The angular momentum of galaxies (galaxy spin) contains rich information about the initial condition of the Universe, yet it is challenging to efficiently measure the spin direction for the tremendous amount of galaxies that are being mapped by the ongoing and forthcoming cosmological surveys. We present a machine learning based classifier for the Z-wise vs S-wise spirals, which can help to break the degeneracy in the galaxy spin direction measurement. The proposed Chirality Equivariant Residual Network (CE-ResNet) is manifestly equivariant under a reflection of the input image, which guarantees that there is no inherent asymmetry between the Z-wise and S-wise probability estimators. We train the model with Sloan Digital Sky Survey (SDSS) images, with the training labels given by the Galaxy Zoo 1 (GZ1) project. A combination of data augmentation tricks are used during the training, making the model more robust to be applied to other surveys. We find a $\sim\!30\%$ increase of both types of spirals when Dark Energy Spectroscopic Instrument (DESI) images are used for classification, due to the better imaging quality of DESI. We verify that the $\sim\!7\sigma$ difference between the numbers of Z-wise and S-wise spirals is due to human bias, since the discrepancy drops to $<\!1.8\sigma$ with our CE-ResNet classification results. We discuss the potential systematics that are relevant to the future cosmological applications.

To rigorously certify the robustness of neural networks to adversarial perturbations, most state-of-the-art techniques rely on a triangle-shaped linear programming (LP) relaxation of the ReLU activation. While the LP relaxation is exact for a single neuron, recent results suggest that it faces an inherent "convex relaxation barrier" as additional activations are added, and as the attack budget is increased. In this paper, we propose a nonconvex relaxation for the ReLU relaxation, based on a low-rank restriction of a semidefinite programming (SDP) relaxation. We show that the nonconvex relaxation has a similar complexity to the LP relaxation, but enjoys improved tightness that is comparable to the much more expensive SDP relaxation. Despite nonconvexity, we prove that the verification problem satisfies constraint qualification, and therefore a Riemannian staircase approach is guaranteed to compute a near-globally optimal solution in polynomial time. Our experiments provide evidence that our nonconvex relaxation almost completely overcome the "convex relaxation barrier" faced by the LP relaxation.

矩阵的完成问题旨在从对其个别元素的观察中恢复低级$ r \ ll d $的$ d \ times d $地面真相矩阵。现实世界中的矩阵完成通常是一个巨大的优化问题，$ d $如此之大，以至于即使是$ O（d）$ o（d）$ o（d）$ o（d）$ o（d）$ o（d）$ o（d）$ o（d）$ o（d）$ o（d）$ o（d）$ o（d）$ o（d）$ d $的昂贵。随机梯度下降（SGD）是少数能够大规模求解矩阵完成的算法之一，也可以自然地通过不断发展的地面真相处理流数据。不幸的是，当底层地面真理不足时，SGD经历了戏剧性的减速。它至少需要$ o（\ kappa \ log（1/\ epsilon））$迭代才能获得$ \ epsilon $ -close $ \ epsilon $ -Close以接地真相矩阵，条件号$ \ kappa $。在本文中，我们提出了一个预处理的SGD版本，该版本保留了SGD的所有有利的实践素质用于大规模的在线优化，同时也使其不可知到$ \ kappa $。对于对称地面真相和根平方错误（RMSE）损失，我们证明预处理的SGD收敛到$ \ epsilon $ -Accuracy in $ o（\ log（1/\ epsilon））$ tererations $迭代，并具有快速的线性线性融合率好像地面真相是完美的条件，$ \ kappa = 1 $。在我们的数值实验中，我们观察到在1位跨透明拷贝损失下进行的不条件矩阵完成的加速度，以及贝叶斯个性化排名（BPR）损失等成对损失。

Benefiting from the intrinsic supervision information exploitation capability, contrastive learning has achieved promising performance in the field of deep graph clustering recently. However, we observe that two drawbacks of the positive and negative sample construction mechanisms limit the performance of existing algorithms from further improvement. 1) The quality of positive samples heavily depends on the carefully designed data augmentations, while inappropriate data augmentations would easily lead to the semantic drift and indiscriminative positive samples. 2) The constructed negative samples are not reliable for ignoring important clustering information. To solve these problems, we propose a Cluster-guided Contrastive deep Graph Clustering network (CCGC) by mining the intrinsic supervision information in the high-confidence clustering results. Specifically, instead of conducting complex node or edge perturbation, we construct two views of the graph by designing special Siamese encoders whose weights are not shared between the sibling sub-networks. Then, guided by the high-confidence clustering information, we carefully select and construct the positive samples from the same high-confidence cluster in two views. Moreover, to construct semantic meaningful negative sample pairs, we regard the centers of different high-confidence clusters as negative samples, thus improving the discriminative capability and reliability of the constructed sample pairs. Lastly, we design an objective function to pull close the samples from the same cluster while pushing away those from other clusters by maximizing and minimizing the cross-view cosine similarity between positive and negative samples. Extensive experimental results on six datasets demonstrate the effectiveness of CCGC compared with the existing state-of-the-art algorithms.

To generate high quality rendering images for real time applications, it is often to trace only a few samples-per-pixel (spp) at a lower resolution and then supersample to the high resolution. Based on the observation that the rendered pixels at a low resolution are typically highly aliased, we present a novel method for neural supersampling based on ray tracing 1/4-spp samples at the high resolution. Our key insight is that the ray-traced samples at the target resolution are accurate and reliable, which makes the supersampling an interpolation problem. We present a mask-reinforced neural network to reconstruct and interpolate high-quality image sequences. First, a novel temporal accumulation network is introduced to compute the correlation between current and previous features to significantly improve their temporal stability. Then a reconstruct network based on a multi-scale U-Net with skip connections is adopted for reconstruction and generation of the desired high-resolution image. Experimental results and comparisons have shown that our proposed method can generate higher quality results of supersampling, without increasing the total number of ray-tracing samples, over current state-of-the-art methods.

Temporal sentence grounding (TSG) aims to identify the temporal boundary of a specific segment from an untrimmed video by a sentence query. All existing works first utilize a sparse sampling strategy to extract a fixed number of video frames and then conduct multi-modal interactions with query sentence for reasoning. However, we argue that these methods have overlooked two indispensable issues: 1) Boundary-bias: The annotated target segment generally refers to two specific frames as corresponding start and end timestamps. The video downsampling process may lose these two frames and take the adjacent irrelevant frames as new boundaries. 2) Reasoning-bias: Such incorrect new boundary frames also lead to the reasoning bias during frame-query interaction, reducing the generalization ability of model. To alleviate above limitations, in this paper, we propose a novel Siamese Sampling and Reasoning Network (SSRN) for TSG, which introduces a siamese sampling mechanism to generate additional contextual frames to enrich and refine the new boundaries. Specifically, a reasoning strategy is developed to learn the inter-relationship among these frames and generate soft labels on boundaries for more accurate frame-query reasoning. Such mechanism is also able to supplement the absent consecutive visual semantics to the sampled sparse frames for fine-grained activity understanding. Extensive experiments demonstrate the effectiveness of SSRN on three challenging datasets.

Representing and synthesizing novel views in real-world dynamic scenes from casual monocular videos is a long-standing problem. Existing solutions typically approach dynamic scenes by applying geometry techniques or utilizing temporal information between several adjacent frames without considering the underlying background distribution in the entire scene or the transmittance over the ray dimension, limiting their performance on static and occlusion areas. Our approach $\textbf{D}$istribution-$\textbf{D}$riven neural radiance fields offers high-quality view synthesis and a 3D solution to $\textbf{D}$etach the background from the entire $\textbf{D}$ynamic scene, which is called $\text{D}^4$NeRF. Specifically, it employs a neural representation to capture the scene distribution in the static background and a 6D-input NeRF to represent dynamic objects, respectively. Each ray sample is given an additional occlusion weight to indicate the transmittance lying in the static and dynamic components. We evaluate $\text{D}^4$NeRF on public dynamic scenes and our urban driving scenes acquired from an autonomous-driving dataset. Extensive experiments demonstrate that our approach outperforms previous methods in rendering texture details and motion areas while also producing a clean static background. Our code will be released at https://github.com/Luciferbobo/D4NeRF.

Deploying reliable deep learning techniques in interdisciplinary applications needs learned models to output accurate and ({even more importantly}) explainable predictions. Existing approaches typically explicate network outputs in a post-hoc fashion, under an implicit assumption that faithful explanations come from accurate predictions/classifications. We have an opposite claim that explanations boost (or even determine) classification. That is, end-to-end learning of explanation factors to augment discriminative representation extraction could be a more intuitive strategy to inversely assure fine-grained explainability, e.g., in those neuroimaging and neuroscience studies with high-dimensional data containing noisy, redundant, and task-irrelevant information. In this paper, we propose such an explainable geometric deep network dubbed as NeuroExplainer, with applications to uncover altered infant cortical development patterns associated with preterm birth. Given fundamental cortical attributes as network input, our NeuroExplainer adopts a hierarchical attention-decoding framework to learn fine-grained attentions and respective discriminative representations to accurately recognize preterm infants from term-born infants at term-equivalent age. NeuroExplainer learns the hierarchical attention-decoding modules under subject-level weak supervision coupled with targeted regularizers deduced from domain knowledge regarding brain development. These prior-guided constraints implicitly maximizes the explainability metrics (i.e., fidelity, sparsity, and stability) in network training, driving the learned network to output detailed explanations and accurate classifications. Experimental results on the public dHCP benchmark suggest that NeuroExplainer led to quantitatively reliable explanation results that are qualitatively consistent with representative neuroimaging studies.

Domain adaptation methods reduce domain shift typically by learning domain-invariant features. Most existing methods are built on distribution matching, e.g., adversarial domain adaptation, which tends to corrupt feature discriminability. In this paper, we propose Discriminative Radial Domain Adaptation (DRDR) which bridges source and target domains via a shared radial structure. It's motivated by the observation that as the model is trained to be progressively discriminative, features of different categories expand outwards in different directions, forming a radial structure. We show that transferring such an inherently discriminative structure would enable to enhance feature transferability and discriminability simultaneously. Specifically, we represent each domain with a global anchor and each category a local anchor to form a radial structure and reduce domain shift via structure matching. It consists of two parts, namely isometric transformation to align the structure globally and local refinement to match each category. To enhance the discriminability of the structure, we further encourage samples to cluster close to the corresponding local anchors based on optimal-transport assignment. Extensively experimenting on multiple benchmarks, our method is shown to consistently outperforms state-of-the-art approaches on varied tasks, including the typical unsupervised domain adaptation, multi-source domain adaptation, domain-agnostic learning, and domain generalization.

The ''Propose-Test-Release'' (PTR) framework is a classic recipe for designing differentially private (DP) algorithms that are data-adaptive, i.e. those that add less noise when the input dataset is nice. We extend PTR to a more general setting by privately testing data-dependent privacy losses rather than local sensitivity, hence making it applicable beyond the standard noise-adding mechanisms, e.g. to queries with unbounded or undefined sensitivity. We demonstrate the versatility of generalized PTR using private linear regression as a case study. Additionally, we apply our algorithm to solve an open problem from ''Private Aggregation of Teacher Ensembles (PATE)'' -- privately releasing the entire model with a delicate data-dependent analysis.