蒙特卡洛方法和深度学习的组合最近导致了在高维度中求解部分微分方程（PDE）的有效算法。相关的学习问题通常被称为基于相关随机微分方程（SDE）的变异公式，可以使用基于梯度的优化方法最小化相应损失。因此，在各自的数值实现中，至关重要的是要依靠足够的梯度估计器，这些梯度估计器表现出较低的差异，以便准确，迅速地达到收敛性。在本文中，我们严格研究了在线性Kolmogorov PDE的上下文中出现的相应数值方面。特别是，我们系统地比较了现有的深度学习方法，并为其表演提供了理论解释。随后，我们建议的新方法在理论上和数字上都可以证明更健壮，从而导致了实质性的改进。

求解高维局部微分方程是经济学，科学和工程的反复挑战。近年来，已经开发了大量的计算方法，其中大多数依赖于蒙特卡罗采样和基于深度学习的近似的组合。对于椭圆形和抛物线问题，现有方法可以广泛地分类为依赖于$ \ Texit {向后随机微分方程} $（BSDES）和旨在最小化回归$ L ^ 2 $ -Error（ $ \ textit {物理信息的神经网络} $，pinns）。在本文中，我们审查了文献，并提出了一种基于新型$ \ Texit的方法{扩散丢失} $，在BSDES和Pinns之间插值。我们的贡献为对高维PDE的数值方法的统一理解开辟了门，以及结合BSDES和PINNS强度的实施方式。我们还向特征值问题提供概括并进行广泛的数值研究，包括计算非线性SCHR \“odinger运营商的地面状态和分子动态相关的委托功能的计算。

Diffusion models have shown a great ability at bridging the performance gap between predictive and generative approaches for speech enhancement. We have shown that they may even outperform their predictive counterparts for non-additive corruption types or when they are evaluated on mismatched conditions. However, diffusion models suffer from a high computational burden, mainly as they require to run a neural network for each reverse diffusion step, whereas predictive approaches only require one pass. As diffusion models are generative approaches they may also produce vocalizing and breathing artifacts in adverse conditions. In comparison, in such difficult scenarios, predictive models typically do not produce such artifacts but tend to distort the target speech instead, thereby degrading the speech quality. In this work, we present a stochastic regeneration approach where an estimate given by a predictive model is provided as a guide for further diffusion. We show that the proposed approach uses the predictive model to remove the vocalizing and breathing artifacts while producing very high quality samples thanks to the diffusion model, even in adverse conditions. We further show that this approach enables to use lighter sampling schemes with fewer diffusion steps without sacrificing quality, thus lifting the computational burden by an order of magnitude. Source code and audio examples are available online (https://uhh.de/inf-sp-storm).

State-of-the-art language models are often accurate on many question-answering benchmarks with well-defined questions. Yet, in real settings questions are often unanswerable without asking the user for clarifying information. We show that current SotA models often do not ask the user for clarification when presented with imprecise questions and instead provide incorrect answers or "hallucinate". To address this, we introduce CLAM, a framework that first uses the model to detect ambiguous questions, and if an ambiguous question is detected, prompts the model to ask the user for clarification. Furthermore, we show how to construct a scalable and cost-effective automatic evaluation protocol using an oracle language model with privileged information to provide clarifying information. We show that our method achieves a 20.15 percentage point accuracy improvement over SotA on a novel ambiguous question-answering answering data set derived from TriviaQA.

Compartmental models are a tool commonly used in epidemiology for the mathematical modelling of the spread of infectious diseases, with their most popular representative being the Susceptible-Infected-Removed (SIR) model and its derivatives. However, current SIR models are bounded in their capabilities to model government policies in the form of non-pharmaceutical interventions (NPIs) and weather effects and offer limited predictive power. More capable alternatives such as agent based models (ABMs) are computationally expensive and require specialized hardware. We introduce a neural network augmented SIR model that can be run on commodity hardware, takes NPIs and weather effects into account and offers improved predictive power as well as counterfactual analysis capabilities. We demonstrate our models improvement of the state-of-the-art modeling COVID-19 in Austria during the 03.2020 to 03.2021 period and provide an outlook for the future up to 01.2024.

Nucleolar organizer regions (NORs) are parts of the DNA that are involved in RNA transcription. Due to the silver affinity of associated proteins, argyrophilic NORs (AgNORs) can be visualized using silver-based staining. The average number of AgNORs per nucleus has been shown to be a prognostic factor for predicting the outcome of many tumors. Since manual detection of AgNORs is laborious, automation is of high interest. We present a deep learning-based pipeline for automatically determining the AgNOR-score from histopathological sections. An additional annotation experiment was conducted with six pathologists to provide an independent performance evaluation of our approach. Across all raters and images, we found a mean squared error of 0.054 between the AgNOR- scores of the experts and those of the model, indicating that our approach offers performance comparable to humans.

We present a unified probabilistic model that learns a representative set of discrete vehicle actions and predicts the probability of each action given a particular scenario. Our model also enables us to estimate the distribution over continuous trajectories conditioned on a scenario, representing what each discrete action would look like if executed in that scenario. While our primary objective is to learn representative action sets, these capabilities combine to produce accurate multimodal trajectory predictions as a byproduct. Although our learned action representations closely resemble semantically meaningful categories (e.g., "go straight", "turn left", etc.), our method is entirely self-supervised and does not utilize any manually generated labels or categories. Our method builds upon recent advances in variational inference and deep unsupervised clustering, resulting in full distribution estimates based on deterministic model evaluations.

Convolutional neural networks (CNN) define the state-of-the-art solution on many perceptual tasks. However, current CNN approaches largely remain vulnerable against adversarial perturbations of the input that have been crafted specifically to fool the system while being quasi-imperceptible to the human eye. In recent years, various approaches have been proposed to defend CNNs against such attacks, for example by model hardening or by adding explicit defence mechanisms. Thereby, a small "detector" is included in the network and trained on the binary classification task of distinguishing genuine data from data containing adversarial perturbations. In this work, we propose a simple and light-weight detector, which leverages recent findings on the relation between networks' local intrinsic dimensionality (LID) and adversarial attacks. Based on a re-interpretation of the LID measure and several simple adaptations, we surpass the state-of-the-art on adversarial detection by a significant margin and reach almost perfect results in terms of F1-score for several networks and datasets. Sources available at: https://github.com/adverML/multiLID

Diffusion-based generative models have had a high impact on the computer vision and speech processing communities these past years. Besides data generation tasks, they have also been employed for data restoration tasks like speech enhancement and dereverberation. While discriminative models have traditionally been argued to be more powerful e.g. for speech enhancement, generative diffusion approaches have recently been shown to narrow this performance gap considerably. In this paper, we systematically compare the performance of generative diffusion models and discriminative approaches on different speech restoration tasks. For this, we extend our prior contributions on diffusion-based speech enhancement in the complex time-frequency domain to the task of bandwith extension. We then compare it to a discriminatively trained neural network with the same network architecture on three restoration tasks, namely speech denoising, dereverberation and bandwidth extension. We observe that the generative approach performs globally better than its discriminative counterpart on all tasks, with the strongest benefit for non-additive distortion models, like in dereverberation and bandwidth extension. Code and audio examples can be found online at https://uhh.de/inf-sp-sgmsemultitask

在本文中，我们考虑了通过风险最小化监督学习中变异模型的问题。我们的目标是通过双层优化和通过算法展开对学习变异模型的两种方法进行更深入的了解。前者将变分模型视为低于风险最小化问题的较低级别优化问题，而后者将较低级别优化问题替换为解决上述问题的算法。两种方法都在实践中使用，但是从计算的角度来看，展开要简单得多。为了分析和比较两种方法，我们考虑了一个简单的玩具模型，并明确计算所有风险和各自的估计器。我们表明，展开可能比双重优化方法更好，而且展开的性能可以显着取决于进一步的参数，有时会以意外的方式：虽然展开的算法的步骤大小很重要，但展开的迭代数量只有很重要如果数字是偶数或奇数，并且这两种情况截然不同。