arXiv subjects

Babette Dellen

Publications and source records attributed to Babette Dellen.

9 recordsLinked to original sources

arXiv2026

PU-UNet: Stable Multiplicative Interactions for Medical Image Segmentation

Many dense prediction networks rely on additive feature transformations and model higher-order feature interactions only implicitly. Product units provide an explicit mechanism for multiplicative feature modeling, but their logarithmic--exponential formulation can cause numerical instability, which has limited their use in deep dense prediction networks. In this work, we propose Product-Unit U-Net (PU-UNet), a residual U-Net that integrates stable product-unit residual blocks into rich low-resolution stages for medical image segmentation. The proposed formulation combines smooth positivity mapping with log-domain clipping, enabling stable multiplicative feature learning with negligible computational overhead. On ISIC 2018, Kvasir-SEG, and BUSI, PU-UNet achieves Dice scores of 0.942, 0.959, and up to 0.925, respectively. Compared with a matched Residual U-Net baseline, PU-UNet consistently improves Dice and IoU while keeping parameters, FLOPs, and inference latency nearly unchanged, and reduces the image-level false-positive rate on normal BUSI cases from 0.077 to zero. Ablation studies suggest that the gains are associated with product-unit interactions, are strongest under low-resolution placement, and benefit from the proposed stabilization design. These results suggest that stable product-unit residual learning can be an effective way to enhance U-Net-style segmentation networks with explicit multiplicative interactions.

cs.CV↗

arXiv2026

Product units in gated recurrent units improve nuclear-mass prediction

The prediction of masses of atomic nuclei using machine learning can complement theoretical models and advance the exploration of poorly known domains of the nuclear chart. We propose a machine learning technique based on gated recurrent units (GRU), which have demonstrated competitive performance in nuclear-mass prediction by exploiting long-term dependencies. By integrating multiplicative interactions and product-unit transformations within recurrent units, we report significant improvements in nuclear-mass prediction. Computations are performed in the complex domain to jointly capture amplitude and phase dynamics. For interpolation and temporal-extrapolation tasks based on the atomic mass evaluation (AME2016 and AME2020), the complex additive-multiplicative product-unit gated recurrent unit (AM-PU-GRU) model consistently achieves the lowest prediction errors, with an interpolation RMSE of 0.227 $\pm$ 0.004 MeV and an extrapolation RMSE of 0.179 $\pm$ 0.015 MeV. These results surpass other state-of-the-art machine learning models and also outperform the real-valued GRU baseline and product-unit ablation variants, while remaining robust to different theoretical priors, including WS4 and SEMF. Our findings establish complex-valued product-unit recurrent networks as a new benchmark for sequence-based nuclear-mass prediction.

cs.LG↗

arXiv2026

Modeling Nonlinear Feature Interactions with Product-Unit Residual Networks

Understanding nonlinear feature interactions is crucial in science and engineering, yet standard multilayer perceptrons (MLPs) often capture such interactions only implicitly, leading to entangled representations that can impair robustness and interpretability. We investigate product-unit residual networks (PURe) that integrate multiplicative product units with residual connections to explicitly model cross-feature couplings while stabilizing optimization. We conduct a systematic evaluation on an interaction-driven synthetic benchmark and two real-world datasets, assessing predictive accuracy, robustness to Gaussian feature noise, and performance under limited training data, and we compare real- and complex-valued variants under a matched parameter budget. Beyond accuracy, SHapley Additive exPlanations (SHAP)-based interaction analyses show that PURe learns more concentrated and structurally coherent interaction patterns than MLP baselines. Overall, PURe achieves competitive or improved performance, better robustness and sample efficiency in low-data regimes, and enhanced interaction-level interpretability.

cs.LG↗

arXiv2026

Model discovery for dynamical systems with complex-valued product units

Discovering the governing equations of a dynamical system from observed trajectories provides deeper insight into its structure than mere prediction of future states. We present a data-driven approach to model discovery based on complex-valued product-unit networks, in which each unit represents a complex monomial and the network output is a sparse linear combination of such monomials. In contrast to established library-based methods such as SINDy, our approach does not require a predefined set of candidate functions: the relevant monomials, including those with fractional or negative exponents, are learned directly from data. Across four chaotic benchmark systems (Lorenz63, Lorenz84, the Four-Wing attractor, and a fractional variant of Lorenz63), we recover the exact governing equations in 90% of trials for the first three systems, and in 70-90% of trials for the fractional case, using at least 3000 training points. Applied to real-world human-gait accelerometer signals, the model produced stable trajectories with bounded prediction errors, corresponding to an RMSE of approximately 12-14% of the signal amplitude range over a test horizon three times longer than the training interval, demonstrating its potential for high-dimensional systems in which analytic equations are unavailable.

cs.CV↗

arXiv2026

Anatomy-Informed Deep Learning for Abdominal Aortic Aneurysm Segmentation

In CT angiography, the accurate segmentation of abdominal aortic aneurysms (AAAs) is difficult due to large anatomical variability, low-contrast vessel boundaries, and the close proximity of organs whose intensities resemble vascular structures, often leading to false positives. To address these challenges, we propose an anatomy-aware segmentation framework that integrates organ exclusion masks derived from TotalSegmentator into the training process. These masks encode explicit anatomical priors by identifying non-vascular organsand penalizing aneurysm predictions within these regions, thereby guiding the U-Net to focus on the aorta and its pathological dilation while suppressing anatomically implausible predictions. Despite being trained on a relatively small dataset, the anatomy-aware model achieves high accuracy, substantially reduces false positives, and improves boundary consistency compared to a standard U-Net baseline. The results demonstrate that incorporating anatomical knowledge through exclusion masks provides an efficient mechanism to enhance robustness and generalization, enabling reliable AAA segmentation even with limited training data.

cs.CV↗

arXiv2025

PURe: A Plug-and-Play Product-Unit Residual Module for Vision Networks

Modern vision networks are dominated by additive local transformations, whereas explicit multiplicative local interactions remain underexplored. Product units offer a direct approach to modeling such interactions, but their use in deep architectures has been limited by optimization instability. In this work, we propose PURe, a product-unit Residual Module for deep vision networks. PURe is built around a 2D product unit with a real-valued log-domain formulation that makes multiplicative local aggregation practical within deep residual hierarchies. The resulting module serves as a drop-in replacement for native residual units. We instantiate PURe in residual CNNs for image classification and in 2D residual encoder--decoder networks for slice-based segmentation on volumetric CT data. Across Galaxy10 DECaLS, ImageNet, and CIFAR-10, PURe consistently improves residual CNNs and yields a more favorable accuracy--parameter trade-off, allowing moderately deep models to match or surpass substantially deeper ResNet baselines with much smaller parameter budgets. On the AMOS benchmark, PURe also improves slice-based CT segmentation under 3D case-level evaluation. These results show that explicit multiplicative local interaction is a practical and effective design primitive for deep residual vision networks.

cs.CV↗

arXiv2023

Predicting nuclear masses with product-unit networks

Accurate estimation of nuclear masses and their prediction beyond the experimentally explored domains of the nuclear landscape are crucial to an understanding of the fundamental origin of nuclear properties and to many applications of nuclear science, most notably in quantifying the $r$-process of stellar nucleosynthesis. Neural networks have been applied with some success to the prediction of nuclear masses, but they are known to have shortcomings in application to extrapolation tasks. In this work, we propose and explore a novel type of neural network for mass prediction in which the usual neuron-like processing units are replaced by complex-valued product units that permit multiplicative couplings of inputs to be learned from the input data. This generalized network model is tested on both interpolation and extrapolation data sets drawn from the Atomic Mass Evaluation. Its performance is compared with that of several neural-network architectures, substantiating its suitability for nuclear mass prediction. Additionally, a prediction-uncertainty measure for such complex-valued networks is proposed that serves to identify regions of expected low prediction error.

nucl-th↗

arXiv2022

3D object reconstruction and 6D-pose estimation from 2D shape for robotic grasping of objects

We propose a method for 3D object reconstruction and 6D-pose estimation from 2D images that uses knowledge about object shape as the primary key. In the proposed pipeline, recognition and labeling of objects in 2D images deliver 2D segment silhouettes that are compared with the 2D silhouettes of projections obtained from various views of a 3D model representing the recognized object class. By computing transformation parameters directly from the 2D images, the number of free parameters required during the registration process is reduced, making the approach feasible. Furthermore, 3D transformations and projective geometry are employed to arrive at a full 3D reconstruction of the object in camera space using a calibrated set up. Inclusion of a second camera allows resolving remaining ambiguities. The method is quantitatively evaluated using synthetic data and tested with real data, and additional results for the well-known Linemod data set are shown. In robot experiments, successful grasping of objects demonstrates its usability in real-world environments, and, where possible, a comparison with other methods is provided. The method is applicable to scenarios where 3D object models, e.g., CAD-models or point clouds, are available and precise pixel-wise segmentation maps of 2D images can be obtained. Different from other methods, the method does not use 3D depth for training, widening the domain of application.

cs.CV↗

arXiv2019

Feature selection of neural networks is skewed towards the less abstract cue

Artificial neural networks (ANNs) have become an important tool for image classification with many applications in research and industry. However, it remains largely unknown how relevant image features are selected and how data properties affect this process. In particular, we are interested whether the abstraction level of image cues correlating with class membership influences feature selection. We perform experiments with binary images that contain a combination of cues, representing two different levels of abstractions: one is a pattern drawn from a random distribution where class membership correlates with the statistics of the pattern, the other a combination of symbol-like entities, where the symbolic code correlates with class membership. When the network is trained with data in which both cues are equally significant, we observe that the cues at the lower abstraction level, i.e., the pattern, is learned, while the symbolic information is largely ignored, even in networks with many layers. Symbol-like entities are only learned if the importance of low-level cues is reduced compared to the high-level ones. These findings raise important questions about the relevance of features that are learned by deep ANNs and how learning could be shifted towards symbolic features.

cs.CV↗