在这项工作中，我们研究了随机特征矩阵$ m = yy ^ \ ast $的渐近光谱密度用一个单独的层神经网络生成的$ y = f（wx）$，其中$ w $和$ x $是带有IID的随机矩形矩阵中心条目和$ F $是一种非线性光滑功能，其应用进入明智。我们证明了限制光谱分布的Stieltjes转换大致满足四个自我一致的等式，这正是通过[Pennityton，Worah]和[Benigni，P \'E]获得的等式。我们将以前的结果扩展到附加偏见$ Y = F（WX + B）$的情况下，以$ B $为一个独立的秩 - 一个高斯随机矩阵，更接近实践中遇到的神经网络基础架构。我们的主要发现是，在添加剂偏差的情况下，不可能选择保持层到层奇异值分布的激活函数，与无偏置的情况鲜明对比，其中简单的积分约束足以实现非偏光曲线。为了获得经验谱密度的渐近学，我们通过累积扩展来遵循从随机矩阵理论的解析方法。我们发现这种方法比瞬间方法更强大，而且组合较少，并期望它也适用于前者的组合物变得棘手的模型。已经广泛采用了解析方法，但与以前的作品相比，这里应用于非线性随机矩阵。

The analysis of network structure is essential to many scientific areas, ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO based approach that only needs number-of-nodes many qubits and is represented by a QUBO-matrix as sparse as the input graph's adjacency matrix. The substantial improvement on the sparsity of the QUBO-matrix, which is typically very dense in related work, is achieved through the novel concept of separation-nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which -- upon its removal from the graph -- yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept. This work hence displays a promising approach to NISQ ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large scale, real world problem instances.

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal prediction in order to obtain coverage guarantees for the error bounds, without making any assumption on the underlying data distribution. It is generally applicable to Bayesian regularization approaches, independent, e.g., of the concrete choice of the prior. Furthermore, the coverage guarantees can also be obtained in case only approximate sampling from the posterior is possible. With this in particular, the proposed framework is able to incorporate any learned prior in a black-box manner. Guaranteed coverage without assumptions on the underlying distributions is only achievable since the magnitude of the error bounds is, in general, unknown in advance. Nevertheless, experiments with multiple regularization approaches presented in the paper confirm that in practice, the obtained error bounds are rather tight. For realizing the numerical experiments, also a novel primal-dual Langevin algorithm for sampling from non-smooth distributions is introduced in this work.

Machine learning (ML) on graph-structured data has recently received deepened interest in the context of intrusion detection in the cybersecurity domain. Due to the increasing amounts of data generated by monitoring tools as well as more and more sophisticated attacks, these ML methods are gaining traction. Knowledge graphs and their corresponding learning techniques such as Graph Neural Networks (GNNs) with their ability to seamlessly integrate data from multiple domains using human-understandable vocabularies, are finding application in the cybersecurity domain. However, similar to other connectionist models, GNNs are lacking transparency in their decision making. This is especially important as there tend to be a high number of false positive alerts in the cybersecurity domain, such that triage needs to be done by domain experts, requiring a lot of man power. Therefore, we are addressing Explainable AI (XAI) for GNNs to enhance trust management by exploring combining symbolic and sub-symbolic methods in the area of cybersecurity that incorporate domain knowledge. We experimented with this approach by generating explanations in an industrial demonstrator system. The proposed method is shown to produce intuitive explanations for alerts for a diverse range of scenarios. Not only do the explanations provide deeper insights into the alerts, but they also lead to a reduction of false positive alerts by 66% and by 93% when including the fidelity metric.

This paper extends quantile factor analysis to a probabilistic variant that incorporates regularization and computationally efficient variational approximations. By means of synthetic and real data experiments it is established that the proposed estimator can achieve, in many cases, better accuracy than a recently proposed loss-based estimator. We contribute to the literature on measuring uncertainty by extracting new indexes of low, medium and high economic policy uncertainty, using the probabilistic quantile factor methodology. Medium and high indexes have clear contractionary effects, while the low index is benign for the economy, showing that not all manifestations of uncertainty are the same.

Earthquakes, fire, and floods often cause structural collapses of buildings. The inspection of damaged buildings poses a high risk for emergency forces or is even impossible, though. We present three recent selected missions of the Robotics Task Force of the German Rescue Robotics Center, where both ground and aerial robots were used to explore destroyed buildings. We describe and reflect the missions as well as the lessons learned that have resulted from them. In order to make robots from research laboratories fit for real operations, realistic test environments were set up for outdoor and indoor use and tested in regular exercises by researchers and emergency forces. Based on this experience, the robots and their control software were significantly improved. Furthermore, top teams of researchers and first responders were formed, each with realistic assessments of the operational and practical suitability of robotic systems.

The number of international benchmarking competitions is steadily increasing in various fields of machine learning (ML) research and practice. So far, however, little is known about the common practice as well as bottlenecks faced by the community in tackling the research questions posed. To shed light on the status quo of algorithm development in the specific field of biomedical imaging analysis, we designed an international survey that was issued to all participants of challenges conducted in conjunction with the IEEE ISBI 2021 and MICCAI 2021 conferences (80 competitions in total). The survey covered participants' expertise and working environments, their chosen strategies, as well as algorithm characteristics. A median of 72% challenge participants took part in the survey. According to our results, knowledge exchange was the primary incentive (70%) for participation, while the reception of prize money played only a minor role (16%). While a median of 80 working hours was spent on method development, a large portion of participants stated that they did not have enough time for method development (32%). 25% perceived the infrastructure to be a bottleneck. Overall, 94% of all solutions were deep learning-based. Of these, 84% were based on standard architectures. 43% of the respondents reported that the data samples (e.g., images) were too large to be processed at once. This was most commonly addressed by patch-based training (69%), downsampling (37%), and solving 3D analysis tasks as a series of 2D tasks. K-fold cross-validation on the training set was performed by only 37% of the participants and only 50% of the participants performed ensembling based on multiple identical models (61%) or heterogeneous models (39%). 48% of the respondents applied postprocessing steps.

Modeling perception sensors is key for simulation based testing of automated driving functions. Beyond weather conditions themselves, sensors are also subjected to object dependent environmental influences like tire spray caused by vehicles moving on wet pavement. In this work, a novel modeling approach for spray in lidar data is introduced. The model conforms to the Open Simulation Interface (OSI) standard and is based on the formation of detection clusters within a spray plume. The detections are rendered with a simple custom ray casting algorithm without the need of a fluid dynamics simulation or physics engine. The model is subsequently used to generate training data for object detection algorithms. It is shown that the model helps to improve detection in real-world spray scenarios significantly. Furthermore, a systematic real-world data set is recorded and published for analysis, model calibration and validation of spray effects in active perception sensors. Experiments are conducted on a test track by driving over artificially watered pavement with varying vehicle speeds, vehicle types and levels of pavement wetness. All models and data of this work are available open source.

The text-to-image model Stable Diffusion has recently become very popular. Only weeks after its open source release, millions are experimenting with image generation. This is due to its ease of use, since all it takes is a brief description of the desired image to "prompt" the generative model. Rarely do the images generated for a new prompt immediately meet the user's expectations. Usually, an iterative refinement of the prompt ("prompt engineering") is necessary for satisfying images. As a new perspective, we recast image prompt engineering as interactive image retrieval - on an "infinite index". Thereby, a prompt corresponds to a query and prompt engineering to query refinement. Selected image-prompt pairs allow direct relevance feedback, as the model can modify an image for the refined prompt. This is a form of one-sided interactive retrieval, where the initiative is on the user side, whereas the server side remains stateless. In light of an extensive literature review, we develop these parallels in detail and apply the findings to a case study of a creative search task on such a model. We note that the uncertainty in searching an infinite index is virtually never-ending. We also discuss future research opportunities related to retrieval models specialized for generative models and interactive generative image retrieval. The application of IR technology, such as query reformulation and relevance feedback, will contribute to improved workflows when using generative models, while the notion of an infinite index raises new challenges in IR research.

Large, text-conditioned generative diffusion models have recently gained a lot of attention for their impressive performance in generating high-fidelity images from text alone. However, achieving high-quality results is almost unfeasible in a one-shot fashion. On the contrary, text-guided image generation involves the user making many slight changes to inputs in order to iteratively carve out the envisioned image. However, slight changes to the input prompt often lead to entirely different images being generated, and thus the control of the artist is limited in its granularity. To provide flexibility, we present the Stable Artist, an image editing approach enabling fine-grained control of the image generation process. The main component is semantic guidance (SEGA) which steers the diffusion process along variable numbers of semantic directions. This allows for subtle edits to images, changes in composition and style, as well as optimization of the overall artistic conception. Furthermore, SEGA enables probing of latent spaces to gain insights into the representation of concepts learned by the model, even complex ones such as 'carbon emission'. We demonstrate the Stable Artist on several tasks, showcasing high-quality image editing and composition.