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Nils Strodthoff

Nils Strodthoff appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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hep-phhep-thMachine Learningnucl-thhep-latArtificial Intelligenceeess.SPComputer Visioncond-mat.stat-mechphysics.comp-ph

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Published work

26 published item(s)

preprint2026arXiv

A Multimodal Deep Learning Framework for Predicting ICU Deterioration: Integrating ECG Waveforms with Clinical Data and Clinician Benchmarking

Artificial intelligence holds strong potential to support clinical decision making in intensive care units where timely and accurate risk assessment is critical. However, many existing models focus on isolated outcomes or limited data types, while clinicians integrate longitudinal history, real time physiology, and heterogeneous clinical information. To address this gap, we developed MDS ICU, a unified multimodal machine learning framework that fuses routinely collected data including demographics, biometrics, vital signs, laboratory values, ECG waveforms, surgical procedures, and medical device usage to provide continuous predictive support during ICU stays. Using 63001 samples from 27062 patients in MIMIC IV, we trained a deep learning architecture that combines structured state space S4 encoders for ECG waveforms with multilayer perceptron RealMLP encoders for tabular data to jointly predict 33 clinically relevant outcomes spanning mortality, organ dysfunction, medication needs, and acute deterioration. The model achieved strong discrimination with AUROCs of 0.90 for 24 hour mortality, 0.92 for sedative administration, 0.97 for invasive mechanical ventilation, and 0.93 for coagulation dysfunction. Calibration analysis showed close agreement between predicted and observed risks, with consistent gains from ECG waveform integration. Comparisons with clinicians and large language models showed that model predictions alone outperformed both, and that providing model outputs as decision support further improved their performance. These results demonstrate that multimodal AI can deliver clinically meaningful risk stratification across diverse ICU outcomes while augmenting rather than replacing clinical expertise, establishing a scalable foundation for precision critical care decision support.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

FeatInv: Spatially resolved mapping from feature space to input space using conditional diffusion models

Internal representations are crucial for understanding deep neural networks, such as their properties and reasoning patterns, but remain difficult to interpret. While mapping from feature space to input space aids in interpreting the former, existing approaches often rely on crude approximations. We propose using a conditional diffusion model - a pretrained high-fidelity diffusion model conditioned on spatially resolved feature maps - to learn such a mapping in a probabilistic manner. We demonstrate the feasibility of this approach across various pretrained image classifiers from CNNs to ViTs, showing excellent reconstruction capabilities. Through qualitative comparisons and robustness analysis, we validate our method and showcase possible applications, such as the visualization of concept steering in input space or investigations of the composite nature of the feature space. This approach has broad potential for improving feature space understanding in computer vision models.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

FeatMap: Understanding image manipulation in the feature space and its implications for feature space geometry

Intermediate feature representations represent the backbone for the expressivity and adaptability of deep neural networks. However, their geometric structure remains poorly understood. In this submission, we provide indirect insights into this matter by applying a broad selection of manipulations in input space, ranging from geometric and photometric transformations to local masking and semantic manipulations using generative image editing models, and assess the feasibility of learning a mapping in the feature space, mapping from the original to the manipulated feature map. To this end, we devise different types of mappings, from linear to non-linear and local to global mappings and assess both the reconstruction quality of the mapping as well as the semantic content of the mapped representations. We demonstrate the feasibility of learning such mappings for all considered transformations. While global (transformer) models that operate on the full feature map often achieve best results, we show that the same can be achieved with a shared linear model operating on a single feature vector typically with very little degradation in reconstruction quality, even for highly non-trivial semantic manipulations. We analyze the corresponding mappings across different feature layers and characterize them according to dominance of weight vs. bias and the effective rank of the linear transformations. These results provide hints for the hypothesis that the feature space is to a first degree of approximation organized in linear structures. From a broader perspective, the study demonstrates that generative image editing models might open the door to a deeper understanding of the feature space through input manipulation.

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preprint2026arXiv

Pretraining Strategies and Scaling for ECG Foundation Models: A Systematic Study

Specialized foundation models are beginning to emerge in various medical subdomains, but pretraining methodologies and parametric scaling with the size of the pretraining dataset are rarely assessed systematically and in a like-for-like manner. This work focuses on foundation models for electrocardiography (ECG) data, one of the most widely captured physiological time series world-wide. We present a comprehensive assessment of pretraining methodologies, covering five different contrastive and non-contrastive self-supervised learning objectives for ECG foundation models, and investigate their scaling behavior with pretraining dataset sizes up to 11M input samples, exclusively from publicly available sources. Pretraining strategy has a meaningful and consistent impact on downstream performance, with contrastive predictive coding (slightly ahead of JEPA) yielding the most transferable representations across diverse clinical tasks. Scaling pretraining data continues to yield meaningful improvements up to 11M samples for most objectives. We also compare model architectures across all pretraining methodologies and find evidence for a clear superiority of structured state space models compared to transformers and CNN models. We hypothesize that the strong inductive biases of structured state space models, rather than pretraining scale alone, are the primary driver of effective ECG representation learning, with important implications for future foundation model development in this and potentially other physiological signal domains.

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preprint2026arXiv

Uncertainty Reliability Under Domain Shift: An Investigation for Data-Driven Blood Pressure Estimation in Photoplethysmography

Uncertainty quantification (UQ) is critical for safety-critical domains like healthcare, yet it is rarely evaluated under realistic out-of-distribution (OOD) conditions. Here, we assessed predictive performance and uncertainty reliability for deep learning-based blood pressure (BP) estimation from photoplethysmography (PPG) signals under both in-distribution (ID) and OOD settings. Using an XResNet1D-50 trained on PulseDB and tested on four external datasets, we compared deep ensembles (DE) and Monte Carlo dropout (MCD) with Gaussian negative log-likelihood (GNLL) and mean squared error (MSE) losses, optionally followed by post-hoc recalibration via conformal prediction (CP), temperature scaling (TS), and isotonic regression (IR). The key findings of our study are as follows: (1) DE provides stronger predictive robustness under domain shift than MCD, an advantage that becomes clear primarily under external shift. (2) Recalibrated GNLL-based methods yield the best uncertainty calibration (e.g., GNLL+DE+CP for systolic blood pressure (SBP), GNLL+DE+TS for diastolic blood pressure (DBP)), while MSE-based uncertainty requires recalibration to become practically useful. (3) Across settings, CP and TS offer the most consistent gains, with IR remaining competitive in several cases. Overall, our results identify DE-based methods as most robust for predictive performance under domain shift, GNLL as strongest for native UQ, and recalibration as essential for making MSE-based uncertainty practical. These findings highlight the need to jointly assess predictive accuracy and calibration on external data for trustworthy cuffless BP estimation

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preprint2022arXiv

Self-supervised representation learning from 12-lead ECG data

Clinical 12-lead electrocardiography (ECG) is one of the most widely encountered kinds of biosignals. Despite the increased availability of public ECG datasets, label scarcity remains a central challenge in the field. Self-supervised learning represents a promising way to alleviate this issue. In this work, we put forward the first comprehensive assessment of self-supervised representation learning from clinical 12-lead ECG data. To this end, we adapt state-of-the-art self-supervised methods based on instance discrimination and latent forecasting to the ECG domain. In a first step, we learn contrastive representations and evaluate their quality based on linear evaluation performance on a recently established, comprehensive, clinical ECG classification task. In a second step, we analyze the impact of self-supervised pretraining on finetuned ECG classifiers as compared to purely supervised performance. For the best-performing method, an adaptation of contrastive predictive coding, we find a linear evaluation performance only 0.5% below supervised performance. For the finetuned models, we find improvements in downstream performance of roughly 1% compared to supervised performance, label efficiency, as well as robustness against physiological noise. This work clearly establishes the feasibility of extracting discriminative representations from ECG data via self-supervised learning and the numerous advantages when finetuning such representations on downstream tasks as compared to purely supervised training. As first comprehensive assessment of its kind in the ECG domain carried out exclusively on publicly available datasets, we hope to establish a first step towards reproducible progress in the rapidly evolving field of representation learning for biosignals.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Sparse Subspace Clustering for Concept Discovery (SSCCD)

Concepts are key building blocks of higher level human understanding. Explainable AI (XAI) methods have shown tremendous progress in recent years, however, local attribution methods do not allow to identify coherent model behavior across samples and therefore miss this essential component. In this work, we study concept-based explanations and put forward a new definition of concepts as low-dimensional subspaces of hidden feature layers. We novelly apply sparse subspace clustering to discover these concept subspaces. Moving forward, we derive insights from concept subspaces in terms of localized input (concept) maps, show how to quantify concept relevances and lastly, evaluate similarities and transferability between concepts. We empirically demonstrate the soundness of the proposed Sparse Subspace Clustering for Concept Discovery (SSCCD) method for a variety of different image classification tasks. This approach allows for deeper insights into the actual model behavior that would remain hidden from conventional input-level heatmaps.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Asymptotically unbiased estimation of physical observables with neural samplers

We propose a general framework for the estimation of observables with generative neural samplers focusing on modern deep generative neural networks that provide an exact sampling probability. In this framework, we present asymptotically unbiased estimators for generic observables, including those that explicitly depend on the partition function such as free energy or entropy, and derive corresponding variance estimators. We demonstrate their practical applicability by numerical experiments for the 2d Ising model which highlight the superiority over existing methods. Our approach greatly enhances the applicability of generative neural samplers to real-world physical systems.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Deep Learning for ECG Analysis: Benchmarks and Insights from PTB-XL

Electrocardiography is a very common, non-invasive diagnostic procedure and its interpretation is increasingly supported by automatic interpretation algorithms. The progress in the field of automatic ECG interpretation has up to now been hampered by a lack of appropriate datasets for training as well as a lack of well-defined evaluation procedures to ensure comparability of different algorithms. To alleviate these issues, we put forward first benchmarking results for the recently published, freely accessible PTB-XL dataset, covering a variety of tasks from different ECG statement prediction tasks over age and gender prediction to signal quality assessment. We find that convolutional neural networks, in particular resnet- and inception-based architectures, show the strongest performance across all tasks outperforming feature-based algorithms by a large margin. These results are complemented by deeper insights into the classification algorithm in terms of hidden stratification, model uncertainty and an exploratory interpretability analysis. We also put forward benchmarking results for the ICBEB2018 challenge ECG dataset and discuss prospects of transfer learning using classifiers pretrained on PTB-XL. With this resource, we aim to establish the PTB-XL dataset as a resource for structured benchmarking of ECG analysis algorithms and encourage other researchers in the field to join these efforts.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning

Machine learning has the potential to aid our understanding of phase structures in lattice quantum field theories through the statistical analysis of Monte Carlo samples. Available algorithms, in particular those based on deep learning, often demonstrate remarkable performance in the search for previously unidentified features, but tend to lack transparency if applied naively. To address these shortcomings, we propose representation learning in combination with interpretability methods as a framework for the identification of observables. More specifically, we investigate action parameter regression as a pretext task while using layer-wise relevance propagation (LRP) to identify the most important observables depending on the location in the phase diagram. The approach is put to work in the context of a scalar Yukawa model in (2+1)d. First, we investigate a multilayer perceptron to determine an importance hierarchy of several predefined, standard observables. The method is then applied directly to the raw field configurations using a convolutional network, demonstrating the ability to reconstruct all order parameters from the learned filter weights. Based on our results, we argue that due to its broad applicability, attribution methods such as LRP could prove a useful and versatile tool in our search for new physical insights. In the case of the Yukawa model, it facilitates the construction of an observable that characterises the symmetric phase.

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preprint2016arXiv

Landau gauge Yang-Mills correlation functions

We investigate Landau gauge $SU(3)$ Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Chiral Mirror-Baryon-Meson Model and Nuclear Matter beyond Mean-Field

We consider a chiral baryon-meson model for nucleons and their parity partners in mirror assignment interacting with pions, sigma and omega mesons to describe the liquid-gas transition of nuclear matter together with chiral symmetry restoration in the high density phase. Within the mean-field approximation the model is known to provide a phenomenologically successful description of the nuclear-matter transition. Here, we go beyond this approximation and include mesonic fluctuations by means of the functional renormalization group. While these fluctuations do not lead to major qualitative changes in the phase diagram of the model, beyond mean-field, one is no-longer free to adjust the parameters so as to reproduce the binding energy per nucleon, the nuclear saturation density, and the nucleon sigma term all at the same time. However, the prediction of a clear first-order chiral transition at low temperatures inside the high baryon-density phase appears to be robust.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Spectral Functions for the Quark-Meson Model Phase Diagram from the Functional Renormalization Group

We present a method to obtain spectral functions at finite temperature and density from the Functional Renormalization Group. Our method is based on a thermodynamically consistent truncation of the flow equations for 2-point functions with analytically continued frequency components in the originally Euclidean external momenta. For the uniqueness of this continuation at finite temperature we furthermore implement the physical Baym-Mermin boundary conditions. We demonstrate the feasibility of the method by calculating the mesonic spectral functions in the quark-meson model along the temperature axis of the phase diagram, and at finite quark chemical potential along the fixed-temperature line that crosses the critical endpoint of the model.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Chiral symmetry breaking in continuum QCD

We present a quantitative analysis of chiral symmetry breaking in two-flavour continuum QCD in the quenched limit. The theory is set-up at perturbative momenta, where asymptotic freedom leads to precise results. The evolution of QCD towards the hadronic phase is achieved by means of dynamical hadronisation in the non-perturbative functional renormalisation group approach. We use a vertex expansion scheme based on gauge-invariant operators and discuss its convergence properties and the remaining systematic errors. In particular we present results for the quark propagator, the full tensor structure and momentum dependence of the quark-gluon vertex, and the four-fermi scatterings.

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preprint2014arXiv

Polyakov-Quark-Meson-Diquark Model for two-color QCD

We present an update on the phase diagram of two-color QCD from a chiral effective model approach based on a quark-meson-diquark model using the Functional Renormalization Group (FRG). We discuss the impact of perturbative UV contributions, the inclusion of gauge field dynamics via a phenomenological Polyakov loop potential, and the impact of matter backcoupling on the gauge sector. The corresponding phase diagram including these effects is found to be in qualitative agreement with recent lattice investigations.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group

In the framework of the functional renormalization group (FRG) we present a simple truncation scheme for the computation of real-time mesonic n-point functions, consistent with the derivative expansion of the effective action. Via analytic continuation on the level of the flow equations we perform calculations of mesonic spectral functions in the scalar O(N) model, which we use as an exploratory example. By investigating the renormalization-scale dependence of the 2-point functions we shed light on the nature of the sigma meson, whose spectral properties are predominantly of dynamical origin.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Spectral Functions from the Functional Renormalization Group

In this article we wish to present a new method to obtain spectral functions at finite temperature and density from the Functional Renormalization Group (FRG). The FRG offers a powerful non-perturbative tool to deal with phase transitions in strong-interaction matter under extreme conditions and their fluctuation properties. Based on a thermodynamically consistent truncation we derive flow equations for pertinent two-point functions in Minkowski space-time. We demonstrate the feasibility of the method by calculating mesonic spectral functions in hot and dense hadronic matter using the quark-meson model as a simple example.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Spectral functions from the functional renormalization group at finite temperature and density

We present a viable method to obtain real-time quantities such as spectral functions or transport coefficients at finite temperature and density within a non-perturbative Functional Renormalization Group approach. Our method is based on a thermodynamically consistent truncation of the flow equations for 2-point functions with analytically continued frequency components in the originally Euclidean external momenta. We demonstrate its feasibility by calculating the mesonic spectral functions in the quark-meson model at different temperatures and quark chemical potentials, in particular around the critical endpoint in the phase diagram of the model.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Towards quantitative precision in the chiral crossover: masses and fluctuation scales

We investigate the relation between the physical pion pole and screening masses and the mesonic fluctuation scale in low-energy QCD, which relates to the curvature of the mesonic effective potential. This relation is important for the correct relative weight of quantum, thermal and density fluctuations. Hence, it governs the location of phase boundaries as well as the phase structure of QCD. The identification of the correct physics scales is also primarily important for the correct adjustment of the parameters of effective models for low-energy QCD. It is shown that subject to an appropriate definition of the latter, all these scales agree at vanishing temperature, while they deviate from each other at finite temperature.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Transport Coefficients in Yang--Mills Theory and QCD

We calculate the shear viscosity over entropy density ratio $η/s$ in Yang--Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of $η/s$ over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently we provide a first estimate for $η/s$ in QCD.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Finite-Temperature Spectral Functions from the Functional Renormalization Group

We present a method to obtain spectral functions at finite temperature from the Functional Renormalization Group. Our method is based on a thermodynamically consistent truncation of the flow equations for 2-point functions with analytically continued frequency components in the originally Euclidean external momenta. For the uniqueness of this continuation at finite temperature we furthermore implement the physical Baym-Mermin boundary conditions. Results are presented for mesonic spectral functions obtained from a two-flavor quark-meson model.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Fluctuations in the quark-meson model for QCD with isospin chemical potential

We study the two-flavor quark-meson (QM) model with the functional renormalization group (FRG) to describe the effects of collective mesonic fluctuations on the phase diagram of QCD at finite baryon and isospin chemical potentials, $μ_B$ and $μ_I$. With only isospin chemical potential there is a precise equivalence between the competing dynamics of chiral versus pion condensation and that of collective mesonic and baryonic fluctuations in the quark-meson-diquark model for two-color QCD at finite baryon chemical potential. Here, finite $μ_B=3μ$ introduces an additional dimension to the phase diagram as compared to two-color QCD, however. At zero temperature, the ($μ_I,μ$)-plane of this phase diagram is strongly constrained by the "Silver Blaze problem." In particular, the onset of pion condensation must occur at $μ_I= m_π/2$, independent of $μ$ as long as $μ+ μ_I$ stays below the constituent quark mass of the QM model or the liquid-gas transition line of nuclear matter in QCD. In order to maintain this relation beyond mean field it is crucial to compute the pion mass from its timelike correlator with the FRG in a consistent way.

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preprint2012arXiv

Quark-meson-diquark model for two-color QCD

We introduce a two-flavor quark-meson-diquark model for two-color QCD and its extensions to include gauge-field dynamics as described by the Polakov loop. Grand potential and phase structure are being studied both in mean-field approximation and with the functional renormalization group. The model provides an explicit example for the importance of baryonic degrees of freedom: When they are omitted, the phase diagram closely resembles that of the corresponding (Polyakov)-quark-meson models for QCD, in particular including their critical endpoint. In order to reproduce the well established main features based on the symmetries and breaking patterns of two-color QCD, however, they must be included and there is no critical endpoint. The competing dynamics of collective mesonic and baryonic fluctuations is well described by the functional renormalization group equation in lowest order derivative expansion for the effective potential which we solve numerically on a two-dimensional grid in field space.

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preprint2010arXiv

SU(3) Deconfinement in (2+1)d from Twisted Boundary Conditions and Self-Duality

We study the pure SU(3) gauge theory in 2+1 dimensions on the lattice using 't Hooft's twisted boundary conditions to force non-vanishing center flux through the finite volume. In this way we measure the free energy of spacelike center vortices as an order parameter for the deconfinement transition. The transition is of 2nd order in the universality class of the 2d 3-state Potts model, which is self-dual. This self-duality can be observed directly in the SU(3) gauge theory, and it can be exploited to extract critical couplings with high precision in rather small volumes. We furthermore obtain estimates for critical exponents and the critical temperature in units of the dimensionful continuum coupling. Finally, we also apply our methods to the (2+1)d SU(4) gauge theory which was previously found to have a weak 1st order transition. We nevertheless observe at least approximate q = 4 Potts scaling at length scales corresponding to the lattice sizes used in our simulations.

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preprint2010arXiv

Universal Aspects of Deconfinement in 2+1 Dimensions

The 2+1 dimensional pure SU(N) gauge theories with N <= 4 are candidates for applying the powerful tools of scaling and universality to their deconfinement transitions at finite temperature. The corresponding 2 dimensional q-state Potts models with q <= 4 have 2nd order transitions, and we can exploit many exact results to obtain accurate critical couplings, transition temperatures, critical exponents, and the leading behavior of the continuum string tension near the phase transition on one side, together with its dual on the other. Thereby, the self-duality of the 2d spin models is reflected in a duality between spacelike vortices and confining electric fluxes. We also discuss the relevance of center symmetry and the corresponding vortices for confinement in full QCD when the electromagnetic interactions of fractionally charged quarks are included.

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preprint2010arXiv

Universal Aspects of Deconfinement: Interfaces, Flux Tubes and Self-Duality in 2+1 Dimensions

We study center vortex free energies and 't Hooft's electric fluxes on the lattice in 2+1 dimensions, where SU(2) for example, is in the universality class of the 2d Ising model. This places a wealth of exact results at our fingertips. In particular, spacelike center vortices in SU(2) near criticality correspond to spin interfaces in the 2d Ising model, whose universal scaling functions are known exactly. We exploit this to locate the deconfinement transition with unprecedented precision and subsequently for a finite size scaling analysis, where the self-duality of the $2d$ spin model is reflected in a duality between the spacelike vortices and confining electric fluxes. The corresponding relation between the string tension and its dual in the high temperature phase is arguably the simplest example of a universal amplitude ratio. Around the transition, both can be efficiently extracted from the exact results with a global one-parameter fit which allows straightforward continuum extrapolation.

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