通过内插机器在信号处理和机器学习中的新兴作用的推动，这项工作考虑了过度参数化矩阵分子的计算方面。在这种情况下，优化景观可能包含虚假的固定点（SSP），其被证明是全级矩阵。这些SSP的存在意味着不可能希望任何全球担保过度参数化矩阵分解。例如，当在SSP上初始化时，梯度流将永远被删除。尽管如此，尽管有这些SSP，我们在这项工作中建立了相应的优势函数的梯度流到全局最小化器，只要其初始化是缺陷并且足够接近可行性问题的可行性集合。我们在数值上观察到，当随机初始化时，通过原始 - 双算法启发的提出梯度流的启发式离散化是成功的。我们的结果与当地的细化方法形成鲜明的对比，该方法需要初始化接近优化问题的最佳集合。更具体地，我们成功避免了SSPS设置的陷阱，因为梯度流始终仍然是缺陷，而不是因为附近没有SSP。后者是本地细化方法的情况。此外，广泛使用的限制性肌肉属性在我们的主要结果中没有作用。

过度分辨率是指选择神经网络的宽度，使得学习算法可以在非凸训练中可被估计零损失的重要现象。现有理论建立了各种初始化策略，培训修改和宽度缩放等全局融合。特别地，最先进的结果要求宽度以二次逐步缩放，并在实践中使用的标准初始化策略下进行培训数据的数量，以获得最佳泛化性能。相比之下，最新的结果可以获得线性缩放，需要导致导致“懒惰训练”的初始化，或者仅训练单层。在这项工作中，我们提供了一个分析框架，使我们能够采用标准的初始化策略，可能避免懒惰的训练，并在基本浅色神经网络中同时培训所有层，同时获得网络宽度的理想子标缩放。我们通过Polyak-Lojasiewicz条件，平滑度和数据标准假设实现了Desiderata，并使用随机矩阵理论的工具。

We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the rank minimization of a nonlinear feature map applied to the original matrix, which is then further approximated by a constrained non-convex optimization problem involving the Grassmann manifold. We propose two sets of algorithms, one arising from Riemannian optimization and the other as an alternating minimization scheme, both of which include first- and second-order variants. Both sets of algorithms have theoretical guarantees. In particular, for the alternating minimization, we establish global convergence and worst-case complexity bounds. Additionally, using the Kurdyka-Lojasiewicz property, we show that the alternating minimization converges to a unique limit point. We provide extensive numerical results for the recovery of union of subspaces and clustering under entry sampling and dense Gaussian sampling. Our methods are competitive with existing approaches and, in particular, high accuracy is achieved in the recovery using Riemannian second-order methods.

State space models (SSMs) have demonstrated state-of-the-art sequence modeling performance in some modalities, but underperform attention in language modeling. Moreover, despite scaling nearly linearly in sequence length instead of quadratically, SSMs are still slower than Transformers due to poor hardware utilization. In this paper, we make progress on understanding the expressivity gap between SSMs and attention in language modeling, and on reducing the hardware barrier between SSMs and attention. First, we use synthetic language modeling tasks to understand the gap between SSMs and attention. We find that existing SSMs struggle with two capabilities: recalling earlier tokens in the sequence and comparing tokens across the sequence. To understand the impact on language modeling, we propose a new SSM layer, H3, that is explicitly designed for these abilities. H3 matches attention on the synthetic languages and comes within 0.4 PPL of Transformers on OpenWebText. Furthermore, a hybrid 125M-parameter H3-attention model that retains two attention layers surprisingly outperforms Transformers on OpenWebText by 1.0 PPL. Next, to improve the efficiency of training SSMs on modern hardware, we propose FlashConv. FlashConv uses a fused block FFT algorithm to improve efficiency on sequences up to 8K, and introduces a novel state passing algorithm that exploits the recurrent properties of SSMs to scale to longer sequences. FlashConv yields 2$\times$ speedup on the long-range arena benchmark and allows hybrid language models to generate text 1.6$\times$ faster than Transformers. Using FlashConv, we scale hybrid H3-attention language models up to 1.3B parameters on the Pile and find promising initial results, achieving lower perplexity than Transformers and outperforming Transformers in zero- and few-shot learning on a majority of tasks in the SuperGLUE benchmark.

Recently, Smart Video Surveillance (SVS) systems have been receiving more attention among scholars and developers as a substitute for the current passive surveillance systems. These systems are used to make the policing and monitoring systems more efficient and improve public safety. However, the nature of these systems in monitoring the public's daily activities brings different ethical challenges. There are different approaches for addressing privacy issues in implementing the SVS. In this paper, we are focusing on the role of design considering ethical and privacy challenges in SVS. Reviewing four policy protection regulations that generate an overview of best practices for privacy protection, we argue that ethical and privacy concerns could be addressed through four lenses: algorithm, system, model, and data. As an case study, we describe our proposed system and illustrate how our system can create a baseline for designing a privacy perseverance system to deliver safety to society. We used several Artificial Intelligence algorithms, such as object detection, single and multi camera re-identification, action recognition, and anomaly detection, to provide a basic functional system. We also use cloud-native services to implement a smartphone application in order to deliver the outputs to the end users.

In recent years, nonlinear model predictive control (NMPC) has been extensively used for solving automotive motion control and planning tasks. In order to formulate the NMPC problem, different coordinate systems can be used with different advantages. We propose and compare formulations for the NMPC related optimization problem, involving a Cartesian and a Frenet coordinate frame (CCF/ FCF) in a single nonlinear program (NLP). We specify costs and collision avoidance constraints in the more advantageous coordinate frame, derive appropriate formulations and compare different obstacle constraints. With this approach, we exploit the simpler formulation of opponent vehicle constraints in the CCF, as well as road aligned costs and constraints related to the FCF. Comparisons to other approaches in a simulation framework highlight the advantages of the proposed approaches.

Automated Program Repair (APR) is defined as the process of fixing a bug/defect in the source code, by an automated tool. APR tools have recently experienced promising results by leveraging state-of-the-art Neural Language Processing (NLP) techniques. APR tools such as TFix and CodeXGLUE combine text-to-text transformers with software-specific techniques are outperforming alternatives, these days. However, in most APR studies the train and test sets are chosen from the same set of projects. In reality, however, APR models are meant to be generalizable to new and different projects. Therefore, there is a potential threat that reported APR models with high effectiveness perform poorly when the characteristics of the new project or its bugs are different than the training set's(Domain Shift). In this study, we first define and measure the domain shift problem in automated program repair. Then, we then propose a domain adaptation framework that can adapt an APR model for a given target project. We conduct an empirical study with three domain adaptation methods FullFineTuning, TuningWithLightWeightAdapterLayers, and CurriculumLearning using two state-of-the-art domain adaptation tools (TFix and CodeXGLUE) and two APR models on 611 bugs from 19 projects. The results show that our proposed framework can improve the effectiveness of TFix by 13.05% and CodeXGLUE by 23.4%. Another contribution of this study is the proposal of a data synthesis method to address the lack of labelled data in APR. We leverage transformers to create a bug generator model. We use the generated synthetic data to domain adapt TFix and CodeXGLUE on the projects with no data (Zero-shot learning), which results in an average improvement of 5.76% and 24.42% for TFix and CodeXGLUE, respectively.

In recent years, we have seen a significant interest in data-driven deep learning approaches for video anomaly detection, where an algorithm must determine if specific frames of a video contain abnormal behaviors. However, video anomaly detection is particularly context-specific, and the availability of representative datasets heavily limits real-world accuracy. Additionally, the metrics currently reported by most state-of-the-art methods often do not reflect how well the model will perform in real-world scenarios. In this article, we present the Charlotte Anomaly Dataset (CHAD). CHAD is a high-resolution, multi-camera anomaly dataset in a commercial parking lot setting. In addition to frame-level anomaly labels, CHAD is the first anomaly dataset to include bounding box, identity, and pose annotations for each actor. This is especially beneficial for skeleton-based anomaly detection, which is useful for its lower computational demand in real-world settings. CHAD is also the first anomaly dataset to contain multiple views of the same scene. With four camera views and over 1.15 million frames, CHAD is the largest fully annotated anomaly detection dataset including person annotations, collected from continuous video streams from stationary cameras for smart video surveillance applications. To demonstrate the efficacy of CHAD for training and evaluation, we benchmark two state-of-the-art skeleton-based anomaly detection algorithms on CHAD and provide comprehensive analysis, including both quantitative results and qualitative examination.

In many high-dimensional prediction or classification tasks, complementary data on the features are available, e.g. prior biological knowledge on (epi)genetic markers. Here we consider tasks with numerical prior information that provide an insight into the importance (weight) and the direction (sign) of the feature effects, e.g. regression coefficients from previous studies. We propose an approach for integrating multiple sources of such prior information into penalised regression. If suitable co-data are available, this improves the predictive performance, as shown by simulation and application. The proposed method is implemented in the R package `transreg' (https://github.com/lcsb-bds/transreg).

Early on during a pandemic, vaccine availability is limited, requiring prioritisation of different population groups. Evaluating vaccine allocation is therefore a crucial element of pandemics response. In the present work, we develop a model to retrospectively evaluate age-dependent counterfactual vaccine allocation strategies against the COVID-19 pandemic. To estimate the effect of allocation on the expected severe-case incidence, we employ a simulation-assisted causal modelling approach which combines a compartmental infection-dynamics simulation, a coarse-grained, data-driven causal model and literature estimates for immunity waning. We compare Israel's implemented vaccine allocation strategy in 2021 to counterfactual strategies such as no prioritisation, prioritisation of younger age groups or a strict risk-ranked approach; we find that Israel's implemented strategy was indeed highly effective. We also study the marginal impact of increasing vaccine uptake for a given age group and find that increasing vaccinations in the elderly is most effective at preventing severe cases, whereas additional vaccinations for middle-aged groups reduce infections most effectively. Due to its modular structure, our model can easily be adapted to study future pandemics. We demonstrate this flexibility by investigating vaccine allocation strategies for a pandemic with characteristics of the Spanish Flu. Our approach thus helps evaluate vaccination strategies under the complex interplay of core epidemic factors, including age-dependent risk profiles, immunity waning, vaccine availability and spreading rates.