在本文中，我们考虑Barron函数$ f：[0,1]^d \ to \ mathbb {r} $的平滑度$ \ sigma> 0 $，这是可以写入\ [f（x）=的函数\ int _ {\ mathbb {r}^d} f（\ xi）\，e^{2 \ pi i \ langle x，\ xi \ rangle} \，d \ xi \ xi \ quad \ quad \ quad \ text \ text} {\ mathbb {r}^d} | f（\ xi）| \ cdot（1 + | \ xi |）^{\ sigma} \，d \ xi <\ infty。 \]对于$ \ sigma = 1 $，这些功能在机器学习中起着重要的作用，因为它们可以通过（浅）神经网络有效地近似，而不会受到维数的诅咒。对于这些函数，我们研究以下问题：给定$ m $ point样用$ f（x_1），\ dots，f（x_m）$的barron函数$ f：[0,1]^d \ to \ mathbb { r} $的平滑度$ \ sigma $，从这些样品中可以如何回收$ f $，以最佳选择采样点和重建过程？表示$ s_m（\ sigma; l^p）$在$ l^p $中测量的最佳重建错误，我们表明\ [m^{ - \ frac {1} {\ max \ max \ {p，2 \}}}} - \ \ frac {\ sigma} {d}} \ sillssim s_m（\ sigma; l^p）\ sillesim（\ ln（e + m））^{\ alpha（\ alpha（\ sigma，d） / p} \ cdot m^cdot m^ { - \ frac {1} {\ max \ {p，2 \}} - \ frac {\ sigma} {d}}}}}}}，\ \]，其中隐含常数仅取决于$ \ sigma $和$ d $ \ alpha（\ sigma，d）$保持为$ d \ to \ infty $。

我们在决策边界是一定规律的假设下，研究从无噪声训练样本的学习分类功能的问题。我们为这一估计问题建立了普遍的下限，对于连续决策边界的一般阶级。对于本地禁区的类别，我们发现最佳估计率基本上独立于底层维度，并且可以通过在适当类的深神经网络上通过经验风险最小化方法实现。这些结果基于$ l ^ 1 $和$ l ^ \ infty $ intty $ inthty $ off的禁区常规职能的新颖估计数。

We generalize the classical universal approximation theorem for neural networks to the case of complex-valued neural networks. Precisely, we consider feedforward networks with a complex activation function $\sigma : \mathbb{C} \to \mathbb{C}$ in which each neuron performs the operation $\mathbb{C}^N \to \mathbb{C}, z \mapsto \sigma(b + w^T z)$ with weights $w \in \mathbb{C}^N$ and a bias $b \in \mathbb{C}$, and with $\sigma$ applied componentwise. We completely characterize those activation functions $\sigma$ for which the associated complex networks have the universal approximation property, meaning that they can uniformly approximate any continuous function on any compact subset of $\mathbb{C}^d$ arbitrarily well. Unlike the classical case of real networks, the set of "good activation functions" which give rise to networks with the universal approximation property differs significantly depending on whether one considers deep networks or shallow networks: For deep networks with at least two hidden layers, the universal approximation property holds as long as $\sigma$ is neither a polynomial, a holomorphic function, or an antiholomorphic function. Shallow networks, on the other hand, are universal if and only if the real part or the imaginary part of $\sigma$ is not a polyharmonic function.

We address the challenge of building domain-specific knowledge models for industrial use cases, where labelled data and taxonomic information is initially scarce. Our focus is on inductive link prediction models as a basis for practical tools that support knowledge engineers with exploring text collections and discovering and linking new (so-called open-world) entities to the knowledge graph. We argue that - though neural approaches to text mining have yielded impressive results in the past years - current benchmarks do not reflect the typical challenges encountered in the industrial wild properly. Therefore, our first contribution is an open benchmark coined IRT2 (inductive reasoning with text) that (1) covers knowledge graphs of varying sizes (including very small ones), (2) comes with incidental, low-quality text mentions, and (3) includes not only triple completion but also ranking, which is relevant for supporting experts with discovery tasks. We investigate two neural models for inductive link prediction, one based on end-to-end learning and one that learns from the knowledge graph and text data in separate steps. These models compete with a strong bag-of-words baseline. The results show a significant advance in performance for the neural approaches as soon as the available graph data decreases for linking. For ranking, the results are promising, and the neural approaches outperform the sparse retriever by a wide margin.

Machine learning models are typically evaluated by computing similarity with reference annotations and trained by maximizing similarity with such. Especially in the bio-medical domain, annotations are subjective and suffer from low inter- and intra-rater reliability. Since annotations only reflect the annotation entity's interpretation of the real world, this can lead to sub-optimal predictions even though the model achieves high similarity scores. Here, the theoretical concept of Peak Ground Truth (PGT) is introduced. PGT marks the point beyond which an increase in similarity with the reference annotation stops translating to better Real World Model Performance (RWMP). Additionally, a quantitative technique to approximate PGT by computing inter- and intra-rater reliability is proposed. Finally, three categories of PGT-aware strategies to evaluate and improve model performance are reviewed.

Efficient surrogate modelling is a key requirement for uncertainty quantification in data-driven scenarios. In this work, a novel approach of using Sparse Random Features for surrogate modelling in combination with self-supervised dimensionality reduction is described. The method is compared to other methods on synthetic and real data obtained from crashworthiness analyses. The results show a superiority of the here described approach over state of the art surrogate modelling techniques, Polynomial Chaos Expansions and Neural Networks.

In recent years distributional reinforcement learning has produced many state of the art results. Increasingly sample efficient Distributional algorithms for the discrete action domain have been developed over time that vary primarily in the way they parameterize their approximations of value distributions, and how they quantify the differences between those distributions. In this work we transfer three of the most well-known and successful of those algorithms (QR-DQN, IQN and FQF) to the continuous action domain by extending two powerful actor-critic algorithms (TD3 and SAC) with distributional critics. We investigate whether the relative performance of the methods for the discrete action space translates to the continuous case. To that end we compare them empirically on the pybullet implementations of a set of continuous control tasks. Our results indicate qualitative invariance regarding the number and placement of distributional atoms in the deterministic, continuous action setting.

Artificial Intelligence (AI) has become commonplace to solve routine everyday tasks. Because of the exponential growth in medical imaging data volume and complexity, the workload on radiologists is steadily increasing. We project that the gap between the number of imaging exams and the number of expert radiologist readers required to cover this increase will continue to expand, consequently introducing a demand for AI-based tools that improve the efficiency with which radiologists can comfortably interpret these exams. AI has been shown to improve efficiency in medical-image generation, processing, and interpretation, and a variety of such AI models have been developed across research labs worldwide. However, very few of these, if any, find their way into routine clinical use, a discrepancy that reflects the divide between AI research and successful AI translation. To address the barrier to clinical deployment, we have formed MONAI Consortium, an open-source community which is building standards for AI deployment in healthcare institutions, and developing tools and infrastructure to facilitate their implementation. This report represents several years of weekly discussions and hands-on problem solving experience by groups of industry experts and clinicians in the MONAI Consortium. We identify barriers between AI-model development in research labs and subsequent clinical deployment and propose solutions. Our report provides guidance on processes which take an imaging AI model from development to clinical implementation in a healthcare institution. We discuss various AI integration points in a clinical Radiology workflow. We also present a taxonomy of Radiology AI use-cases. Through this report, we intend to educate the stakeholders in healthcare and AI (AI researchers, radiologists, imaging informaticists, and regulators) about cross-disciplinary challenges and possible solutions.

Understanding our brain is one of the most daunting tasks, one we cannot expect to complete without the use of technology. MindBigData aims to provide a comprehensive and updated dataset of brain signals related to a diverse set of human activities so it can inspire the use of machine learning algorithms as a benchmark of 'decoding' performance from raw brain activities into its corresponding (labels) mental (or physical) tasks. Using commercial of the self, EEG devices or custom ones built by us to explore the limits of the technology. We describe the data collection procedures for each of the sub datasets and with every headset used to capture them. Also, we report possible applications in the field of Brain Computer Interfaces or BCI that could impact the life of billions, in almost every sector like healthcare game changing use cases, industry or entertainment to name a few, at the end why not directly using our brains to 'disintermediate' senses, as the final HCI (Human-Computer Interaction) device? simply what we call the journey from Type to Touch to Talk to Think.

Modern mobile burst photography pipelines capture and merge a short sequence of frames to recover an enhanced image, but often disregard the 3D nature of the scene they capture, treating pixel motion between images as a 2D aggregation problem. We show that in a "long-burst", forty-two 12-megapixel RAW frames captured in a two-second sequence, there is enough parallax information from natural hand tremor alone to recover high-quality scene depth. To this end, we devise a test-time optimization approach that fits a neural RGB-D representation to long-burst data and simultaneously estimates scene depth and camera motion. Our plane plus depth model is trained end-to-end, and performs coarse-to-fine refinement by controlling which multi-resolution volume features the network has access to at what time during training. We validate the method experimentally, and demonstrate geometrically accurate depth reconstructions with no additional hardware or separate data pre-processing and pose-estimation steps.