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We study the dynamics near the central singularity in spherically symmetric collapse of a massless scalar field toward Schwarzschild black hole formation. The equations of motion take different simplified forms in the early and late stages of the singularity curve. We report some fine structures of the analytic solutions and universal features for the metric functions and matter near the singularity., Comment: 10 pages, 10 figures

Whether what you see in Figure 1 is a "flamingo" or a "bird", is the question we ask in this paper. While fine-grained visual classification (FGVC) strives to arrive at the former, for the majority of us non-experts just "bird" would probably suffice. The real question is therefore -- how can we tailor for different fine-grained definitions under divergent levels of expertise. For that, we re-envisage the traditional setting of FGVC, from single-label classification, to that of top-down traversal of a pre-defined coarse-to-fine label hierarchy -- so that our answer becomes "bird"-->"Phoenicopteriformes"-->"Phoenicopteridae"-->"flamingo". To approach this new problem, we first conduct a comprehensive human study where we confirm that most participants prefer multi-granularity labels, regardless whether they consider themselves experts. We then discover the key intuition that: coarse-level label prediction exacerbates fine-grained feature learning, yet fine-level feature betters the learning of coarse-level classifier. This discovery enables us to design a very simple albeit surprisingly effective solution to our new problem, where we (i) leverage level-specific classification heads to disentangle coarse-level features with fine-grained ones, and (ii) allow finer-grained features to participate in coarser-grained label predictions, which in turn helps with better disentanglement. Experiments show that our method achieves superior performance in the new FGVC setting, and performs better than state-of-the-art on traditional single-label FGVC problem as well. Thanks to its simplicity, our method can be easily implemented on top of any existing FGVC frameworks and is parameter-free., Comment: Accepted as an oral of CVPR2021. Code: https://github.com/PRIS-CV/Fine-Grained-or-Not

This paper proposes a dual-supervised uncertainty inference (DS-UI) framework for improving Bayesian estimation-based uncertainty inference (UI) in deep neural network (DNN)-based image recognition. In the DS-UI, we combine the classifier of a DNN, i.e., the last fully-connected (FC) layer, with a mixture of Gaussian mixture models (MoGMM) to obtain an MoGMM-FC layer. Unlike existing UI methods for DNNs, which only calculate the means or modes of the DNN outputs' distributions, the proposed MoGMM-FC layer acts as a probabilistic interpreter for the features that are inputs of the classifier to directly calculate the probability density of them for the DS-UI. In addition, we propose a dual-supervised stochastic gradient-based variational Bayes (DS-SGVB) algorithm for the MoGMM-FC layer optimization. Unlike conventional SGVB and optimization algorithms in other UI methods, the DS-SGVB not only models the samples in the specific class for each Gaussian mixture model (GMM) in the MoGMM, but also considers the negative samples from other classes for the GMM to reduce the intra-class distances and enlarge the inter-class margins simultaneously for enhancing the learning ability of the MoGMM-FC layer in the DS-UI. Experimental results show the DS-UI outperforms the state-of-the-art UI methods in misclassification detection. We further evaluate the DS-UI in open-set out-of-domain/-distribution detection and find statistically significant improvements. Visualizations of the feature spaces demonstrate the superiority of the DS-UI.

Contrastive learning relies on constructing a collection of negative examples that are sufficiently hard to discriminate against positive queries when their representations are self-trained. Existing contrastive learning methods either maintain a queue of negative samples over minibatches while only a small portion of them are updated in an iteration, or only use the other examples from the current minibatch as negatives. They could not closely track the change of the learned representation over iterations by updating the entire queue as a whole, or discard the useful information from the past minibatches. Alternatively, we present to directly learn a set of negative adversaries playing against the self-trained representation. Two players, the representation network and negative adversaries, are alternately updated to obtain the most challenging negative examples against which the representation of positive queries will be trained to discriminate. We further show that the negative adversaries are updated towards a weighted combination of positive queries by maximizing the adversarial contrastive loss, thereby allowing them to closely track the change of representations over time. Experiment results demonstrate the proposed Adversarial Contrastive (AdCo) model not only achieves superior performances (a top-1 accuracy of 73.2\% over 200 epochs and 75.7\% over 800 epochs with linear evaluation on ImageNet), but also can be pre-trained more efficiently with fewer epochs., Comment: Appendices with more results on symmetric loss, different numbers of negative samples, computing costs is presented. We also discuss "whether we still need negative examples" in Appendix C, a question emerging from the comparison with the BYOL. The source code is also available at https://github.com/maple-research-lab/AdCo/

The critical collapse of a scalar field is a threshold solution of black hole formation, in which a naked singularity arises. We study here the curvature strength of this singularity using a numerical ansatz. The behavior of the Jacobi volume forms is examined along a non-spacelike geodesic in the limit of approach to the singularity. These are seen to be vanishing, thus showing that all physical objects will be crushed to zero size near the singularity. Consequently, although the critical collapse is considered to be a fine-tuning problem, the naked singularity forming is gravitationally strong. This implies that the spacetime cannot be extended beyond the singularity, thus making the singularity genuine and physically interesting. These results imply that the nature of critical collapse may need to be examined and explored further., Comment: 5 pages, 3 figures

We investigate here the thermal properties of accretion disks in a spacetime for some galactic density profiles in spherical symmetry. The matter distributions have a finite outer radius with a naked central singularity. The luminosities of the accretion disks for some density profile models are found to be higher than those for a Schwarzschild black hole of the same mass. The slopes for the luminosity distributions with respect to frequencies are significantly different, especially at higher frequencies, from that in the Schwarzschild black hole case. Such features may be used to distinguish black holes from naked singularities. The efficiencies for the conversion of the mass energy of the accreting gas into radiation and the strength of naked singularities are analyzed. The novel feature that we find is, the strength of the singularity is different depending on the profiles considered, and the stronger the singularity is, the higher is the efficiency for the accretion disk., Comment: 23 pages, 9 figures, 2 tables