We investigate the sample complexity of bounded two-layer neural networks using different activation functions. In particular, we consider the class \[ \mathcal{H} = \left\{\textbf{x}\mapsto \langle \textbf{v}, \sigma \circ W\textbf{x} + \textbf{b} \rangle : \textbf{b}\in\mathbb{R}^d, W \in \mathbb{R}^{T\times d}, \textbf{v} \in \mathbb{R}^{T}\right\} \] where the spectral norm of $W$ and $\textbf{v}$ is bounded by $O(1)$, the Frobenius norm of $W$ is bounded from its initialization by $R > 0$, and $\sigma$ is a Lipschitz activation function. We prove that if $\sigma$ is element-wise, then the sample complexity of $\mathcal{H}$ is width independent and that this complexity is tight. Moreover, we show that the element-wise property of $\sigma$ is essential for width-independent bound, in the sense that there exist non-element-wise activation functions whose sample complexity is provably width-dependent. For the upper bound, we use the recent approach for norm-based bounds named Approximate Description Length (ADL) by arXiv:1910.05697. We further develop new techniques and tools for this approach, that will hopefully inspire future works.

最近，Daniely和Granot [Arxiv：1910.05697]引入了一种新的复杂性概念，称为近似描述长度（ADL）。他们用它来得出神经网络的新概括范围，尽管大量工作，但仍无法实现更古典的技术，例如离散化，覆盖数量和ademacher的复杂性。在本文中，我们探讨了ADL与功能复杂性的经典概念（例如覆盖数字和VC维度）的关系。我们发现，对于其范围是真实的函数，ADL基本上等同于这些经典的复杂性度量。但是，这种等效性破坏了高维范围的功能。

训练数据的量是决定学习算法的概括能力的关键因素之一。直观地，人们期望随着训练数据的增加，错误率将降低。也许令人惊讶的是，自然尝试正式化这种直觉引起了有趣且具有挑战性的数学问题。例如，在他们关于模式识别的古典书籍中，Devroye，Gyorfi和Lugosi（1996）询问是否存在{单调}贝叶斯一致的算法。这个问题一直开放25年以上，直到最近Pestov（2021）使用单调贝叶斯一致算法的复杂构造解决了该问题进行二进制分类。我们得出了多类分类的一般结果，表明每个学习算法A都可以转换为具有相似性能的单调。此外，转换是有效的，仅使用黑盒甲骨文访问A。 Loog（2019），Viering and Loog（2021）和Mhammedi（2021）。我们的转换很容易意味着在各种情况下单调学习者：例如，它将Pestov的结果扩展到具有任意数量的标签的分类任务。这与针对二进制分类量身定制的Pestov的工作形成鲜明对比。另外，我们在单调算法的误差上提供统一的边界。这使我们的转换适用于无分销设置。例如，在PAC学习中，这意味着每个可学习的课程都接受单调PAC学习者。这通过Viering，Mey和Loog（2019）解决了问题； Viering and Loog（2021）; Mhammedi（2021）。

我们考虑随着延迟梯度的随机优化，在每次步骤$ $，该算法使用步骤$ t-d_t $的陈旧随机梯度进行更新，从而为某些任意延迟$ d_t $。此设置摘要异步分布式优化，其中中央服务器接收由工作人员计算的渐变更新。这些机器可以体验可能随时间变化而变化的计算和通信负载。在一般的非凸平滑优化设置中，我们提供了一种简单且高效的算法，需要$ o（\ sigma ^ 2 / \ epsilon ^ 4 + \ tau / epsilon ^ 2）$步骤查找$ \ epsilon $ - 静止点$ x $，其中$ \ tau $是\ emph {平均}延迟$ \ smash {\ frac {1} {t} \ sum_ {t = 1} ^ t d_t} $和$ \ sigma ^ 2 $是随机梯度的方差。这改善了以前的工作，这表明随机梯度体面可以实现相同的速率，而是相对于\ emph {maximal}延迟$ \ max_ {t} d_t $，这可以显着大于平均延迟，特别是在异构分布式系统中。我们的实验证明了我们算法在延迟分布歪斜或重尾的情况下的效力和稳健性。

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.