从样本中学习概率分布的任务在整个自然科学中无处不在。局部量子电路的输出分布构成了一类特别有趣的分布类别，对量子优势提案和各种量子机学习算法都具有关键的重要性。在这项工作中，我们提供了局部量子电路输出分布的可学习性的广泛表征。我们的第一个结果可以深入了解这些分布的有效学习性与有效的可模拟性之间的关系。具体而言，我们证明与Clifford电路相关的密度建模问题可以有效地解决，而对于深度$ d = n^{\ omega（1）} $电路，将单个$ t $ gate注入到电路中，这使这是如此问题很难。该结果表明，有效的模拟性并不意味着有效的可学习性。我们的第二组结果提供了对量子生成建模算法的潜在和局限性的见解。我们首先证明与深度$ d = n^{\ omega（1）} $局部量子电路相关的生成建模问题对于任何学习算法，经典或量子都很难。结果，一个人不能使用量子算法来为此任务获得实际优势。然后，我们证明，对于各种最实际相关的学习算法（包括混合量词古典算法），即使是与深度$ d = \ omega（\ log（n））$ Clifford Circuits相关的生成建模问题也是如此难的。该结果对近期混合量子古典生成建模算法的适用性造成了限制。

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.

For small training set sizes $P$, the generalization error of wide neural networks is well-approximated by the error of an infinite width neural network (NN), either in the kernel or mean-field/feature-learning regime. However, after a critical sample size $P^*$, we empirically find the finite-width network generalization becomes worse than that of the infinite width network. In this work, we empirically study the transition from infinite-width behavior to this variance limited regime as a function of sample size $P$ and network width $N$. We find that finite-size effects can become relevant for very small dataset sizes on the order of $P^* \sim \sqrt{N}$ for polynomial regression with ReLU networks. We discuss the source of these effects using an argument based on the variance of the NN's final neural tangent kernel (NTK). This transition can be pushed to larger $P$ by enhancing feature learning or by ensemble averaging the networks. We find that the learning curve for regression with the final NTK is an accurate approximation of the NN learning curve. Using this, we provide a toy model which also exhibits $P^* \sim \sqrt{N}$ scaling and has $P$-dependent benefits from feature learning.