Causal phenomena associated with rare events frequently occur across a wide range of engineering and mathematical problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal discovery are often unable to uncover causal links between random variables that manifest only when the variables first experience low-probability realizations. To address this issue, we introduce a novel algorithm that performs statistical independence tests on data collected from time-invariant dynamical systems in which rare but consequential events occur. We seek to understand if the state of the dynamical system causally affects the likelihood of the rare event. In particular, we exploit the time-invariance of the underlying data to superimpose the occurrences of rare events, thus creating a new dataset, with rare events are better represented, on which conditional independence tests can be more efficiently performed. We provide non-asymptotic bounds for the consistency of our algorithm, and validate the performance of our algorithm across various simulated scenarios, with applications to traffic accidents.

经常部署同时本地化和映射（SLAM）算法以支持广泛的机器人应用程序，例如在未知环境中的自主导航以及虚拟现实中的场景映射。这些应用中的许多应用都需要在场景中使用高度动态的对象执行SLAM的自动源代理。为此，本教程将最近引入的，将基于优化的SLAM后端框架统一到具有移动对象和功能的环境。使用此框架，我们考虑了动态大满贯最新进展的和解。此外，我们提出了一种基于新颖的，基于过滤的动态大满贯算法，在我们的框架内命名为Dynamic EKF SLAM，并证明它在数学上与经典EKF SLAM算法直接扩展到动态环境设置。使用模拟数据的经验结果表明，动态EKF SLAM可以实现较高的本地化和移动对象姿势估计精度以及高地图精度。

我们考虑在高维空间中学习数据的判别性表示的问题，并在多个低维线性子空间上或周围支持分布。也就是说，我们希望计算数据的线性注射映射，以便该功能位于多个正交子空间上。我们没有使用多个PCAS处理这个学习问题，而是使用最近提出的用于学习一般低维基符号的判别性和生成性表示的闭环转录（CTRL）框架作为顺序游戏。我们证明，游戏的平衡解决方案确实提供了正确的表示。我们的方法通过表明可以证明使用现代表示学习工具包可以解决子空间学习问题，从而将学习子空间的经典方法统一了学习子空间。此外，在线性子空间的重要情况下，我们的工作为CTRL框架提供了第一个理论理由。我们以令人信服的经验证据来支持我们的理论发现。我们还将顺序的游戏公式推广到更通用的表示学习问题。我们的代码，包括容易复制实验结果的方法，在GitHub上公开可用。

在多游戏设置中运行的机器人必须同时对共享环境的人类或机器人代理的环境和行为进行建模。通常使用同时定位和映射（SLAM）进行这种建模；但是，SLAM算法通常忽略了多人相互作用。相比之下，运动计划文献经常使用动态游戏理论来在具有完美本地化的已知环境中明确对多个代理的非合作相互作用进行建模。在这里，我们介绍了GTP-Slam，这是一种基于迭代最佳响应的小说最佳SLAM算法，可以准确执行状态定位和映射重建，同时使用游戏理论先验来捕获未知场景中多个代理之间固有的非合作互动。通过将基本的大满贯问题作为潜在游戏，我们继承了强有力的融合保证。经验结果表明，当部署在现实的交通模拟中时，我们的方法比在广泛的噪声水平上的标准捆绑捆绑调整算法更准确地进行本地化和映射。

It is well established in neuroscience that color vision plays an essential part in the human visual perception system. Meanwhile, many novel designs for computer vision inspired by human vision have achieved success in a wide range of tasks and applications. Nonetheless, how color differences affect machine vision has not been well explored. Our work tries to bridge this gap between the human color vision aspect of visual recognition and that of the machine. To achieve this, we curate two datasets: CIFAR10-F and CIFAR100-F, which are based on the foreground colors of the popular CIFAR datasets. Together with CIFAR10-B and CIFAR100-B, the existing counterpart datasets with information on the background colors of CIFAR test sets, we assign each image based on its color contrast level per its foreground and background color labels and use this as a proxy to study how color contrast affects machine vision. We first conduct a proof-of-concept study, showing the effect of color difference and validate our datasets. Furthermore, on a broader level, an important characteristic of human vision is its robustness against ambient changes; therefore, drawing inspirations from ophthalmology and the robustness literature, we analogize contrast sensitivity from the human visual aspect to machine vision and complement the current robustness study using corrupted images with our CIFAR-CoCo datasets. In summary, motivated by neuroscience and equipped with the datasets we curate, we devise a new framework in two dimensions to perform extensive analyses on the effect of color contrast and corrupted images: (1) model architecture, (2) model size, to measure the perception ability of machine vision beyond total accuracy. We also explore how task complexity and data augmentation play a role in this setup. Our results call attention to new evaluation approaches for human-like machine perception.

It is no secret that deep learning models exhibit undesirable behaviors such as learning spurious correlations instead of learning correct relationships between input/output pairs. Prior works on robustness study datasets that mix low-level features to quantify how spurious correlations affect predictions instead of considering natural semantic factors due to limitations in accessing realistic datasets for comprehensive evaluation. To bridge this gap, in this paper we first investigate how natural background colors play a role as spurious features in image classification tasks by manually splitting the test sets of CIFAR10 and CIFAR100 into subgroups based on the background color of each image. We name our datasets CIFAR10-B and CIFAR100-B. We find that while standard CNNs achieve human-level accuracy, the subgroup performances are not consistent, and the phenomenon remains even after data augmentation (DA). To alleviate this issue, we propose FlowAug, a semantic DA method that leverages the decoupled semantic representations captured by a pre-trained generative flow. Experimental results show that FlowAug achieves more consistent results across subgroups than other types of DA methods on CIFAR10 and CIFAR100. Additionally, it shows better generalization performance. Furthermore, we propose a generic metric for studying model robustness to spurious correlations, where we take a macro average on the weighted standard deviations across different classes. Per our metric, FlowAug demonstrates less reliance on spurious correlations. Although this metric is proposed to study our curated datasets, it applies to all datasets that have subgroups or subclasses. Lastly, aside from less dependence on spurious correlations and better generalization on in-distribution test sets, we also show superior out-of-distribution results on CIFAR10.1 and competitive performances on CIFAR10-C and CIFAR100-C.

This paper introduces the use of evolutionary algorithms for solving differential equations. The solution is obtained by optimizing a deep neural network whose loss function is defined by the residual terms from the differential equations. Recent studies have used stochastic gradient descent (SGD) variants to train these physics-informed neural networks (PINNs), but these methods can struggle to find accurate solutions due to optimization challenges. When solving differential equations, it is important to find the globally optimum parameters of the network, rather than just finding a solution that works well during training. SGD only searches along a single gradient direction, so it may not be the best approach for training PINNs with their accompanying complex optimization landscapes. In contrast, evolutionary algorithms perform a parallel exploration of different solutions in order to avoid getting stuck in local optima and can potentially find more accurate solutions. However, evolutionary algorithms can be slow, which can make them difficult to use in practice. To address this, we provide a set of five benchmark problems with associated performance metrics and baseline results to support the development of evolutionary algorithms for enhanced PINN training. As a baseline, we evaluate the performance and speed of using the widely adopted Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for solving PINNs. We provide the loss and training time for CMA-ES run on TensorFlow, and CMA-ES and SGD run on JAX (with GPU acceleration) for the five benchmark problems. Our results show that JAX-accelerated evolutionary algorithms, particularly CMA-ES, can be a useful approach for solving differential equations. We hope that our work will support the exploration and development of alternative optimization algorithms for the complex task of optimizing PINNs.

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.

Universal Image Segmentation is not a new concept. Past attempts to unify image segmentation in the last decades include scene parsing, panoptic segmentation, and, more recently, new panoptic architectures. However, such panoptic architectures do not truly unify image segmentation because they need to be trained individually on the semantic, instance, or panoptic segmentation to achieve the best performance. Ideally, a truly universal framework should be trained only once and achieve SOTA performance across all three image segmentation tasks. To that end, we propose OneFormer, a universal image segmentation framework that unifies segmentation with a multi-task train-once design. We first propose a task-conditioned joint training strategy that enables training on ground truths of each domain (semantic, instance, and panoptic segmentation) within a single multi-task training process. Secondly, we introduce a task token to condition our model on the task at hand, making our model task-dynamic to support multi-task training and inference. Thirdly, we propose using a query-text contrastive loss during training to establish better inter-task and inter-class distinctions. Notably, our single OneFormer model outperforms specialized Mask2Former models across all three segmentation tasks on ADE20k, CityScapes, and COCO, despite the latter being trained on each of the three tasks individually with three times the resources. With new ConvNeXt and DiNAT backbones, we observe even more performance improvement. We believe OneFormer is a significant step towards making image segmentation more universal and accessible. To support further research, we open-source our code and models at https://github.com/SHI-Labs/OneFormer

Online continual learning (OCL) aims to enable model learning from a non-stationary data stream to continuously acquire new knowledge as well as retain the learnt one, under the constraints of having limited system size and computational cost, in which the main challenge comes from the "catastrophic forgetting" issue -- the inability to well remember the learnt knowledge while learning the new ones. With the specific focus on the class-incremental OCL scenario, i.e. OCL for classification, the recent advance incorporates the contrastive learning technique for learning more generalised feature representation to achieve the state-of-the-art performance but is still unable to fully resolve the catastrophic forgetting. In this paper, we follow the strategy of adopting contrastive learning but further introduce the semantically distinct augmentation technique, in which it leverages strong augmentation to generate more data samples, and we show that considering these samples semantically different from their original classes (thus being related to the out-of-distribution samples) in the contrastive learning mechanism contributes to alleviate forgetting and facilitate model stability. Moreover, in addition to contrastive learning, the typical classification mechanism and objective (i.e. softmax classifier and cross-entropy loss) are included in our model design for faster convergence and utilising the label information, but particularly equipped with a sampling strategy to tackle the tendency of favouring the new classes (i.e. model bias towards the recently learnt classes). Upon conducting extensive experiments on CIFAR-10, CIFAR-100, and Mini-Imagenet datasets, our proposed method is shown to achieve superior performance against various baselines.