Jan Macdonald

Joana Reuss, Jan Macdonald, Simon Becker et al.

We introduce EuroCropsML, an analysis-ready remote sensing machine learning dataset for time series crop type classification of agricultural parcels in Europe. It is the first dataset designed to benchmark transnational few-shot crop type classification algorithms that supports advancements in algorithmic development and research comparability. It comprises 706 683 multi-class labeled data points across 176 classes, featuring annual time series of per-parcel median pixel values from Sentinel-2 L1C data for 2021, along with crop type labels and spatial coordinates. Based on the open-source EuroCrops collection, EuroCropsML is publicly available on Zenodo.

Theophil Trippe, Martin Genzel, Jan Macdonald et al.

This work presents a novel deep-learning-based pipeline for the inverse problem of image deblurring, leveraging augmentation and pre-training with synthetic data. Our results build on our winning submission to the recent Helsinki Deblur Challenge 2021, whose goal was to explore the limits of state-of-the-art deblurring algorithms in a real-world data setting. The task of the challenge was to deblur out-of-focus images of random text, thereby in a downstream task, maximizing an optical-character-recognition-based score function. A key step of our solution is the data-driven estimation of the physical forward model describing the blur process. This enables a stream of synthetic data, generating pairs of ground-truth and blurry images on-the-fly, which is used for an extensive augmentation of the small amount of challenge data provided. The actual deblurring pipeline consists of an approximate inversion of the radial lens distortion (determined by the estimated forward model) and a U-Net architecture, which is trained end-to-end. Our algorithm was the only one passing the hardest challenge level, achieving over $70\%$ character recognition accuracy. Our findings are well in line with the paradigm of data-centric machine learning, and we demonstrate its effectiveness in the context of inverse problems. Apart from a detailed presentation of our methodology, we also analyze the importance of several design choices in a series of ablation studies. The code of our challenge submission is available under https://github.com/theophil-trippe/HDC_TUBerlin_version_1.

Martin Genzel, Ingo Gühring, Jan Macdonald et al.

This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time, focusing on a prototypical computed tomography (CT) setup. We demonstrate that an iterative end-to-end network scheme enables reconstructions close to numerical precision, comparable to classical compressed sensing strategies. Our results build on our winning submission to the recent AAPM DL-Sparse-View CT Challenge. Its goal was to identify the state-of-the-art in solving the sparse-view CT inverse problem with data-driven techniques. A specific difficulty of the challenge setup was that the precise forward model remained unknown to the participants. Therefore, a key feature of our approach was to initially estimate the unknown fanbeam geometry in a data-driven calibration step. Apart from an in-depth analysis of our methodology, we also demonstrate its state-of-the-art performance on the open-access real-world dataset LoDoPaB CT.

Joana Reuss, Jan Macdonald, Simon Becker et al.

Accurate crop-type classification from satellite time series is essential for agricultural monitoring. While various machine learning algorithms have been developed to enhance performance on data-scarce tasks, their evaluation often lacks real-world scenarios. Consequently, their efficacy in challenging practical applications has not yet been profoundly assessed. To facilitate future research in this domain, we present the first comprehensive benchmark for evaluating supervised and SSL methods for crop-type classification under real-world conditions. This benchmark study relies on the EuroCropsML time-series dataset, which combines farmer-reported crop data with Sentinel-2 satellite observations from Estonia, Latvia, and Portugal. Our findings indicate that MAML-based meta-learning algorithms achieve slightly higher accuracy compared to supervised transfer learning and SSL methods. However, compared to simpler transfer learning, the improvement of meta-learning comes at the cost of increased computational demands and training time. Moreover, supervised methods benefit most when pre-trained and fine-tuned on geographically close regions. In addition, while SSL generally lags behind meta-learning, it demonstrates advantages over training from scratch, particularly in capturing fine-grained features essential for real-world crop-type classification, and also surpasses standard transfer learning. This highlights its practical value when labeled pre-training crop data is scarce. Our insights underscore the trade-offs between accuracy and computational demand in selecting supervised machine learning methods for real-world crop-type classification tasks and highlight the difficulties of knowledge transfer across diverse geographic regions. Furthermore, they demonstrate the practical value of SSL approaches when labeled pre-training crop data is scarce.

Jan Macdonald, Stephan Wäldchen

We give a complete characterisation of families of probability distributions that are invariant under the action of ReLU neural network layers. The need for such families arises during the training of Bayesian networks or the analysis of trained neural networks, e.g., in the context of uncertainty quantification (UQ) or explainable artificial intelligence (XAI). We prove that no invariant parametrised family of distributions can exist unless at least one of the following three restrictions holds: First, the network layers have a width of one, which is unreasonable for practical neural networks. Second, the probability measures in the family have finite support, which basically amounts to sampling distributions. Third, the parametrisation of the family is not locally Lipschitz continuous, which excludes all computationally feasible families. Finally, we show that these restrictions are individually necessary. For each of the three cases we can construct an invariant family exploiting exactly one of the restrictions but not the other two.

Jan Macdonald, Mathieu Besançon, Sebastian Pokutta

We study the effects of constrained optimization formulations and Frank-Wolfe algorithms for obtaining interpretable neural network predictions. Reformulating the Rate-Distortion Explanations (RDE) method for relevance attribution as a constrained optimization problem provides precise control over the sparsity of relevance maps. This enables a novel multi-rate as well as a relevance-ordering variant of RDE that both empirically outperform standard RDE and other baseline methods in a well-established comparison test. We showcase several deterministic and stochastic variants of the Frank-Wolfe algorithm and their effectiveness for RDE.

Martin Genzel, Jan Macdonald, Maximilian März

This report is dedicated to a short motivation and description of our contribution to the AAPM DL-Sparse-View CT Challenge (team name: "robust-and-stable"). The task is to recover breast model phantom images from limited view fanbeam measurements using data-driven reconstruction techniques. The challenge is distinctive in the sense that participants are provided with a collection of ground truth images and their noiseless, subsampled sinograms (as well as the associated limited view filtered backprojection images), but not with the actual forward model. Therefore, our approach first estimates the fanbeam geometry in a data-driven geometric calibration step. In a subsequent two-step procedure, we design an iterative end-to-end network that enables the computation of near-exact solutions.

Martin Genzel, Jan Macdonald, Maximilian März

In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory. Recent works have pointed out instabilities of deep neural networks for several image reconstruction tasks. In analogy to adversarial attacks in classification, it was shown that slight distortions in the input domain may cause severe artifacts. The present article sheds new light on this concern, by conducting an extensive study of the robustness of deep-learning-based algorithms for solving underdetermined inverse problems. This covers compressed sensing with Gaussian measurements as well as image recovery from Fourier and Radon measurements, including a real-world scenario for magnetic resonance imaging (using the NYU-fastMRI dataset). Our main focus is on computing adversarial perturbations of the measurements that maximize the reconstruction error. A distinctive feature of our approach is the quantitative and qualitative comparison with total-variation minimization, which serves as a provably robust reference method. In contrast to previous findings, our results reveal that standard end-to-end network architectures are not only resilient against statistical noise, but also against adversarial perturbations. All considered networks are trained by common deep learning techniques, without sophisticated defense strategies.

Jan Macdonald, Maximilian März, Luis Oala et al.

This work investigates the detection of instabilities that may occur when utilizing deep learning models for image reconstruction tasks. Although neural networks often empirically outperform traditional reconstruction methods, their usage for sensitive medical applications remains controversial. Indeed, in a recent series of works, it has been demonstrated that deep learning approaches are susceptible to various types of instabilities, caused for instance by adversarial noise or out-of-distribution features. It is argued that this phenomenon can be observed regardless of the underlying architecture and that there is no easy remedy. Based on this insight, the present work demonstrates on two use cases how uncertainty quantification methods can be employed as instability detectors. In particular, it is shown that the recently proposed Interval Neural Networks are highly effective in revealing instabilities of reconstructions. Such an ability is crucial to ensure a safe use of deep learning-based methods for medical image reconstruction.

Luis Oala, Cosmas Heiß, Jan Macdonald et al.

We propose a fast, non-Bayesian method for producing uncertainty scores in the output of pre-trained deep neural networks (DNNs) using a data-driven interval propagating network. This interval neural network (INN) has interval valued parameters and propagates its input using interval arithmetic. The INN produces sensible lower and upper bounds encompassing the ground truth. We provide theoretical justification for the validity of these bounds. Furthermore, its asymmetric uncertainty scores offer additional, directional information beyond what Gaussian-based, symmetric variance estimation can provide. We find that noise in the data is adequately captured by the intervals produced with our method. In numerical experiments on an image reconstruction task, we demonstrate the practical utility of INNs as a proxy for the prediction error in comparison to two state-of-the-art uncertainty quantification methods. In summary, INNs produce fast, theoretically justified uncertainty scores for DNNs that are easy to interpret, come with added information and pose as improved error proxies - features that may prove useful in advancing the usability of DNNs especially in sensitive applications such as health care.

Jan Macdonald, Stephan Wäldchen, Sascha Hauch et al.

We formalise the widespread idea of interpreting neural network decisions as an explicit optimisation problem in a rate-distortion framework. A set of input features is deemed relevant for a classification decision if the expected classifier score remains nearly constant when randomising the remaining features. We discuss the computational complexity of finding small sets of relevant features and show that the problem is complete for $\mathsf{NP}^\mathsf{PP}$, an important class of computational problems frequently arising in AI tasks. Furthermore, we show that it even remains $\mathsf{NP}$-hard to only approximate the optimal solution to within any non-trivial approximation factor. Finally, we consider a continuous problem relaxation and develop a heuristic solution strategy based on assumed density filtering for deep ReLU neural networks. We present numerical experiments for two image classification data sets where we outperform established methods in particular for sparse explanations of neural network decisions.

Dominik Alfke, Weston Baines, Jan Blechschmidt et al.

We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results. Having access to a sufficiently large amount of labelled training data, our methodology is capable of predicting the labels of the test data almost always even if the training data is entirely unrelated to the test data. In other words, we prove in a specific setting that as long as one has access to enough data points, the quality of the data is irrelevant.