立方正则化方法（CR）是一种流行的算法，用于无限制的非凸优化。在每次迭代中，CR解决了一个立方正规化的二次问题，称为立方正则化子问题（CRS）。解决CRS的一种方法依赖于解决世俗方程，其计算瓶颈在于计算Hessian矩阵的所有特征值。在本文中，我们根据近似的世俗方程提出和分析了一种新颖的CRS求解器，该方程仅需要一些Hessian特征值，因此更有效。开发了两个近似的世俗方程（ASE）。对于这两个ASE，我们首先研究其根的存在和独特性，然后在根部和标准世俗方程之间的间隙上建立上层界限。这样的上限可以依次用于绑定从基于AS的近似CRS解决方案到真实CRS解决方案的距离，从而为我们的CRS求解器提供理论保证。我们CRS求解器的理想特征是它仅需要矩阵向量乘法，而不需要矩阵反转，这使其特别适合于无限制的非凸优化的高维应用，例如低级别恢复和深度学习。进行合成和实际数据集的数值实验是为了研究拟议的CRS求解器的实际性能。实验结果表明，所提出的求解器的表现优于两种最先进的方法。

算法追索权旨在推荐提供丰富的反馈，以推翻不利的机器学习决策。我们在本文中介绍了贝叶斯追索权，这是一种模型不足的追索权，可最大程度地减少后验概率比值比。此外，我们介绍了其最小的稳健对应物，目的是对抗机器学习模型参数的未来变化。强大的对应物明确考虑了使用最佳传输（Wasserstein）距离规定的高斯混合物中数据的扰动。我们表明，可以将最终的最差目标函数分解为求解一系列二维优化子问题，因此，最小值追索问题发现问题可用于梯度下降算法。与现有的生成健壮的回流的方法相反，可靠的贝叶斯追索不需要线性近似步骤。数值实验证明了我们提出的稳健贝叶斯追索权面临模型转移的有效性。我们的代码可在https://github.com/vinairesearch/robust-bayesian-recourse上找到。

Few Shot Instance Segmentation (FSIS) requires models to detect and segment novel classes with limited several support examples. In this work, we explore a simple yet unified solution for FSIS as well as its incremental variants, and introduce a new framework named Reference Twice (RefT) to fully explore the relationship between support/query features based on a Transformer-like framework. Our key insights are two folds: Firstly, with the aid of support masks, we can generate dynamic class centers more appropriately to re-weight query features. Secondly, we find that support object queries have already encoded key factors after base training. In this way, the query features can be enhanced twice from two aspects, i.e., feature-level and instance-level. In particular, we firstly design a mask-based dynamic weighting module to enhance support features and then propose to link object queries for better calibration via cross-attention. After the above steps, the novel classes can be improved significantly over our strong baseline. Additionally, our new framework can be easily extended to incremental FSIS with minor modification. When benchmarking results on the COCO dataset for FSIS, gFSIS, and iFSIS settings, our method achieves a competitive performance compared to existing approaches across different shots, e.g., we boost nAP by noticeable +8.2/+9.4 over the current state-of-the-art FSIS method for 10/30-shot. We further demonstrate the superiority of our approach on Few Shot Object Detection. Code and model will be available.

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.

In robust Markov decision processes (MDPs), the uncertainty in the transition kernel is addressed by finding a policy that optimizes the worst-case performance over an uncertainty set of MDPs. While much of the literature has focused on discounted MDPs, robust average-reward MDPs remain largely unexplored. In this paper, we focus on robust average-reward MDPs, where the goal is to find a policy that optimizes the worst-case average reward over an uncertainty set. We first take an approach that approximates average-reward MDPs using discounted MDPs. We prove that the robust discounted value function converges to the robust average-reward as the discount factor $\gamma$ goes to $1$, and moreover, when $\gamma$ is large, any optimal policy of the robust discounted MDP is also an optimal policy of the robust average-reward. We further design a robust dynamic programming approach, and theoretically characterize its convergence to the optimum. Then, we investigate robust average-reward MDPs directly without using discounted MDPs as an intermediate step. We derive the robust Bellman equation for robust average-reward MDPs, prove that the optimal policy can be derived from its solution, and further design a robust relative value iteration algorithm that provably finds its solution, or equivalently, the optimal robust policy.

Differentiable Architecture Search (DARTS) has attracted considerable attention as a gradient-based Neural Architecture Search (NAS) method. Since the introduction of DARTS, there has been little work done on adapting the action space based on state-of-art architecture design principles for CNNs. In this work, we aim to address this gap by incrementally augmenting the DARTS search space with micro-design changes inspired by ConvNeXt and studying the trade-off between accuracy, evaluation layer count, and computational cost. To this end, we introduce the Pseudo-Inverted Bottleneck conv block intending to reduce the computational footprint of the inverted bottleneck block proposed in ConvNeXt. Our proposed architecture is much less sensitive to evaluation layer count and outperforms a DARTS network with similar size significantly, at layer counts as small as 2. Furthermore, with less layers, not only does it achieve higher accuracy with lower GMACs and parameter count, GradCAM comparisons show that our network is able to better detect distinctive features of target objects compared to DARTS.

Automatic font generation without human experts is a practical and significant problem, especially for some languages that consist of a large number of characters. Existing methods for font generation are often in supervised learning. They require a large number of paired data, which are labor-intensive and expensive to collect. In contrast, common unsupervised image-to-image translation methods are not applicable to font generation, as they often define style as the set of textures and colors. In this work, we propose a robust deformable generative network for unsupervised font generation (abbreviated as DGFont++). We introduce a feature deformation skip connection (FDSC) to learn local patterns and geometric transformations between fonts. The FDSC predicts pairs of displacement maps and employs the predicted maps to apply deformable convolution to the low-level content feature maps. The outputs of FDSC are fed into a mixer to generate final results. Moreover, we introduce contrastive self-supervised learning to learn a robust style representation for fonts by understanding the similarity and dissimilarities of fonts. To distinguish different styles, we train our model with a multi-task discriminator, which ensures that each style can be discriminated independently. In addition to adversarial loss, another two reconstruction losses are adopted to constrain the domain-invariant characteristics between generated images and content images. Taking advantage of FDSC and the adopted loss functions, our model is able to maintain spatial information and generates high-quality character images in an unsupervised manner. Experiments demonstrate that our model is able to generate character images of higher quality than state-of-the-art methods.

Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator applications has thus far been data-driven, which neglects the intrinsic preservation of fundamental physical laws in data. In this paper, we introduce a novel integral neural operator architecture, to learn physical models with fundamental conservation laws automatically guaranteed. In particular, by replacing the frame-dependent position information with its invariant counterpart in the kernel space, the proposed neural operator is by design translation- and rotation-invariant, and consequently abides by the conservation laws of linear and angular momentums. As applications, we demonstrate the expressivity and efficacy of our model in learning complex material behaviors from both synthetic and experimental datasets, and show that, by automatically satisfying these essential physical laws, our learned neural operator is not only generalizable in handling translated and rotated datasets, but also achieves state-of-the-art accuracy and efficiency as compared to baseline neural operator models.

The development of deep learning models in medical image analysis is majorly limited by the lack of large-sized and well-annotated datasets. Unsupervised learning does not require labels and is more suitable for solving medical image analysis problems. However, most of the current unsupervised learning methods need to be applied to large datasets. To make unsupervised learning applicable to small datasets, we proposed Swin MAE, which is a masked autoencoder with Swin Transformer as its backbone. Even on a dataset of only a few thousand medical images and without using any pre-trained models, Swin MAE is still able to learn useful semantic features purely from images. It can equal or even slightly outperform the supervised model obtained by Swin Transformer trained on ImageNet in terms of the transfer learning results of downstream tasks. The code will be publicly available soon.

Graph Neural Networks (GNNs) have been widely applied to different tasks such as bioinformatics, drug design, and social networks. However, recent studies have shown that GNNs are vulnerable to adversarial attacks which aim to mislead the node or subgraph classification prediction by adding subtle perturbations. Detecting these attacks is challenging due to the small magnitude of perturbation and the discrete nature of graph data. In this paper, we propose a general adversarial edge detection pipeline EDoG without requiring knowledge of the attack strategies based on graph generation. Specifically, we propose a novel graph generation approach combined with link prediction to detect suspicious adversarial edges. To effectively train the graph generative model, we sample several sub-graphs from the given graph data. We show that since the number of adversarial edges is usually low in practice, with low probability the sampled sub-graphs will contain adversarial edges based on the union bound. In addition, considering the strong attacks which perturb a large number of edges, we propose a set of novel features to perform outlier detection as the preprocessing for our detection. Extensive experimental results on three real-world graph datasets including a private transaction rule dataset from a major company and two types of synthetic graphs with controlled properties show that EDoG can achieve above 0.8 AUC against four state-of-the-art unseen attack strategies without requiring any knowledge about the attack type; and around 0.85 with knowledge of the attack type. EDoG significantly outperforms traditional malicious edge detection baselines. We also show that an adaptive attack with full knowledge of our detection pipeline is difficult to bypass it.