arXiv subjects

Klaus-Robert Müller

Publications and source records attributed to Klaus-Robert Müller.

At least 37 records · Page 2Linked to original sources

arXiv2026

How Atoms Interact Within Molecules

Fundamental understanding of interatomic forces in molecules must emerge from quantum mechanics, yet widely used empirical force fields rely on simplified mechanistic approximations that often fail to capture the complexity of many-body systems. Here we employ recent developments in quantum field theory (QFT) for long-range electron correlation and machine learning force fields (MLFFs) to directly compute the depth and scatter of interatomic forces for molecular systems containing hundreds of atoms. We find that while the average interaction strength decays polynomially with interatomic separation, the interaction scatter remains robust and exhibits substantial anisotropy. Both QFT and MLFFs demonstrate that increasing the molecular size further amplifies this scatter and anisotropy -- a phenomenon not considered in traditional textbook empirical models. These results provide new benchmarks for force models, shift the focus from interacting atoms to interacting ``hotspots'' that might determine the folding pathways of (bio)polymers, and rationalize why MLFFs are uniquely successful in capturing the nuances of complex molecular systems. Our findings offer a roadmap for the development of more accurate and quantum-aware molecular force fields.

physics.chem-ph↗

arXiv2026

Relevant Walk Search for Explaining Graph Neural Networks

Graph Neural Networks (GNNs) have become important machine learning tools for graph analysis, and its explainability is crucial for safety, fairness, and robustness. Layer-wise relevance propagation for GNNs (GNN-LRP) evaluates the relevance of \emph{walks} to reveal important information flows in the network, and provides higher-order explanations, which have been shown to be superior to the lower-order, i.e., node-/edge-level, explanations. However, identifying relevant walks by GNN-LRP requires {\em exponential} computational complexity with respect to the network depth, which we will remedy in this paper. Specifically, we propose {\em polynomial-time} algorithms for finding top-$K$ relevant walks, which drastically reduces the computation and thus increases the applicability of GNN-LRP to large-scale problems. Our proposed algorithms are based on the \emph{max-product} algorithm -- a common tool for finding the maximum likelihood configurations in probabilistic graphical models -- and can find the most relevant walks exactly at the neuron level and approximately at the node level. Our experiments demonstrate the performance of our algorithms at scale and their utility across application domains, i.e., on epidemiology, molecular, and natural language benchmarks. We provide our codes under \href{https://github.com/xiong-ping/rel_walk_gnnlrp}{github.com/xiong-ping/rel\_walk\_gnnlrp}.

cs.LG↗

arXiv2026

Efficient Higher-order Subgraph Attribution via Message Passing

Explaining graph neural networks (GNNs) has become more and more important recently. Higher-order interpretation schemes, such as GNN-LRP (layer-wise relevance propagation for GNN), emerged as powerful tools for unraveling how different features interact thereby contributing to explaining GNNs. GNN-LRP gives a relevance attribution of walks between nodes at each layer, and the subgraph attribution is expressed as a sum over exponentially many such walks. In this work, we demonstrate that such exponential complexity can be avoided. In particular, we propose novel algorithms that enable to attribute subgraphs with GNN-LRP in linear-time (w.r.t. the network depth). Our algorithms are derived via message passing techniques that make use of the distributive property, thereby directly computing quantities for higher-order explanations. We further adapt our efficient algorithms to compute a generalization of subgraph attributions that also takes into account the neighboring graph features. Experimental results show the significant acceleration of the proposed algorithms and demonstrate the high usefulness and scalability of our novel generalized subgraph attribution method.

cs.LG↗

arXiv2026

Generative Pseudo-Force Fields for Molecular Generation

Generating stable molecular conformations typically forces a tradeoff between the physical realism of energy-based relaxation and the sampling efficiency of data-driven generative models. While machine learning force fields (MLFFs) can sample stable conformations by relaxing molecular geometries according to physical forces, they require costly ab-initio training data. Conversely, diffusion models (DMs) learn from equilibrium data alone but are dependent on noise schedules and time-step conditioning. In this work, we propose generative pseudo-force fields (GPFFs) to bridge these paradigms by training an MLFF on a quadratic pseudo-potential energy surface relative to reference equilibrium structures. Because no ab-initio calculations are required for the perturbed geometries, non-equilibrium training data can be generated on the fly by perturbing the equilibria with Gaussian noise. We show that GPFFs constitute a time-step-agnostic variant of variance exploding DMs: the score comes from the predicted pseudo-forces but because force magnitudes implicitly encode the noise level, no time-step conditioning is needed. Our GPFF can hence be used as a drop-in replacement in standard diffusion sampling (ancestral, Heun) but also facilitates more efficient, adaptive variants and an MLFF inspired direct denoising scheme. Our proposed sampling algorithms support arbitrary structural priors and geometric constraints. On QM9, GPFF has 100 % validity at 256 neural function evaluations (NFE) and over 50 % at just 6 NFE, outperforming diffusion baselines across all samplers. Combined with custom priors, we showcase the fast and accurate generation process of our method in a molecular editor for a drug design setting, where a molecule is generated in real time.

cs.LG↗

arXiv2026

Reliable Modeling of Distribution Shifts via Displacement-Reshaped Optimal Transport

Optimal transport (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not violate the true geometry of change. We propose Displacement-Reshaped Optimal Transport (ReshapeOT), a method that reshapes the ground metric by integrating observed sample displacements as an additional source of knowledge. Technically, ReshapeOT replaces the Euclidean metric with a Mahalanobis distance estimated from displacement second moments. This effectively carves expressways through the input space, inviting transport solutions that better align with observed displacements. Our method is computationally lightweight, integrates seamlessly into any OT solver that operates on a cost matrix, and can be kernelized for further flexibility. Experiments on synthetic and real-world data show that ReshapeOT achieves substantial gains in transport reliability. We further demonstrate our method's usefulness in two practical use cases.

cs.LG↗

arXiv2026

Enhancing molecular dynamics with equivariant machine-learned densities

Machine-learning interatomic potentials (MLIPs) have enabled molecular dynamics at near ab initio accuracy, yet remain limited to energies and forces by construction, leaving electronic observables such as dipole moments and polarizabilities inaccessible. We introduce DenSNet, a density-first approach to machine-learned electronic structure that learns the Hohenberg--Kohn map from nuclear configurations to the ground-state electron density. Our approach employs an SE(3)-equivariant neural network to predict density coefficients of a flexible atom-centered Gaussian basis, combined with a $Δ$-learning strategy that uses superposed atomic densities as a prior to accelerate training. A second equivariant network then maps the predicted density to the total energy, providing a unified framework for molecular dynamics and electronic structure. We validate DenSNet on ethanol, ethanethiol, and resorcinol, where infrared spectra from machine-learned trajectories show excellent agreement with experimental gas-phase measurements. To test scalability, we train on polythiophene oligomers with 1--6 monomers and extrapolate to chains of up to 12 monomers, generating stable long-time trajectories whose infrared spectra agree with reference density functional theory calculations. Here, we show that reinstating the electron density as the central learned quantity opens a practical route to transferable prediction of spectroscopic and electronic observables in large-scale molecular simulations.

physics.chem-ph↗

arXiv2026

Context Sensitivity Improves Human-Machine Visual Alignment

Modern machine learning models typically represent inputs as fixed points in a high-dimensional embedding space. While this approach has been proven powerful for a wide range of downstream tasks, it fundamentally differs from the way humans process information. Because humans are constantly adapting to their environment, they represent objects and their relationships in a highly context-sensitive manner. To address this gap, we propose a method for context-sensitive similarity computation from neural network embeddings, applied to modeling a triplet odd-one-out task with an anchor image serving as simultaneous context. Modeling context enables us to achieve up to a 15% improvement in odd-one-out accuracy over a context-insensitive model. We find that this improvement is consistent across both original and "human-aligned" vision foundation models.

cs.CV↗

arXiv2026

OpenTME: An Open Dataset of AI-powered H&E Tumor Microenvironment Profiles from TCGA

The tumor microenvironment (TME) plays a central role in cancer progression, treatment response, and patient outcomes, yet large-scale, consistent, and quantitative TME characterization from routine hematoxylin and eosin (H&E)-stained histopathology remains scarce. We introduce OpenTME, an open-access dataset of pre-computed TME profiles derived from 3,634 H&E-stained whole-slide images across five cancer types (bladder, breast, colorectal, liver, and lung cancer) from The Cancer Genome Atlas (TCGA). All outputs were generated using Atlas H&E-TME, an AI-powered application built on the Atlas family of pathology foundation models, which performs tissue quality control, tissue segmentation, cell detection and classification, and spatial neighborhood analysis, yielding over 4,500 quantitative readouts per slide at cell-level resolution. OpenTME is available for non-commercial academic research on Hugging Face. We will continue to expand OpenTME over time and anticipate it will serve as a resource for biomarker discovery, spatial biology research, and the development of computational methods for TME analysis.

cs.CV↗

arXiv2026

Characterizing High-Capacity Janus Aminobenzene-Graphene Anode for Sodium-Ion Batteries with Machine Learning

Sodium-ion batteries require anodes that combine high capacity, low operating voltage, fast Na-ion transport, and mechanical stability, which conventional anodes struggle to deliver. Here, we use the SpookyNet machine-learning force field (MLFF) together with all-electron density-functional theory calculations to characterize Na storage in aminobenzene-functionalized Janus graphene (Na$_x$AB) at room-temperature. Simulations across state of charge reveal a three-stage storage mechanism-site-specific adsorption at aminobenzene groups and Na$_n$@AB$_m$ structure formation, followed by interlayer gallery filling-contrasting the multi-stage pore-, graphite-interlayer-, and defect-controlled behavior in hard carbon. This leads to an OCV profile with an extended low-voltage plateau of 0.15 V vs. Na/Na$^{+}$, an estimated gravimetric capacity of $\sim$400 mAh g$^{-1}$, negligible volume change, and Na diffusivities of $\sim10^{-6}$ cm$^{2}$ s$^{-1}$, two to three orders of magnitude higher than in hard carbon. Our results establish Janus aminobenzene-graphene as a promising, structurally defined high-capacity Na-ion anode and illustrate the power of MLFF-based simulations for characterizing electrode materials.

cond-mat.mtrl-sci↗

arXiv2026

Enhancing Brain Source Reconstruction by Initializing 3D Neural Networks with Physical Inverse Solutions

Reconstructing brain sources is a fundamental challenge in neuroscience, crucial for understanding brain function and dysfunction. Electroencephalography (EEG) signals have a high temporal resolution. However, identifying the correct spatial location of brain sources from these signals remains difficult due to the ill-posed structure of the problem. Traditional methods predominantly rely on manually crafted priors, missing the flexibility of data-driven learning, while recent deep learning approaches focus on end-to-end learning, typically using the physical information of the forward model only for generating training data. We propose the novel hybrid method 3D-PIUNet for EEG source localization that effectively integrates the strengths of traditional and deep learning techniques. 3D-PIUNet starts from an initial physics-informed estimate by using the pseudo inverse to map from measurements to source space. Secondly, by viewing the brain as a 3D volume, we use a 3D convolutional U-Net to capture spatial dependencies and refine the solution according to the learned data prior. Training the model relies on simulated pseudo-realistic brain source data, covering different source distributions. Trained on this data, our model significantly improves spatial accuracy, demonstrating superior performance over both traditional and end-to-end data-driven methods. Additionally, we validate our findings with real EEG data from a visual task, where 3D-PIUNet successfully identifies the visual cortex and reconstructs the expected temporal behavior, thereby showcasing its practical applicability.

eess.IV↗

arXiv2026

Beyond Attention Heatmaps: How to Get Better Explanations for Multiple Instance Learning Models in Histopathology

Multiple instance learning (MIL) has enabled substantial progress in computational histopathology, where a large amount of patches from gigapixel whole slide images are aggregated into slide-level predictions. Heatmaps are widely used to validate MIL models and to discover tissue biomarkers. Yet, the validity of these heatmaps has barely been investigated. In this work, we introduce a general framework for evaluating the quality of MIL heatmaps without requiring additional labels. We conduct a large-scale benchmark experiment to assess six explanation methods across histopathology task types (classification, regression, survival), MIL model architectures (Attention-, Transformer-, Mamba-based), and patch encoder backbones (UNI2, Virchow2). Our results show that explanation quality mostly depends on MIL model architecture and task type, with perturbation ("Single"), layer-wise relevance propagation (LRP), and integrated gradients (IG) consistently outperforming attention-based and gradient-based saliency heatmaps, which often fail to reflect model decision mechanisms. We further demonstrate the advanced capabilities of the best-performing explanation methods: (i) We provide a proof-of-concept that MIL heatmaps of a bulk gene expression prediction model can be correlated with spatial transcriptomics for biological validation, and (ii) showcase the discovery of distinct model strategies for predicting human papillomavirus (HPV) infection from head and neck cancer slides. Our work highlights the importance of validating MIL heatmaps and establishes that improved explainability can enable more reliable model validation and yield biological insights, making a case for a broader adoption of explainable AI in digital pathology. Our code is provided in a public GitHub repository: https://github.com/bifold-pathomics/xMIL/tree/xmil-journal

cs.CV↗

arXiv2026

Investigating the Robustness of Subtask Distillation under Spurious Correlation

Subtask distillation is an emerging paradigm in which compact, specialized models are extracted from large, general-purpose 'foundation models' for deployment in environments with limited resources or in standalone computer systems. Although distillation uses a teacher model, it still relies on a dataset that is often limited in size and may lack representativeness or exhibit spurious correlations. In this paper, we evaluate established distillation methods, as well as the recent SubDistill method, when using data with spurious correlations for distillation. As the strength of the correlations increases, we observe a widening gap between advanced methods, such as SubDistill, which remain fairly robust, and some baseline methods, which degrade to near-random performance. Overall, our study underscores the challenges of knowledge distillation when applied to imperfect, real-world datasets, particularly those with spurious correlations.

cs.LG↗

arXiv2026

How simple can you go? An off-the-shelf transformer approach to molecular dynamics

Most current neural networks for molecular dynamics (MD) include physical inductive biases, resulting in specialized and complex architectures. This is in contrast to most other machine learning domains, where specialist approaches are increasingly replaced by general-purpose architectures trained on vast datasets. In line with this trend, several recent studies have questioned the necessity of architectural features commonly found in MD models, such as built-in rotational equivariance or energy conservation. In this work, we contribute to the ongoing discussion by evaluating the performance of an MD model with as few specialized architectural features as possible. We present a recipe for MD using an Edge Transformer, an ``off-the-shelf'' transformer architecture that has been minimally modified for the MD domain, termed MD-ET. Our model implements neither built-in equivariance nor energy conservation. We use a simple supervised pre-training scheme on $\sim$30 million molecular structures from the QCML database. Using this ``off-the-shelf'' approach, we show state-of-the-art results on several benchmarks after fine-tuning for a small number of steps. Additionally, we examine the effects of being only approximately equivariant and energy conserving for MD simulations, proposing a novel method for distinguishing the errors resulting from non-equivariance from other sources of inaccuracies like numerical rounding errors. While our model exhibits runaway energy increases on larger structures, we show approximately energy-conserving NVE simulations for a range of small structures.

cs.LG↗

arXiv2026

Manipulating Feature Visualizations with Gradient Slingshots

Feature Visualization (FV) is a widely used technique for interpreting concepts learned by Deep Neural Networks (DNNs), which synthesizes input patterns that maximally activate a given feature. Despite its popularity, the trustworthiness of FV explanations has received limited attention. We introduce Gradient Slingshots, a novel method that enables FV manipulation without modifying model architecture or significantly degrading performance. By shaping new trajectories in off-distribution regions of a feature's activation landscape, we coerce the optimization process to converge to a predefined visualization. We evaluate our approach on several DNN architectures, demonstrating its ability to replace faithful FVs with arbitrary targets. These results expose a critical vulnerability: auditors relying solely on FV may accept entirely fabricated explanations. To mitigate this risk, we propose a straightforward defense and quantitatively demonstrate its effectiveness.

cs.LG↗

arXiv2026

Distilling Lightweight Domain Experts from Large ML Models by Identifying Relevant Subspaces

Knowledge distillation involves transferring the predictive capabilities of large, high-performing AI models (teachers) to smaller models (students) that can operate in environments with limited computing power. In this paper, we address the scenario in which only a few classes and their associated intermediate concepts are relevant to distill. This scenario is common in practice, yet few existing distillation methods explicitly focus on the relevant subtask. To address this gap, we introduce 'SubDistill', a new distillation algorithm with improved numerical properties that only distills the relevant components of the teacher model at each layer. Experiments on CIFAR-100 and ImageNet with Convolutional and Transformer models demonstrate that SubDistill outperforms existing layer-wise distillation techniques on a representative set of subtasks. Our benchmark evaluations are complemented by Explainable AI analyses showing that our distilled student models more closely match the decision structure of the original teacher model.

cs.LG↗

arXiv2025

Sampling 3D Molecular Conformers with Diffusion Transformers

Diffusion Transformers (DiTs) have demonstrated strong performance in generative modeling, particularly in image synthesis, making them a compelling choice for molecular conformer generation. However, applying DiTs to molecules introduces novel challenges, such as integrating discrete molecular graph information with continuous 3D geometry, handling Euclidean symmetries, and designing conditioning mechanisms that generalize across molecules of varying sizes and structures. We propose DiTMC, a framework that adapts DiTs to address these challenges through a modular architecture that separates the processing of 3D coordinates from conditioning on atomic connectivity. To this end, we introduce two complementary graph-based conditioning strategies that integrate seamlessly with the DiT architecture. These are combined with different attention mechanisms, including both standard non-equivariant and SO(3)-equivariant formulations, enabling flexible control over the trade-off between between accuracy and computational efficiency. Experiments on standard conformer generation benchmarks (GEOM-QM9, -DRUGS, -XL) demonstrate that DiTMC achieves state-of-the-art precision and physical validity. Our results highlight how architectural choices and symmetry priors affect sample quality and efficiency, suggesting promising directions for large-scale generative modeling of molecular structures. Code is available at https://github.com/ML4MolSim/dit_mc.

cs.LG↗

arXiv2025

Explaining Bayesian Neural Networks

To advance the transparency of learning machines such as Deep Neural Networks (DNNs), the field of Explainable AI (XAI) was established to provide interpretations of DNNs' predictions. While different explanation techniques exist, a popular approach is given in the form of attribution maps, which illustrate, given a particular data point, the relevant patterns the model has used for making its prediction. Although Bayesian models such as Bayesian Neural Networks (BNNs) have a limited form of transparency built-in through their prior weight distribution, they lack explanations of their predictions for given instances. In this work, we take a step toward combining these two perspectives by examining how local attributions can be extended to BNNs. Within the Bayesian framework, network weights follow a probability distribution; hence, the standard point explanation extends naturally to an explanation distribution. Viewing explanations probabilistically, we aggregate and analyze multiple local attributions drawn from an approximate posterior to explore variability in explanation patterns. The diversity of explanations offers a way to further explore how predictive rationales may vary across posterior samples. Quantitative and qualitative experiments on toy and benchmark data, as well as on a real-world pathology dataset, illustrate that our framework enriches standard explanations with uncertainty information and may support the visualization of explanation stability.

cs.LG↗

arXiv2025

Noise & pattern: identity-anchored Tikhonov regularization for robust structural anomaly detection

Anomaly detection plays a pivotal role in automated industrial inspection, aiming to identify subtle or rare defects in otherwise uniform visual patterns. As collecting representative examples of all possible anomalies is infeasible, we tackle structural anomaly detection using a self-supervised autoencoder that learns to repair corrupted inputs. To this end, we introduce a corruption model that injects artificial disruptions into training images to mimic structural defects. While reminiscent of denoising autoencoders, our approach differs in two key aspects. First, instead of unstructured i.i.d.\ noise, we apply structured, spatially coherent perturbations that make the task a hybrid of segmentation and inpainting. Second, and counterintuitively, we add and preserve Gaussian noise on top of the occlusions, which acts as a Tikhonov regularizer anchoring the Jacobian of the reconstruction function toward identity. This identity-anchored regularization stabilizes reconstruction and further improves both detection and segmentation accuracy. On the MVTec AD benchmark, our method achieves state-of-the-art results (I/P-AUROC: 99.9/99.4), supporting our theoretical framework and demonstrating its practical relevance for automatic inspection.

cs.CV↗