This paper describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to higher-order logic in the TPTP languages using an embedding approach, and solved using higher-order logic ATP systems. Additionally, the results from native modal logic ATP systems are considered, and compared with those from the embedding approach. The conclusions are that (i) The embedding process is reliable and successful. (ii) The choice of backend ATP system can significantly impact the performance of the embedding approach. (iii) Native modal logic ATP systems outperform the embedding approach. (iv) The embedding approach can cope with a wider range modal logics than the native modal systems considered.

LegalRuleml是一个全面的基于XML的表示框架，用于建模和交换规范规则。另一方面，TPTP输入和输出格式是与自动推理系统相互作用的通用标准。在本文中，我们通过（i）基于TPTP格式定义逻辑多同性规范性推理语言，提供了两个社区之间的桥梁，（ii）在合法方面的相关片段和该语言之间提供翻译方案，以及（iii）建议基于此翻译的自动规范推理的灵活体系结构。我们用三种不同的规范逻辑实例化并证明了该方法。

我们报告了使用高阶自动定理掠夺（ATP）对Boolos奇怪推理变体的探索。令人惊讶的是，仍然只需要手工提供单个速记符号。计算机会自动发现所有获得简短证明所需的高阶引理。鉴于本文的观察和建议，Boolos在证明长度的加速和相关示例中的示例的全面自动化似乎是高阶ATP的范围。

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.