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In this article, we give an explicit and uniform lower bound of the arithmetic Hilbert-Samuel function of projective hypersurfaces, which has the optimal dominant term. As an application, we apply this lower bound in the determinant method., Comment: 46 pages. arXiv admin note: substantial text overlap with arXiv:1808.03451

We investigate thermodynamics of apparent horizon in the $f(Q)$ universe with trivial and nontrivial connections. We first explore the perspectives of the first law, generalized second law and $P-V$ phase transition with trivial connection. We show that the lowest-order correction of entropy has the same form as that in loop quantum gravity, and the critical exponents of the phase transition caused by the lowest-order correction are consistent with those in mean field theory. We then examine the thermodynamic implication of nontrivial connections. We find that nontrivial connections in the $f(Q)$ universe imply non-equilibrium states from the perspective of thermodynamics., Comment: 23 pages, 1 figure

In this paper, we will prove an analogue of Fujita's approximation theorem under the framework of Arakelov theory over adelic curves, which proves a conjecture of Huayi Chen and Atsushi Moriwaki., Comment: 25 pages

In this paper, we will give a uniform upper bound of the number of rational points of bounded height in non-singular curves by applying the global determinant method., Comment: An unrepairable mistake is found

We investigate the cosmological perturbations around all three branches of spatially flat universe with different connections in symmetric teleparallel gravity. The model we consider can cover both the case of f(Q) model and that of the non-minimal coupling between a scalar field and the non-metricity scalar. We focus on analyzing and comparing the propagation behavior and stability of the tensorial and non-tensorial gravitational waves on spatially flat universe with different connections., Comment: 18 pages, 0 figure

Video-text retrieval is a class of cross-modal representation learning problems, where the goal is to select the video which corresponds to the text query between a given text query and a pool of candidate videos. The contrastive paradigm of vision-language pretraining has shown promising success with large-scale datasets and unified transformer architecture, and demonstrated the power of a joint latent space. Despite this, the intrinsic divergence between the visual domain and textual domain is still far from being eliminated, and projecting different modalities into a joint latent space might result in the distorting of the information inside the single modality. To overcome the above issue, we present a novel mechanism for learning the translation relationship from a source modality space $\mathcal{S}$ to a target modality space $\mathcal{T}$ without the need for a joint latent space, which bridges the gap between visual and textual domains. Furthermore, to keep cycle consistency between translations, we adopt a cycle loss involving both forward translations from $\mathcal{S}$ to the predicted target space $\mathcal{T'}$, and backward translations from $\mathcal{T'}$ back to $\mathcal{S}$. Extensive experiments conducted on MSR-VTT, MSVD, and DiDeMo datasets demonstrate the superiority and effectiveness of our LaT approach compared with vanilla state-of-the-art methods.

Temporal action segmentation is a task to classify each frame in the video with an action label. However, it is quite expensive to annotate every frame in a large corpus of videos to construct a comprehensive supervised training dataset. Thus in this work we propose an unsupervised method, namely SSCAP, that operates on a corpus of unlabeled videos and predicts a likely set of temporal segments across the videos. SSCAP leverages Self-Supervised learning to extract distinguishable features and then applies a novel Co-occurrence Action Parsing algorithm to not only capture the correlation among sub-actions underlying the structure of activities, but also estimate the temporal path of the sub-actions in an accurate and general way. We evaluate on both classic datasets (Breakfast, 50Salads) and the emerging fine-grained action dataset (FineGym) with more complex activity structures and similar sub-actions. Results show that SSCAP achieves state-of-the-art performance on all datasets and can even outperform some weakly-supervised approaches, demonstrating its effectiveness and generalizability., Comment: WACV 2022 camera ready

We introduce Video Transformer (VidTr) with separable-attention for video classification. Comparing with commonly used 3D networks, VidTr is able to aggregate spatio-temporal information via stacked attentions and provide better performance with higher efficiency. We first introduce the vanilla video transformer and show that transformer module is able to perform spatio-temporal modeling from raw pixels, but with heavy memory usage. We then present VidTr which reduces the memory cost by 3.3$\times$ while keeping the same performance. To further optimize the model, we propose the standard deviation based topK pooling for attention ($pool_{topK\_std}$), which reduces the computation by dropping non-informative features along temporal dimension. VidTr achieves state-of-the-art performance on five commonly used datasets with lower computational requirement, showing both the efficiency and effectiveness of our design. Finally, error analysis and visualization show that VidTr is especially good at predicting actions that require long-term temporal reasoning., Comment: ICCV 2021 Accepted

We propose TubeR: a simple solution for spatio-temporal video action detection. Different from existing methods that depend on either an off-line actor detector or hand-designed actor-positional hypotheses like proposals or anchors, we propose to directly detect an action tubelet in a video by simultaneously performing action localization and recognition from a single representation. TubeR learns a set of tubelet-queries and utilizes a tubelet-attention module to model the dynamic spatio-temporal nature of a video clip, which effectively reinforces the model capacity compared to using actor-positional hypotheses in the spatio-temporal space. For videos containing transitional states or scene changes, we propose a context aware classification head to utilize short-term and long-term context to strengthen action classification, and an action switch regression head for detecting the precise temporal action extent. TubeR directly produces action tubelets with variable lengths and even maintains good results for long video clips. TubeR outperforms the previous state-of-the-art on commonly used action detection datasets AVA, UCF101-24 and JHMDB51-21., Comment: Accepted at CVPR 2022 (Oral)

Most action recognition solutions rely on dense sampling to precisely cover the informative temporal clip. Extensively searching temporal region is expensive for a real-world application. In this work, we focus on improving the inference efficiency of current action recognition backbones on trimmed videos, and illustrate that one action model can also cover then informative region by dropping non-informative features. We present Selective Feature Compression (SFC), an action recognition inference strategy that greatly increase model inference efficiency without any accuracy compromise. Differently from previous works that compress kernel sizes and decrease the channel dimension, we propose to compress feature flow at spatio-temporal dimension without changing any backbone parameters. Our experiments on Kinetics-400, UCF101 and ActivityNet show that SFC is able to reduce inference speed by 6-7x and memory usage by 5-6x compared with the commonly used 30 crops dense sampling procedure, while also slightly improving Top1 Accuracy. We thoroughly quantitatively and qualitatively evaluate SFC and all its components and show how does SFC learn to attend to important video regions and to drop temporal features that are uninformative for the task of action recognition., Comment: Accepted by ICCV 2021

In this paper, we build the global determinant method of Salberger by Arakelov geometry explicitly. As an application, we study the dependence on the degree of the number of rational points of bounded height in plane curves. We will also explain why some constants will be more explicit if we admit the Generalized Riemann Hypothesis., Comment: 39 pages. arXiv admin note: text overlap with arXiv:1910.00306

In the world of action recognition research, one primary focus has been on how to construct and train networks to model the spatial-temporal volume of an input video. These methods typically uniformly sample a segment of an input clip (along the temporal dimension). However, not all parts of a video are equally important to determine the action in the clip. In this work, we focus instead on learning where to extract features, so as to focus on the most informative parts of the video. We propose a method called the non-uniform temporal aggregation (NUTA), which aggregates features only from informative temporal segments. We also introduce a synchronization method that allows our NUTA features to be temporally aligned with traditional uniformly sampled video features, so that both local and clip-level features can be combined. Our model has achieved state-of-the-art performance on four widely used large-scale action-recognition datasets (Kinetics400, Kinetics700, Something-something V2 and Charades). In addition, we have created a visualization to illustrate how the proposed NUTA method selects only the most relevant parts of a video clip.

Video action recognition is one of the representative tasks for video understanding. Over the last decade, we have witnessed great advancements in video action recognition thanks to the emergence of deep learning. But we also encountered new challenges, including modeling long-range temporal information in videos, high computation costs, and incomparable results due to datasets and evaluation protocol variances. In this paper, we provide a comprehensive survey of over 200 existing papers on deep learning for video action recognition. We first introduce the 17 video action recognition datasets that influenced the design of models. Then we present video action recognition models in chronological order: starting with early attempts at adapting deep learning, then to the two-stream networks, followed by the adoption of 3D convolutional kernels, and finally to the recent compute-efficient models. In addition, we benchmark popular methods on several representative datasets and release code for reproducibility. In the end, we discuss open problems and shed light on opportunities for video action recognition to facilitate new research ideas., Comment: Technical report. Code and model zoo can be found at https://cv.gluon.ai/model_zoo/action_recognition.html