最近关于神经象征性归纳逻辑编程的工作导致了有希望的方法，可以从嘈杂，现实世界数据中学习解释规则。虽然一些提议近似逻辑运算符，具有不同的逻辑，从模糊或实际值逻辑，无参数，从而无参数，从而减少它们适合数据的容量，其他方法仅基于逻辑摆动，使得难以解释学习的“规则”。在本文中，我们提出了与最近提出的逻辑神经网络（LNN）的学习规则。与其他人相比，LNN与经典布尔逻辑的强大连接，从而允许精确地解释学习规则，同时覆盆可以用基于梯度的优化训练的参数来有效地拟合数据。我们将LNN扩展以在一阶逻辑中引导规则。我们对标准基准测试任务的实验证实，LNN规则是高度可解释的，并且由于其灵活的参数化而可以实现可比或更高的准确性。

实用值的逻辑是越来越多的神经符号方法的基础，尽管通常仅在定性上表征其逻辑推理能力。我们为建立此类系统的正确性和力量提供了基础。我们提供了声音和强烈完整的公理化，可以参数化以涵盖所有实现的逻辑，包括所有常见的模糊逻辑。我们的一类句子非常丰富，每个句子都描述了一组现实价值逻辑公式集合的可能的真实值，包括实际值的组合是可能的。强大的完整性使我们能够准确地得出有关公式集合的真实价值组合的组合，给出了有关其他几个公式集合的真实价值组合的信息。然后，我们扩展公理化以处理加权的子形成。最后，我们根据线性编程为某些实价逻辑和某些自然假设提供了基于线性编程的决策程序，无论我们的一组句子在逻辑上是否意味着我们的另一种句子。

In the past years, deep learning has seen an increase of usage in the domain of histopathological applications. However, while these approaches have shown great potential, in high-risk environments deep learning models need to be able to judge their own uncertainty and be able to reject inputs when there is a significant chance of misclassification. In this work, we conduct a rigorous evaluation of the most commonly used uncertainty and robustness methods for the classification of Whole-Slide-Images under domain shift using the H\&E stained Camelyon17 breast cancer dataset. Although it is known that histopathological data can be subject to strong domain shift and label noise, to our knowledge this is the first work that compares the most common methods for uncertainty estimation under these aspects. In our experiments, we compare Stochastic Variational Inference, Monte-Carlo Dropout, Deep Ensembles, Test-Time Data Augmentation as well as combinations thereof. We observe that ensembles of methods generally lead to higher accuracies and better calibration and that Test-Time Data Augmentation can be a promising alternative when choosing an appropriate set of augmentations. Across methods, a rejection of the most uncertain tiles leads to a significant increase in classification accuracy on both in-distribution as well as out-of-distribution data. Furthermore, we conduct experiments comparing these methods under varying conditions of label noise. We observe that the border regions of the Camelyon17 dataset are subject to label noise and evaluate the robustness of the included methods against different noise levels. Lastly, we publish our code framework to facilitate further research on uncertainty estimation on histopathological data.

Charisma is considered as one's ability to attract and potentially also influence others. Clearly, there can be considerable interest from an artificial intelligence's (AI) perspective to provide it with such skill. Beyond, a plethora of use cases opens up for computational measurement of human charisma, such as for tutoring humans in the acquisition of charisma, mediating human-to-human conversation, or identifying charismatic individuals in big social data. A number of models exist that base charisma on various dimensions, often following the idea that charisma is given if someone could and would help others. Examples include influence (could help) and affability (would help) in scientific studies or power (could help), presence, and warmth (both would help) as a popular concept. Modelling high levels in these dimensions for humanoid robots or virtual agents, seems accomplishable. Beyond, also automatic measurement appears quite feasible with the recent advances in the related fields of Affective Computing and Social Signal Processing. Here, we, thereforem present a blueprint for building machines that can appear charismatic, but also analyse the charisma of others. To this end, we first provide the psychological perspective including different models of charisma and behavioural cues of it. We then switch to conversational charisma in spoken language as an exemplary modality that is essential for human-human and human-computer conversations. The computational perspective then deals with the recognition and generation of charismatic behaviour by AI. This includes an overview of the state of play in the field and the aforementioned blueprint. We then name exemplary use cases of computational charismatic skills before switching to ethical aspects and concluding this overview and perspective on building charisma-enabled AI.

Deep learning-based 3D human pose estimation performs best when trained on large amounts of labeled data, making combined learning from many datasets an important research direction. One obstacle to this endeavor are the different skeleton formats provided by different datasets, i.e., they do not label the same set of anatomical landmarks. There is little prior research on how to best supervise one model with such discrepant labels. We show that simply using separate output heads for different skeletons results in inconsistent depth estimates and insufficient information sharing across skeletons. As a remedy, we propose a novel affine-combining autoencoder (ACAE) method to perform dimensionality reduction on the number of landmarks. The discovered latent 3D points capture the redundancy among skeletons, enabling enhanced information sharing when used for consistency regularization. Our approach scales to an extreme multi-dataset regime, where we use 28 3D human pose datasets to supervise one model, which outperforms prior work on a range of benchmarks, including the challenging 3D Poses in the Wild (3DPW) dataset. Our code and models are available for research purposes.

This article concerns Bayesian inference using deep linear networks with output dimension one. In the interpolating (zero noise) regime we show that with Gaussian weight priors and MSE negative log-likelihood loss both the predictive posterior and the Bayesian model evidence can be written in closed form in terms of a class of meromorphic special functions called Meijer-G functions. These results are non-asymptotic and hold for any training dataset, network depth, and hidden layer widths, giving exact solutions to Bayesian interpolation using a deep Gaussian process with a Euclidean covariance at each layer. Through novel asymptotic expansions of Meijer-G functions, a rich new picture of the role of depth emerges. Specifically, we find that the posteriors in deep linear networks with data-independent priors are the same as in shallow networks with evidence maximizing data-dependent priors. In this sense, deep linear networks make provably optimal predictions. We also prove that, starting from data-agnostic priors, Bayesian model evidence in wide networks is only maximized at infinite depth. This gives a principled reason to prefer deeper networks (at least in the linear case). Finally, our results show that with data-agnostic priors a novel notion of effective depth given by \[\#\text{hidden layers}\times\frac{\#\text{training data}}{\text{network width}}\] determines the Bayesian posterior in wide linear networks, giving rigorous new scaling laws for generalization error.

In this paper we study the smooth strongly convex minimization problem $\min_{x}\min_y f(x,y)$. The existing optimal first-order methods require $\mathcal{O}(\sqrt{\max\{\kappa_x,\kappa_y\}} \log 1/\epsilon)$ of computations of both $\nabla_x f(x,y)$ and $\nabla_y f(x,y)$, where $\kappa_x$ and $\kappa_y$ are condition numbers with respect to variable blocks $x$ and $y$. We propose a new algorithm that only requires $\mathcal{O}(\sqrt{\kappa_x} \log 1/\epsilon)$ of computations of $\nabla_x f(x,y)$ and $\mathcal{O}(\sqrt{\kappa_y} \log 1/\epsilon)$ computations of $\nabla_y f(x,y)$. In some applications $\kappa_x \gg \kappa_y$, and computation of $\nabla_y f(x,y)$ is significantly cheaper than computation of $\nabla_x f(x,y)$. In this case, our algorithm substantially outperforms the existing state-of-the-art methods.

This paper presents a solution to the GenChal 2022 shared task dedicated to feedback comment generation for writing learning. In terms of this task given a text with an error and a span of the error, a system generates an explanatory note that helps the writer (language learner) to improve their writing skills. Our solution is based on fine-tuning the T5 model on the initial dataset augmented according to syntactical dependencies of the words located within indicated error span. The solution of our team "nigula" obtained second place according to manual evaluation by the organizers.

Autoencoders are a popular model in many branches of machine learning and lossy data compression. However, their fundamental limits, the performance of gradient methods and the features learnt during optimization remain poorly understood, even in the two-layer setting. In fact, earlier work has considered either linear autoencoders or specific training regimes (leading to vanishing or diverging compression rates). Our paper addresses this gap by focusing on non-linear two-layer autoencoders trained in the challenging proportional regime in which the input dimension scales linearly with the size of the representation. Our results characterize the minimizers of the population risk, and show that such minimizers are achieved by gradient methods; their structure is also unveiled, thus leading to a concise description of the features obtained via training. For the special case of a sign activation function, our analysis establishes the fundamental limits for the lossy compression of Gaussian sources via (shallow) autoencoders. Finally, while the results are proved for Gaussian data, numerical simulations on standard datasets display the universality of the theoretical predictions.

We introduce a machine-learning (ML)-based weather simulator--called "GraphCast"--which outperforms the most accurate deterministic operational medium-range weather forecasting system in the world, as well as all previous ML baselines. GraphCast is an autoregressive model, based on graph neural networks and a novel high-resolution multi-scale mesh representation, which we trained on historical weather data from the European Centre for Medium-Range Weather Forecasts (ECMWF)'s ERA5 reanalysis archive. It can make 10-day forecasts, at 6-hour time intervals, of five surface variables and six atmospheric variables, each at 37 vertical pressure levels, on a 0.25-degree latitude-longitude grid, which corresponds to roughly 25 x 25 kilometer resolution at the equator. Our results show GraphCast is more accurate than ECMWF's deterministic operational forecasting system, HRES, on 90.0% of the 2760 variable and lead time combinations we evaluated. GraphCast also outperforms the most accurate previous ML-based weather forecasting model on 99.2% of the 252 targets it reported. GraphCast can generate a 10-day forecast (35 gigabytes of data) in under 60 seconds on Cloud TPU v4 hardware. Unlike traditional forecasting methods, ML-based forecasting scales well with data: by training on bigger, higher quality, and more recent data, the skill of the forecasts can improve. Together these results represent a key step forward in complementing and improving weather modeling with ML, open new opportunities for fast, accurate forecasting, and help realize the promise of ML-based simulation in the physical sciences.