Moritz Weckbecker

Leander Weber, Jim Berend, Moritz Weckbecker et al.

Gradient-based optimization has been a cornerstone of machine learning that enabled the vast advances of Artificial Intelligence (AI) development over the past decades. However, this type of optimization requires differentiation, and with recent evidence of the benefits of non-differentiable (e.g. neuromorphic) architectures over classical models w.r.t. efficiency, such constraints can become limiting in the future. We present Layer-wise Feedback Propagation (LFP), a novel training principle for neural network-like predictors that utilizes methods from the domain of explainability to decompose a reward to individual neurons based on their respective contributions. Leveraging these neuron-wise rewards, our method then implements a greedy approach reinforcing helpful parts of the network and weakening harmful ones. While having comparable computational complexity to gradient descent, LFP does not require gradient computation and generates sparse and thereby memory- and energy-efficient parameter updates and models. We establish the convergence of LFP theoretically and empirically, demonstrating its effectiveness on various models and datasets. Via two applications - neural network pruning and the approximation-free training of Spiking Neural Networks (SNNs) - we demonstrate that LFP combines increased efficiency in terms of computation and representation with flexibility w.r.t. choice of model architecture and objective function. Our code is available at https://github.com/leanderweber/layerwise-feedback-propagation.

Jonas R. Naujoks, Aleksander Krasowski, Moritz Weckbecker et al.

Recently, physics-informed neural networks (PINNs) have emerged as a flexible and promising application of deep learning to partial differential equations in the physical sciences. While offering strong performance and competitive inference speeds on forward and inverse problems, their black-box nature limits interpretability, particularly regarding alignment with expected physical behavior. In the present work, we explore the application of influence functions (IFs) to validate and debug PINNs post-hoc. Specifically, we apply variations of IF-based indicators to gauge the influence of different types of collocation points on the prediction of PINNs applied to a 2D Navier-Stokes fluid flow problem. Our results demonstrate how IFs can be adapted to PINNs to reveal the potential for further studies. The code is publicly available at https://github.com/aleks-krasowski/PINNfluence.

Moritz Weckbecker, Wenkai Xu, Gesine Reinert

Score-based kernelised Stein discrepancy (KSD) tests have emerged as a powerful tool for the goodness of fit tests, especially in high dimensions; however, the test performance may depend on the choice of kernels in an underlying reproducing kernel Hilbert space (RKHS). Here we assess the effect of RKHS choice for KSD tests of random networks models, developed for exponential random graph models (ERGMs) in Xu and Reinert (2021)and for synthetic graph generators in Xu and Reinert (2022). We investigate the power performance and the computational runtime of the test in different scenarios, including both dense and sparse graph regimes. Experimental results on kernel performance for model assessment tasks are shown and discussed on synthetic and real-world network applications.

Galip Ümit Yolcu, Moritz Weckbecker, Thomas Wiegand et al.

Deep learning models achieve remarkable performance, yet their decision-making processes often remain opaque. In response, the field of eXplainable Artificial Intelligence (XAI) has grown significantly over the last decade, primarily focusing on feature attribution methods. Complementing this perspective, Data Attribution (DA) has emerged as a promising paradigm that shifts the focus from features to data provenance. However, existing DA approaches suffer from prohibitively high computational costs and memory demands. Additionally, current attribution methods exhibit low sparsity, hindering the discovery of decisive patterns in the data. We introduce DualXDA, a framework for sparse, efficient and explainable DA, comprised of two interlinked approaches for Dual Data Attribution (DualDA) and eXplainable Data Attribution (XDA): With DualDA, we propose efficient and effective DA, leveraging Support Vector Machine theory to provide fast and naturally sparse data attributions for AI predictions. We demonstrate that DualDA achieves high attribution quality, excels at solving a series of evaluated downstream tasks, while at the same time improving explanation time by a factor of up to 4,100,000$\times$ compared to the original Influence Functions method, and up to 11,000$\times$ compared to the method's most efficient approximation from literature. We further introduce XDA, a method for enhancing Data Attribution with capabilities from feature attribution methods to explain why training samples are relevant for the prediction of a test sample in terms of impactful features. Taken together, our contributions in DualXDA ultimately point towards a future of eXplainable AI applied at unprecedented scale, enabling transparent, efficient and novel analysis of even the largest neural architectures fostering a new generation of accountable AI systems. Code at https://github.com/gumityolcu/DualXDA.

Jonas R. Naujoks, Aleksander Krasowski, Moritz Weckbecker et al.

Physics-informed neural networks (PINNs) offer a powerful approach to solving partial differential equations (PDEs), which are ubiquitous in the quantitative sciences. Applied to both forward and inverse problems across various scientific domains, PINNs have recently emerged as a valuable tool in the field of scientific machine learning. A key aspect of their training is that the data -- spatio-temporal points sampled from the PDE's input domain -- are readily available. Influence functions, a tool from the field of explainable AI (XAI), approximate the effect of individual training points on the model, enhancing interpretability. In the present work, we explore the application of influence function-based sampling approaches for the training data. Our results indicate that such targeted resampling based on data attribution methods has the potential to enhance prediction accuracy in physics-informed neural networks, demonstrating a practical application of an XAI method in PINN training.

Frederik Pahde, Maximilian Dreyer, Leander Weber et al.

With a growing interest in understanding neural network prediction strategies, Concept Activation Vectors (CAVs) have emerged as a popular tool for modeling human-understandable concepts in the latent space. Commonly, CAVs are computed by leveraging linear classifiers optimizing the separability of latent representations of samples with and without a given concept. However, in this paper we show that such a separability-oriented computation leads to solutions, which may diverge from the actual goal of precisely modeling the concept direction. This discrepancy can be attributed to the significant influence of distractor directions, i.e., signals unrelated to the concept, which are picked up by filters (i.e., weights) of linear models to optimize class-separability. To address this, we introduce pattern-based CAVs, solely focussing on concept signals, thereby providing more accurate concept directions. We evaluate various CAV methods in terms of their alignment with the true concept direction and their impact on CAV applications, including concept sensitivity testing and model correction for shortcut behavior caused by data artifacts. We demonstrate the benefits of pattern-based CAVs using the Pediatric Bone Age, ISIC2019, and FunnyBirds datasets with VGG, ResNet, ReXNet, EfficientNet, and Vision Transformer as model architectures.