Recently, substantial research efforts in Deep Metric Learning (DML) focused on designing complex pairwise-distance losses, which require convoluted schemes to ease optimization, such as sample mining or pair weighting. The standard cross-entropy loss for classification has been largely overlooked in DML. On the surface, the cross-entropy may seem unrelated and irrelevant to metric learning as it does not explicitly involve pairwise distances. However, we provide a theoretical analysis that links the cross-entropy to several well-known and recent pairwise losses. Our connections are drawn from two different perspectives: one based on an explicit optimization insight; the other on discriminative and generative views of the mutual information between the labels and the learned features. First, we explicitly demonstrate that the cross-entropy is an upper bound on a new pairwise loss, which has a structure similar to various pairwise losses: it minimizes intra-class distances while maximizing inter-class distances. As a result, minimizing the cross-entropy can be seen as an approximate bound-optimization (or Majorize-Minimize) algorithm for minimizing this pairwise loss. Second, we show that, more generally, minimizing the cross-entropy is actually equivalent to maximizing the mutual information, to which we connect several well-known pairwise losses. Furthermore, we show that various standard pairwise losses can be explicitly related to one another via bound relationships. Our findings indicate that the cross-entropy represents a proxy for maximizing the mutual information -- as pairwise losses do -- without the need for convoluted sample-mining heuristics. Our experiments over four standard DML benchmarks strongly support our findings. We obtain state-of-the-art results, outperforming recent and complex DML methods.
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Many recent successes in sentence representation learning have been achieved by simply fine-tuning on the Natural Language Inference (NLI) datasets with triplet loss or siamese loss. Nevertheless, they share a common weakness: sentences in a contradiction pair are not necessarily from different semantic categories. Therefore, optimizing the semantic entailment and contradiction reasoning objective alone is inadequate to capture the high-level semantic structure. The drawback is compounded by the fact that the vanilla siamese or triplet losses only learn from individual sentence pairs or triplets, which often suffer from bad local optima. In this paper, we propose PairSupCon, an instance discrimination based approach aiming to bridge semantic entailment and contradiction understanding with high-level categorical concept encoding. We evaluate PairSupCon on various downstream tasks that involve understanding sentence semantics at different granularities. We outperform the previous state-of-the-art method with $10\%$--$13\%$ averaged improvement on eight clustering tasks, and $5\%$--$6\%$ averaged improvement on seven semantic textual similarity (STS) tasks.
Contrastive learning allows us to flexibly define powerful losses by contrasting positive pairs from sets of negative samples. Recently, the principle has also been used to learn cross-modal embeddings for video and text, yet without exploiting its full potential. In particular, previous losses do not take the intra-modality similarities into account, which leads to inefficient embeddings, as the same content is mapped to multiple points in the embedding space. With CrossCLR, we present a contrastive loss that fixes this issue. Moreover, we define sets of highly related samples in terms of their input embeddings and exclude them from the negative samples to avoid issues with false negatives. We show that these principles consistently improve the quality of the learned embeddings. The joint embeddings learned with CrossCLR extend the state of the art in video-text retrieval on Youcook2 and LSMDC datasets and in video captioning on Youcook2 dataset by a large margin. We also demonstrate the generality of the concept by learning improved joint embeddings for other pairs of modalities.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
We present self-supervised geometric perception (SGP), the first general framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels (e.g., camera poses, rigid transformations). Our first contribution is to formulate geometric perception as an optimization problem that jointly optimizes the feature descriptor and the geometric models given a large corpus of visual measurements (e.g., images, point clouds). Under this optimization formulation, we show that two important streams of research in vision, namely robust model fitting and deep feature learning, correspond to optimizing one block of the unknown variables while fixing the other block. This analysis naturally leads to our second contribution -- the SGP algorithm that performs alternating minimization to solve the joint optimization. SGP iteratively executes two meta-algorithms: a teacher that performs robust model fitting given learned features to generate geometric pseudo-labels, and a student that performs deep feature learning under noisy supervision of the pseudo-labels. As a third contribution, we apply SGP to two perception problems on large-scale real datasets, namely relative camera pose estimation on MegaDepth and point cloud registration on 3DMatch. We demonstrate that SGP achieves state-of-the-art performance that is on-par or superior to the supervised oracles trained using ground-truth labels.
Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.
Deep embedding learning becomes more attractive for discriminative feature learning, but many methods still require hard-class mining, which is computationally complex and performance-sensitive. To this end, we propose Adaptive Large Margin N-Pair loss (ALMN) to address the aforementioned issues. Instead of exploring hard example-mining strategy, we introduce the concept of large margin constraint. This constraint aims at encouraging local-adaptive large angular decision margin among dissimilar samples in multimodal feature space so as to significantly encourage intraclass compactness and interclass separability. And it is mainly achieved by a simple yet novel geometrical Virtual Point Generating (VPG) method, which converts artificially setting a fixed margin into automatically generating a boundary training sample in feature space and is an open question. We demonstrate the effectiveness of our method on several popular datasets for image retrieval and clustering tasks.
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great successes. Unfortunately, the understanding on how it works remains unclear. It has the central importance to lay down the theoretic foundation for deep learning. In this work, we give a geometric view to understand deep learning: we show that the fundamental principle attributing to the success is the manifold structure in data, namely natural high dimensional data concentrates close to a low-dimensional manifold, deep learning learns the manifold and the probability distribution on it. We further introduce the concepts of rectified linear complexity for deep neural network measuring its learning capability, rectified linear complexity of an embedding manifold describing the difficulty to be learned. Then we show for any deep neural network with fixed architecture, there exists a manifold that cannot be learned by the network. Finally, we propose to apply optimal mass transportation theory to control the probability distribution in the latent space.
Learning compact representation is vital and challenging for large scale multimedia data. Cross-view/cross-modal hashing for effective binary representation learning has received significant attention with exponentially growing availability of multimedia content. Most existing cross-view hashing algorithms emphasize the similarities in individual views, which are then connected via cross-view similarities. In this work, we focus on the exploitation of the discriminative information from different views, and propose an end-to-end method to learn semantic-preserving and discriminative binary representation, dubbed Discriminative Cross-View Hashing (DCVH), in light of learning multitasking binary representation for various tasks including cross-view retrieval, image-to-image retrieval, and image annotation/tagging. The proposed DCVH has the following key components. First, it uses convolutional neural network (CNN) based nonlinear hashing functions and multilabel classification for both images and texts simultaneously. Such hashing functions achieve effective continuous relaxation during training without explicit quantization loss by using Direct Binary Embedding (DBE) layers. Second, we propose an effective view alignment via Hamming distance minimization, which is efficiently accomplished by bit-wise XOR operation. Extensive experiments on two image-text benchmark datasets demonstrate that DCVH outperforms state-of-the-art cross-view hashing algorithms as well as single-view image hashing algorithms. In addition, DCVH can provide competitive performance for image annotation/tagging.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.
Person re-identification (\textit{re-id}) refers to matching pedestrians across disjoint yet non-overlapping camera views. The most effective way to match these pedestrians undertaking significant visual variations is to seek reliably invariant features that can describe the person of interest faithfully. Most of existing methods are presented in a supervised manner to produce discriminative features by relying on labeled paired images in correspondence. However, annotating pair-wise images is prohibitively expensive in labors, and thus not practical in large-scale networked cameras. Moreover, seeking comparable representations across camera views demands a flexible model to address the complex distributions of images. In this work, we study the co-occurrence statistic patterns between pairs of images, and propose to crossing Generative Adversarial Network (Cross-GAN) for learning a joint distribution for cross-image representations in a unsupervised manner. Given a pair of person images, the proposed model consists of the variational auto-encoder to encode the pair into respective latent variables, a proposed cross-view alignment to reduce the view disparity, and an adversarial layer to seek the joint distribution of latent representations. The learned latent representations are well-aligned to reflect the co-occurrence patterns of paired images. We empirically evaluate the proposed model against challenging datasets, and our results show the importance of joint invariant features in improving matching rates of person re-id with comparison to semi/unsupervised state-of-the-arts.
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