Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problems

Conditional generative models became a very powerful tool to sample from Bayesian inverse problem posteriors. It is well-known in classical Bayesian literature that posterior measures are quite robust with respect to perturbations of both the prior measure and the negative log-likelihood, which includes perturbations of the observations. However, to the best of our knowledge, the robustness of conditional generative models with respect to perturbations of the observations has not been investigated yet. In this paper, we prove for the first time that appropriately learned conditional generative models provide robust results for single observations

Analysing gap dynamics in forest canopies with landscape metrics based on multi-temporal airborne laser scanning surveys - A pilot study

For a long time gaps or openings in the forest canopy have been of considerable interest to forest ecologists and to forest managers. In the context of disturbances induced by climate change, canopy gap dynamics are of particular interest, since they can indicate imminent damage to forest resources and irreversible trends such as forest decline. Here, statistical significance is crucial for establishing whether any imminent large-scale threat to the sustainability of forest resources exists. In order to be able to assess significance, we applied the Boolean model, a null or reference model from random set statistics. The Boolean model served as a theoretical benchmark for testing the significance of the observed trends in forest canopy gap dynamics. As a pilot study we analysed airborne laser scan (ALS) data collected in the Krycklan catchment area (Northern Sweden) in 2006 and 2015. The data were analysed using eight different landscape metrics. Despite the moderate resolution of our ALS data the landscape metrics have proved to be useful tools for monitoring canopy gap dynamics of forest ecosystems. The Boolean model has been successful in ascertaining statistical significance and the model parameters indi-cated important trends. In the Krycklan catchment area, there was no significant trend of canopy gap dynamics indicating any harmful development between 2006 and 2015. On the contrary, we found evidence for gaps closing in and gap locations becoming more random whilst the canopy cover increased between the two survey years

Generative Sliced MMD Flows with Riesz Kernels

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels $K(x,y) = - \|x-y\|^r$, $r \in (0,2)$ have exceptional properties which allow for their efficient computation. First, the MMD of Riesz kernels coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for $r=1$, a simple sorting algorithm can be applied to reduce the complexity from $O(MN+N^2)$ to $O((M+N)\log(M+N))$ for two empirical measures with $M$ and $N$ support points. For the implementations we approximate the gradient of the sliced MMD by using only a finite number $P$ of slices. We show that the resulting error has complexity $O(\sqrt{d/P})$, where $d$ is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for large scale applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10

Alpha oscillatory correlates of motor inhibition in the aged brain

Exerting inhibitory control is a cognitive ability mediated by functions known to decline with age. The goal of this study is to add to the mechanistic understanding of cortical inhibition during motor control in aged brains. Based on behavioral findings of impaired inhibitory control with age we hypothesized that elderly will show a reduced or a lack of EEG alpha power increase during tasks that require motor inhibition. Since inhibitory control over movements has been shown to rely on prior motor memory formation, we investigated cortical inhibitory processes at two points in time early after learning and after an overnight consolidation phase and hypothesized an overnight increase of inhibitory capacities. Young and elderly participants acquired a complex finger movement sequence and in each experimental session brain activity during execution and inhibition of the sequence was recorded with multi-channel EEG. We assessed cortical processes of sustained inhibition by means of task-induced changes of alpha oscillatory power. During inhibition of the learned movement, young participants showed a significant alpha power increase at the sensorimotor cortices whereas elderly did not. Interestingly, for both groups, the overnight consolidation phase improved up-regulation of alpha power during sustained inhibition. This points to deficits in the generation and enhancement of local inhibitory mechanisms at the sensorimotor cortices in aged brains. However, the alpha power increase in both groups implies neuroplastic changes that strengthen the network of alpha power generation over time in young as well as elderly brains

Verification of Sigmoidal Artificial Neural Networks using iSAT

This paper presents an approach for verifying the behaviour of nonlinear Artificial Neural Networks (ANNs) found in cyber-physical safety-critical systems. We implement a dedicated interval constraint propagator for the sigmoid function into the SMT solver iSAT and compare this approach with a compositional approach encoding the sigmoid function by basic arithmetic features available in iSAT and an approximating approach. Our experimental results show that the dedicated and the compositional approach clearly outperform the approximating approach. Throughout all our benchmarks, the dedicated approach showed an equal or better performance compared to the compositional approach.Comment: In Proceedings SNR 2021, arXiv:2207.0439

PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization

Learning neural networks using only few available information is an important ongoing research topic with tremendous potential for applications. In this paper, we introduce a powerful regularizer for the variational modeling of inverse problems in imaging. Our regularizer, called patch normalizing flow regularizer (patchNR), involves a normalizing flow learned on small patches of very few images. In particular, the training is independent of the considered inverse problem such that the same regularizer can be applied for different forward operators acting on the same class of images. By investigating the distribution of patches versus those of the whole image class, we prove that our model is indeed a MAP approach. Numerical examples for low-dose and limited-angle computed tomography (CT) as well as superresolution of material images demonstrate that our method provides very high quality results. The training set consists of just six images for CT and one image for superresolution. Finally, we combine our patchNR with ideas from internal learning for performing superresolution of natural images directly from the low-resolution observation without knowledge of any high-resolution image