Petrov-Galerkin formulations with optimal test functions allow for the stabilization of finite element simulations. In particular, given a discrete trial space, the optimal test space induces a numerical scheme delivering the best approximation in terms of a problem-dependent energy norm. This ideal approach has two shortcomings: first, we need to explicitly know the set of optimal test functions; and second, the optimal test functions may have large supports inducing expensive dense linear systems. Nevertheless, parametric families of PDEs are an example where it is worth investing some (offline) computational effort to obtain stabilized linear systems that can be solved efficiently, for a given set of parameters, in an online stage. Therefore, as a remedy for the first shortcoming, we explicitly compute (offline) a function mapping any PDE-parameter, to the matrix of coefficients of optimal test functions (in a basis expansion) associated with that PDE-parameter. Next, as a remedy for the second shortcoming, we use the low-rank approximation to hierarchically compress the (non-square) matrix of coefficients of optimal test functions. In order to accelerate this process, we train a neural network to learn a critical bottleneck of the compression algorithm (for a given set of PDE-parameters). When solving online the resulting (compressed) Petrov-Galerkin formulation, we employ a GMRES iterative solver with inexpensive matrix-vector multiplications thanks to the low-rank features of the compressed matrix. We perform experiments showing that the full online procedure as fast as the original (unstable) Galerkin approach. In other words, we get the stabilization with hierarchical matrices and neural networks practically for free. We illustrate our findings by means of 2D Eriksson-Johnson and Hemholtz model problems.

我们展示了如何构建深度神经网络（DNN）专家，以预测给定计算问题的准最佳$ HP $ - 翻新。主要想法是在执行自适应$ HP $ -FINITE元素方法（$ HP $ -FEM）算法的过程中培训DNN专家，并以后使用它来预测进一步的$ HP $细化。在培训中，我们使用两个网格范式自适应$ HP $ -FEM算法。它采用精细网格为粗网格元素提供最佳$ HP $改进。我们旨在构建DNN专家，以识别粗网格元素的准最佳$ HP $改进。在训练阶段，我们使用直接求解器获取细网元的溶液，以指导粗网格元件上的最佳修补。训练后，我们关闭了自适应$ hp $ -FEM算法，并继续按照受过DNN专家培训的DNN专家提出的准优化细化。我们测试了三维FICHERA和二维L形域问题的方法。我们验证数值相对于网格尺寸的收敛性。我们表明，如果我们继续使用经过适当培训的DNN专家进行改进，则可以保留由自适应$ hp $ -FEM提供的指数融合。因此，在本文中，我们表明，从自适应$ hp $ -fem中，可以训练DNN专家的奇异性位置，并继续选择准最佳的$ hp $ previness该方法的指数收敛性。

The celebrated proverb that "speech is silver, silence is golden" has a long multinational history and multiple specific meanings. In written texts punctuation can in fact be considered one of its manifestations. Indeed, the virtue of effectively speaking and writing involves - often decisively - the capacity to apply the properly placed breaks. In the present study, based on a large corpus of world-famous and representative literary texts in seven major Western languages, it is shown that the distribution of intervals between consecutive punctuation marks in almost all texts can universally be characterised by only two parameters of the discrete Weibull distribution which can be given an intuitive interpretation in terms of the so-called hazard function. The values of these two parameters tend to be language-specific, however, and even appear to navigate translations. The properties of the computed hazard functions indicate that among the studied languages, English turns out to be the least constrained by the necessity to place a consecutive punctuation mark to partition a sequence of words. This may suggest that when compared to other studied languages, English is more flexible, in the sense of allowing longer uninterrupted sequences of words. Spanish reveals similar tendency to only a bit lesser extent.

Recent advances in visual representation learning allowed to build an abundance of powerful off-the-shelf features that are ready-to-use for numerous downstream tasks. This work aims to assess how well these features preserve information about the objects, such as their spatial location, their visual properties and their relative relationships. We propose to do so by evaluating them in the context of visual reasoning, where multiple objects with complex relationships and different attributes are at play. More specifically, we introduce a protocol to evaluate visual representations for the task of Visual Question Answering. In order to decouple visual feature extraction from reasoning, we design a specific attention-based reasoning module which is trained on the frozen visual representations to be evaluated, in a spirit similar to standard feature evaluations relying on shallow networks. We compare two types of visual representations, densely extracted local features and object-centric ones, against the performances of a perfect image representation using ground truth. Our main findings are two-fold. First, despite excellent performances on classical proxy tasks, such representations fall short for solving complex reasoning problem. Second, object-centric features better preserve the critical information necessary to perform visual reasoning. In our proposed framework we show how to methodologically approach this evaluation.

Language models are widely deployed to provide automatic text completion services in user products. However, recent research has revealed that language models (especially large ones) bear considerable risk of memorizing private training data, which is then vulnerable to leakage and extraction by adversaries. In this study, we test the efficacy of a range of privacy-preserving techniques to mitigate unintended memorization of sensitive user text, while varying other factors such as model size and adversarial conditions. We test both "heuristic" mitigations (those without formal privacy guarantees) and Differentially Private training, which provides provable levels of privacy at the cost of some model performance. Our experiments show that (with the exception of L2 regularization), heuristic mitigations are largely ineffective in preventing memorization in our test suite, possibly because they make too strong of assumptions about the characteristics that define "sensitive" or "private" text. In contrast, Differential Privacy reliably prevents memorization in our experiments, despite its computational and model-performance costs.

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.

This paper presents a method for detection and recognition of traffic signs based on information extracted from an event camera. The solution used a FireNet deep convolutional neural network to reconstruct events into greyscale frames. Two YOLOv4 network models were trained, one based on greyscale images and the other on colour images. The best result was achieved for the model trained on the basis of greyscale images, achieving an efficiency of 87.03%.

This paper proposes the use of an event camera as a component of a vision system that enables counting of fast-moving objects - in this case, falling corn grains. These type of cameras transmit information about the change in brightness of individual pixels and are characterised by low latency, no motion blur, correct operation in different lighting conditions, as well as very low power consumption. The proposed counting algorithm processes events in real time. The operation of the solution was demonstrated on a stand consisting of a chute with a vibrating feeder, which allowed the number of grains falling to be adjusted. The objective of the control system with a PID controller was to maintain a constant average number of falling objects. The proposed solution was subjected to a series of tests to determine the correctness of the developed method operation. On their basis, the validity of using an event camera to count small, fast-moving objects and the associated wide range of potential industrial applications can be confirmed.

The Graph Protocol indexes historical blockchain transaction data and makes it available for querying. As the protocol is decentralized, there are many independent Indexers that index and compete with each other for serving queries to the Consumers. One dimension along which Indexers compete is pricing. In this paper, we propose a bandit-based algorithm for maximization of Indexers' revenue via Consumer budget discovery. We present the design and the considerations we had to make for a dynamic pricing algorithm being used by multiple agents simultaneously. We discuss the results achieved by our dynamic pricing bandits both in simulation and deployed into production on one of the Indexers operating on Ethereum. We have open-sourced both the simulation framework and tools we created, which other Indexers have since started to adapt into their own workflows.

We apply the Hierarchical Autoregressive Neural (HAN) network sampling algorithm to the two-dimensional $Q$-state Potts model and perform simulations around the phase transition at $Q=12$. We quantify the performance of the approach in the vicinity of the first-order phase transition and compare it with that of the Wolff cluster algorithm. We find a significant improvement as far as the statistical uncertainty is concerned at a similar numerical effort. In order to efficiently train large neural networks we introduce the technique of pre-training. It allows to train some neural networks using smaller system sizes and then employing them as starting configurations for larger system sizes. This is possible due to the recursive construction of our hierarchical approach. Our results serve as a demonstration of the performance of the hierarchical approach for systems exhibiting bimodal distributions. Additionally, we provide estimates of the free energy and entropy in the vicinity of the phase transition with statistical uncertainties of the order of $10^{-7}$ for the former and $10^{-3}$ for the latter based on a statistics of $10^6$ configurations.