achieved compared with the state-of-the-arts. Most existing 3D object recognition algorithms focus on leveraging the strong discriminative power of deep learning models with softmax loss for the classification of 3D data, while learning discriminative features with deep metric learning for 3D object retrieval is more or less neglected. In the paper, we study variants of deep metric learning losses for 3D object retrieval, which did not receive enough attention from this area. First, two kinds of representative losses, triplet loss and center loss, are introduced which could learn more discriminative features than traditional classification loss. Then, we propose a novel loss named triplet-center loss, which can further enhance the discriminative power of the features. The proposed triplet-center loss learns a center for each class and requires that the distances between samples and centers from the same class are closer than those from different classes. Extensive experimental results on two popular 3D object retrieval benchmarks and two widely-adopted sketch-based 3D shape retrieval benchmarks consistently demonstrate the effectiveness of our proposed loss, and significant improvements have been achieved compared with the state-of-the-arts. We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . Recent innovations in training deep convolutional neural network (ConvNet) models have motivated the design of new methods to automatically learn local image descriptors. The latest deep ConvNets proposed for this task consist of a siamese network that is trained by penalising misclassification of pairs of local image patches. Current results from machine learning show that replacing this siamese by a triplet network can improve the classification accuracy in several problems, but this has yet to be demonstrated for local image descriptor learning. Moreover, current siamese and triplet networks have been trained with stochastic gradient descent that computes the gradient from individual pairs or triplets of local image patches, which can make them prone to overfitting. In this paper, we first propose the use of triplet networks for the problem of local image descriptor learning. Furthermore, we also propose the use of a global loss that minimises the overall classification error in the training set, which can improve the generalisation capability of the model. Using the UBC benchmark dataset for comparing local image descriptors, we show that the triplet network produces a more accurate embedding than the siamese network in terms of the UBC dataset errors. Moreover, we also demonstrate that a combination of the triplet and global losses produces the best embedding in the field, using this triplet network. Finally, we also show that the use of the central-surround siamese network trained with the global loss produces the best result of the field on the UBC dataset. Pre-trained models are available online at this https URL