我们考虑设计统一稳定的一阶优化算法以最小化的问题。统一的稳定性通常用于获得优化算法的概括误差范围，我们对实现它的一般方法感兴趣。对于欧几里得的几何形状，我们建议采用黑盒转换，给定平滑的优化算法，它产生了算法的均匀稳定版本，同时将其收敛速率保持在对数因素上。使用此减少，我们获得了一种（几乎）最佳算法，以平滑优化，并通过收敛速率$ \ widetilde {o}（1/t^2）$和均匀的稳定性$ O（t^2/n）$，解决一个开放的问题Chen等。（2018）;阿蒂亚和科伦（2021）。对于更一般的几何形状，我们开发了一种镜下下降的变体，以平滑优化，收敛速率$ \ widetilde {o}（1/t）$和统一的稳定性$ O（t/n）$（t/n）$，留下了开放的问题转换方法如欧几里得情况。

Most cross-domain unsupervised Video Anomaly Detection (VAD) works assume that at least few task-relevant target domain training data are available for adaptation from the source to the target domain. However, this requires laborious model-tuning by the end-user who may prefer to have a system that works ``out-of-the-box." To address such practical scenarios, we identify a novel target domain (inference-time) VAD task where no target domain training data are available. To this end, we propose a new `Zero-shot Cross-domain Video Anomaly Detection (zxvad)' framework that includes a future-frame prediction generative model setup. Different from prior future-frame prediction models, our model uses a novel Normalcy Classifier module to learn the features of normal event videos by learning how such features are different ``relatively" to features in pseudo-abnormal examples. A novel Untrained Convolutional Neural Network based Anomaly Synthesis module crafts these pseudo-abnormal examples by adding foreign objects in normal video frames with no extra training cost. With our novel relative normalcy feature learning strategy, zxvad generalizes and learns to distinguish between normal and abnormal frames in a new target domain without adaptation during inference. Through evaluations on common datasets, we show that zxvad outperforms the state-of-the-art (SOTA), regardless of whether task-relevant (i.e., VAD) source training data are available or not. Lastly, zxvad also beats the SOTA methods in inference-time efficiency metrics including the model size, total parameters, GPU energy consumption, and GMACs.

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections to avoid the problem of vanishing gradients, they can be viewed as the numerical integration of a differential equation. In this extended abstract, we build upon this connection and propose a modification of the internal architecture of a transformer layer. The proposed model places the multi-head attention sublayer and the MLP sublayer parallel to each other. Our experiments show that this simple modification improves the performance of transformer networks in multiple tasks. Moreover, for the image classification task, we show that using neural ODE solvers with a sophisticated integration scheme further improves performance.

Image segmentation is a fundamental task in computer vision. Data annotation for training supervised methods can be labor-intensive, motivating unsupervised methods. Some existing approaches extract deep features from pre-trained networks and build a graph to apply classical clustering methods (e.g., $k$-means and normalized-cuts) as a post-processing stage. These techniques reduce the high-dimensional information encoded in the features to pair-wise scalar affinities. In this work, we replace classical clustering algorithms with a lightweight Graph Neural Network (GNN) trained to achieve the same clustering objective function. However, in contrast to existing approaches, we feed the GNN not only the pair-wise affinities between local image features but also the raw features themselves. Maintaining this connection between the raw feature and the clustering goal allows to perform part semantic segmentation implicitly, without requiring additional post-processing steps. We demonstrate how classical clustering objectives can be formulated as self-supervised loss functions for training our image segmentation GNN. Additionally, we use the Correlation-Clustering (CC) objective to perform clustering without defining the number of clusters ($k$-less clustering). We apply the proposed method for object localization, segmentation, and semantic part segmentation tasks, surpassing state-of-the-art performance on multiple benchmarks.

In object detection, post-processing methods like Non-maximum Suppression (NMS) are widely used. NMS can substantially reduce the number of false positive detections but may still keep some detections with low objectness scores. In order to find the exact number of objects and their labels in the image, we propose a post processing method called Detection Selection Algorithm (DSA) which is used after NMS or related methods. DSA greedily selects a subset of detected bounding boxes, together with full object reconstructions that give the interpretation of the whole image with highest likelihood, taking into account object occlusions. The algorithm consists of four components. First, we add an occlusion branch to Faster R-CNN to obtain occlusion relationships between objects. Second, we develop a single reconstruction algorithm which can reconstruct the whole appearance of an object given its visible part, based on the optimization of latent variables of a trained generative network which we call the decoder. Third, we propose a whole reconstruction algorithm which generates the joint reconstruction of all objects in a hypothesized interpretation, taking into account occlusion ordering. Finally we propose a greedy algorithm that incrementally adds or removes detections from a list to maximize the likelihood of the corresponding interpretation. DSA with NMS or Soft-NMS can achieve better results than NMS or Soft-NMS themselves, as is illustrated in our experiments on synthetic images with mutiple 3d objects.

Out-of-distribution (OOD) detection has attracted a large amount of attention from the machine learning research community in recent years due to its importance in deployed systems. Most of the previous studies focused on the detection of OOD samples in the multi-class classification task. However, OOD detection in the multi-label classification task remains an underexplored domain. In this research, we propose YolOOD - a method that utilizes concepts from the object detection domain to perform OOD detection in the multi-label classification task. Object detection models have an inherent ability to distinguish between objects of interest (in-distribution) and irrelevant objects (e.g., OOD objects) on images that contain multiple objects from different categories. These abilities allow us to convert a regular object detection model into an image classifier with inherent OOD detection capabilities with just minor changes. We compare our approach to state-of-the-art OOD detection methods and demonstrate YolOOD's ability to outperform these methods on a comprehensive suite of in-distribution and OOD benchmark datasets.

This is a continuation of our recent paper in which we developed the theory of sequential parametrized motion planning. A sequential parametrized motion planning algorithm produced a motion of the system which is required to visit a prescribed sequence of states, in a certain order, at specified moments of time. In the previous publication we analysed the sequential parametrized topological complexity of the Fadell - Neuwirth fibration which in relevant to the problem of moving multiple robots avoiding collisions with other robots and with obstacles in the Euclidean space. Besides, in the preceeding paper we found the sequential parametrised topological complexity of the Fadell - Neuwirth bundle for the case of the Euclidean space $\Bbb R^d$ of odd dimension as well as the case $d=2$. In the present paper we give the complete answer for an arbitrary $d\ge 2$ even. Moreover, we present an explicit motion planning algorithm for controlling multiple robots in $\Bbb R^d$ having the minimal possible topological complexity; this algorithm is applicable to any number $n$ of robots and any number $m\ge 2$ of obstacles.

Domain generalization (DG) aims to train a model to perform well in unseen domains under different distributions. This paper considers a more realistic yet more challenging scenario,namely Single Domain Generalization (Single-DG), where only a single source domain is available for training. To tackle this challenge, we first try to understand when neural networks fail to generalize? We empirically ascertain a property of a model that correlates strongly with its generalization that we coin as "model sensitivity". Based on our analysis, we propose a novel strategy of Spectral Adversarial Data Augmentation (SADA) to generate augmented images targeted at the highly sensitive frequencies. Models trained with these hard-to-learn samples can effectively suppress the sensitivity in the frequency space, which leads to improved generalization performance. Extensive experiments on multiple public datasets demonstrate the superiority of our approach, which surpasses the state-of-the-art single-DG methods.

State-of-the-art object detectors are fast and accurate, but they require a large amount of well annotated training data to obtain good performance. However, obtaining a large amount of training annotations specific to a particular task, i.e., fine-grained annotations, is costly in practice. In contrast, obtaining common-sense relationships from text, e.g., "a table-lamp is a lamp that sits on top of a table", is much easier. Additionally, common-sense relationships like "on-top-of" are easy to annotate in a task-agnostic fashion. In this paper, we propose a probabilistic model that uses such relational knowledge to transform an off-the-shelf detector of coarse object categories (e.g., "table", "lamp") into a detector of fine-grained categories (e.g., "table-lamp"). We demonstrate that our method, RelDetect, achieves performance competitive to finetuning based state-of-the-art object detector baselines when an extremely low amount of fine-grained annotations is available ($0.2\%$ of entire dataset). We also demonstrate that RelDetect is able to utilize the inherent transferability of relationship information to obtain a better performance ($+5$ mAP points) than the above baselines on an unseen dataset (zero-shot transfer). In summary, we demonstrate the power of using relationships for object detection on datasets where fine-grained object categories can be linked to coarse-grained categories via suitable relationships.

Automatic sign language processing is gaining popularity in Natural Language Processing (NLP) research (Yin et al., 2021). In machine translation (MT) in particular, sign language translation based on glosses is a prominent approach. In this paper, we review recent works on neural gloss translation. We find that limitations of glosses in general and limitations of specific datasets are not discussed in a transparent manner and that there is no common standard for evaluation. To address these issues, we put forward concrete recommendations for future research on gloss translation. Our suggestions advocate awareness of the inherent limitations of gloss-based approaches, realistic datasets, stronger baselines and convincing evaluation.