arXiv subjects

Klaus-Robert Müller

Publications and source records attributed to Klaus-Robert Müller.

At least 19 recordsLinked to original sources

arXiv2026

Revisiting Explainable AI through Model-Independent Concept Dictionaries

Modern applications of AI rely on increasingly complex models. Explainable AI (XAI) has emerged as a set of techniques aimed at improving model transparency. However, existing XAI methods typically assume input features to be inherently interpretable, or they rely on intermediate internal abstractions that are difficult to characterize and highly architecture-specific, hindering consistent use across models. To address these limitations, we propose DictXAI, a method that defines concepts directly in the input domain via a dictionary---a large, potentially overcomplete set of predefined elements, each carrying an interpretable meaning. Technically, DictXAI first computes a sparse code of the input and then attributes the model's prediction to the associated dictionary elements. We demonstrate the actionable nature of DictXAI explanations, showing that they can attribute AI malfunctions (e.g., Clever Hans effects) directly to identifiable artifact patterns in the data, while fostering human-AI alignment on intricate biomedical signals. We further demonstrate our method's ability to operate across a wide variety of dictionaries, including learned image bases, analytically defined waveforms for electrocardiography, and experimentally acquired dictionary elements. Overall, our results show that DictXAI provides more interpretable, actionable, and architecture-agnostic insights than classical XAI or existing concept-based approaches.

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arXiv2026

Stability-Shaped Deep Graph Learning

In deep graph neural networks, increasing depth enlarges the receptive field but often leads to over-smoothing, where node representations tend to align. We develop a unified, mode-wise stability framework for deep GNN propagation that provides a principled characterization of over-smoothing. By interpreting layer depth as time and layer updates as graph-coupled dynamics, over-smoothing can be understood as an undesirable dynamical synchronization of features, for which the master stability curve provides a theoretical tool to assess the stability of synchrony. Guided by this theory, we further propose Stability-Shaped Deep Graph Learning (SDGL) to mitigate over-smoothing in deep GNNs. SDGL has two complementary instantiations: one induces controlled Turing instability to replace synchronization with spatial pattern formation, and the other maintains stable near-critical propagation. Experiments on diverse node- and graph-level benchmarks demonstrate the improved depth scaling and consistent accuracy gains over strong baselines, including graphs exhibiting long-range dependencies.

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arXiv2026

Decoupling Time and Space: A Temporally Conditioned Refinement for EEG Source Imaging

Electroencephalography (EEG) offers millisecond temporal resolution, but inferring underlying neural sources is a severely ill-posed spatial inverse problem. While deep learning has advanced spatial reconstruction, current architectures face a critical dilemma: frame-by-frame models discard vital temporal context, whereas full 4D spatiotemporal networks introduce an architectural trade-off between reconstruction accuracy and inference cost. We propose a novel two-stream framework that explicitly decouples global temporal representation learning from per-time-point spatial refinement. A Transformer-based Temporal Condition Encoder processes the entire EEG sequence via factorized spatiotemporal attention, retaining sensor-resolved features. A fixed inverse then maps these features into source-indexed conditioning for a per-timestep Source-Space Transformer or volumetric convolutional refiner. Extensive evaluations on realistic synthetic data demonstrate that this temporal prior dramatically improves spatial localization, outperforming classical and spatiotemporal baselines, particularly in high-noise and multi-source regimes. Training across diverse leadfields and explicit operator mismatches improves transfer to unseen head geometries and brings template-based reconstruction closer to subject-specific inversion. Furthermore, we apply the model trained only on synthetic EEG data to real-world EEG. A logistic regressor fit on source power differences in eyes-open, eyes-closed conditions successfully decodes age groups.

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arXiv2026

Towards Fast and Disentangled Counterfactuals for Visual Foundation Models

Foundation models remain vulnerable to spurious correlations and ``Clever Hans'' strategies. Explainable machine learning can find and remove such strategies for classifiers without metadata. For foundation models, no such option exists yet. We propose Disentangled Diffusion Autoencoders (DiDAE). DiDAE wraps a frozen foundation model in a conditional diffusion decoder. A counterfactual is one closed-form edit along a direction of a disentangled dictionary, followed by decoding. The dictionary can be supervised (Procrustes) or unsupervised (Singular Value Decomposition, Sparse Autoencoders). No gradients are needed, so DiDAE is up to 2000 times faster than the state of the art. We evaluate on six datasets, two synthetic and four real-world. In a desiderata-driven benchmark on three of them, its counterfactuals are on par with or better than the state of the art, and they repair downstream classifiers through Counterfactual Knowledge Distillation (CFKD), where they beat metadata-based correction. The same machinery can rank a pretrained dictionary against a trained classifier. It returns the few directions the classifier actually reads, each causally verified by a counterfactual that flips the decision, and repairs the classifier along those a teacher marks spurious. The workflow is plug-and-play in our open-source Peal library we publish alongside the paper. With a public dictionary and a pretrained decoder, all that remains is a cheap linear distillation of the classifier and its own fine-tuning.

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arXiv2026

A strategic roadmap for an atomistic machine-learning ecosystem

Data-driven machine learning (ML) techniques have become an essential tool in many domains of science. Their application to atomistic simulations of matter is particularly widespread and impactful. This success is due largely to the existence of a well-developed and established physics-based modeling framework, ranging from first-principles electronic-structure calculations to molecular dynamics and statistical sampling, into which ML was integrated naturally to reshape long-standing trade-offs between accuracy, efficiency, and scale. Nevertheless, this integration raises both conceptual and practical challenges, from choosing between data-centric and physics-based modeling approaches to adapting established software stacks to modern hardware accelerators and ML libraries. As the field evolves rapidly, fueled in part by widespread enthusiasm but also by tangible impact, it seems appropriate to take a moment to consider the current state of the art and open challenges, and reflect on what can be done to better coordinate efforts across the community. With this goal in mind, several members of this community met in Lausanne in January 2026 at CECAM to discuss algorithms, models, software and hardware infrastructure, and the most promising scientific applications that have become possible thanks to the use of artificial intelligence in atomic-scale simulations. This strategic roadmap paper summarizes the outcomes of these discussions, suggesting some long-term goals, and some concrete actions, to establish a healthy, sustainable and impactful atomistic ML ecosystem.

physics.chem-ph↗

arXiv2026

In-Context Multiple Instance Learning

Multiple Instance Learning (MIL) addresses problems where supervision is available at the level of bags of instances and has been successfully applied in fields ranging from computational pathology to satellite imagery. Nevertheless, existing algorithms struggle in the low-label regime that characterizes many real-world applications. Flexible models overfit and rigid ones fail to adapt to the task at hand. We show that pretraining an in-context learner with a Perceiver-style architecture on synthetic data yields a model that can solve new tasks from a handful of labeled bags. At inference time, classification happens in a single forward pass and requires no gradient updates. We propose and investigate different synthetic data generators for bag-structured data and find that they capture complementary inductive biases. A model pretrained on a mixture of these generators inherits their per-task strengths and achieves the best average performance across twelve MIL benchmarks, outperforming supervised baselines that require task-specific training.

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arXiv2026

Control Variate Score Matching for Diffusion Models

Sampling from unnormalized probability densities is a pervasive challenge across the computational and physical sciences. Diffusion models provide a powerful generative framework for this task, but their success relies on accurately estimating the score of the perturbed target distribution. Current approaches face a dichotomy between two standard estimation methods: the Denoising Score Identity (DSI) requires data samples and exhibits high variance at low noise levels, whereas the Target Score Identity (TSI) relies on the energy function and suffers from diverging variance at high noise levels. In this work, we reconcile both approaches by introducing the Control Variate Score Identity (CVSI), an unbiased estimator with an analytically optimal, state- and time-dependent control coefficient that theoretically minimizes variance over the entire diffusion process. CVSI serves as a robust plug-in estimator that significantly enhances performance and efficiency in data-free sampler learning and training-free diffusion sampling. These gains scale to complex, high-dimensional energy-based models.

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arXiv2026

LUCAID: Agentic Multimodal AI for Lung Cancer Precision Pathology

Lung cancer tissue diagnostics is complex, as therapy decisions in precision oncology rely on the integration of histomorphological, immunohistochemical, and molecular features. Yet pathological assessment remains largely visual and semi-quantitative and shows interobserver variability, while existing artificial intelligence (AI) tools cover only selected tasks, rarely reach generalizable expert-level performance, and lack prospective clinical validation. To address these challenges, we developed and clinically validated LUCAID, an agentic AI system for precision lung cancer pathology. An integrative agent couples diagnostic reasoning with nine modules that cover the full routine workflow, from quality control, tumor detection and segmentation, histological subtyping, tumor microenvironment profiling, tumor cellularity quantification, and predictive biomarker scoring (PD-L1, MET, TROP-2) to automated structured report generation. LUCAID enables users to interactively query the module outputs and generate reports that contextualize the results. Against large-scale expert ground-truth annotations, the analysis modules achieved F1 scores of 0.82-0.95. In prospective clinical validation, LUCAID reached 93.0% concordance with an expert-panel adjudicated reference standard across clinically actionable decisions, compared with 68.3-81.1% for five experienced thoracic pathologists.

cs.CV↗

arXiv2026

Accurate and Transferable Intermolecular Potential Based on Machine-Learned Molecular Electron Density

Machine-learned force fields (MLFFs) contain many learnable parameters and therefore require large training datasets. This poses a challenge for developing highly accurate, general-purpose MLFFs because generating high-quality ab initio reference data is computationally expensive. Classical empirical potentials offer a potentially inexpensive source of synthetic training data, but existing models often lack the accuracy needed to provide useful reference energies. Here, we introduce the density-based intermolecular potential (DensIP), a physics-based model of intermolecular interactions that uses machine-learned electron densities and only four universal parameters. We train and test DensIP on CCSD(T)/CBS interaction energies from DES15K, a dataset of dimers of small organic molecules. DensIP achieves sub-kcal/mol errors for dimers containing molecules absent from the training set, including molecules in non-equilibrium conformations, demonstrating strong transferability. We further show that DensIP can be applied to molecules as large as drug ligands. Notably, DensIP outperforms state-of-the-art general-purpose MLFFs for long-range interactions, making it a promising approach for generating accurate synthetic training data at scale.

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arXiv2026

Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations

We introduce implicit machine learning force fields (I-MLFFs), which replace explicit stacks of neural network layers with self-consistent fixed-point equations. In molecular simulations, this formulation enables intermediate representations to be reused across successive timesteps, thereby warm-starting force evaluation. The resulting models effectively combine the computational footprint of a shallow, single-layer MLFF with the representational capacity and accuracy of a deep neural network. Our approach unlocks architecture-agnostic efficiency gains that are inaccessible when force prediction and trajectory integration are considered separately. We demonstrate this across three major classes of graph neural networks: invariant, equivariant Cartesian tensor, and SO(3)-equivariant spherical-tensor architectures. Each yields a two- to five-fold reduction in compute and memory footprint. Crucially, these gains are achieved while retaining full atomistic resolution and the original integration timestep, avoiding spatial or temporal coarse graining. Our contribution therefore advances the scaling frontier of quantum-mechanically faithful molecular simulation, enabling longer trajectories and larger atomistic systems within fixed GPU memory and compute budgets, and thereby opening access to new insights across biomolecular and material systems.

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arXiv2026

Atlas 2 -- Foundation models for clinical deployment

Pathology foundation models substantially advanced the possibilities in computational pathology --- yet tradeoffs in terms of performance, robustness, and computational requirements remained, which limited their clinical deployment. In this report, we present Atlas 2, Atlas 2-B, and Atlas 2-S, three pathology vision foundation models which bridge these shortcomings by showing state-of-the-art prediction performance, robustness, and resource efficiency in a comprehensive evaluation across eighty public benchmarks. Our models were trained on the largest pathology foundation model dataset to date comprising 5.5 million histopathology whole slide images, collected from three medical institutions Charité - Universitätsmedizin Berlin, LMU Munich, and Mayo Clinic.

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arXiv2026

Atlas H&E-TME: Scalable AI-Based Tissue Profiling at Expert Pathologist-Level Accuracy

Hematoxylin and eosin (H&E) staining is the cornerstone of histopathology, yet scalable, quantitative analysis of H&E whole-slide images (WSIs) remains a central challenge in computational pathology. We present Atlas H&E-TME, an AI-based system built on the Atlas family of pathology foundation models that predicts tissue quality, tissue region, and cell type labels across multiple cancer types, yielding over 4,500 quantitative readouts per slide at cell-level resolution. A key challenge to validating such systems is overcoming morphological ambiguity inherent to H&E-only ground truth and the limited scalability of more informed references drawing on modalities such as immunohistochemistry (IHC). We address this with a dual validation framework combining biologically grounded depth with technical and morphological breadth. For depth, we propose an IHC-informed multi-pathologist consensus protocol that substantially improves inter-rater agreement over conventional H&E-only annotation. This yields a molecularly grounded reference against which we compare Atlas H&E-TME and pathologists working from H&E alone. For breadth, we benchmark Atlas H&E-TME on over 200,000 high-confidence H&E-only pathologist annotations across 1,500+ cases spanning eight cancer types and their most common metastatic sites, with subtypes covering >90% of clinical cases per cancer type, drawn from 25+ sources and 8+ scanner models. Benchmarked against the IHC-informed consensus, Atlas H&E-TME matches or exceeds pathologist H&E-only performance and generalizes consistently and robustly across this broad morphological and technical scope. In doing so, Atlas H&E-TME turns the H&E slide -- the most ubiquitous data in pathology -- into a scalable, quantitative window into the tumor and its microenvironment, laying a foundation for the next generation of tissue-based biomarkers in translational and clinical research.

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arXiv2026

Explaining Temporal Graph Neural Networks via Feature-induced Information Flow

Event-based Temporal Graph Neural Networks (ETGNNs) have demonstrated strong performance across a wide range of applications, including social network analysis, epidemic tracing, recommender systems, and political event forecasting. However, their increasing complexity poses significant challenges for explainability. Existing explanation methods focus only on a subset of the information flow within ETGNNs, typically tracing contributions from the event-related embeddings to the output. Consequently, they overlook the important pathways through event-induced variables, which mediate interactions between nodes and thereby play a central role in capturing long-range temporal dependencies. To overcome this limitation, we propose a novel attribution method that analyzes the entire information flow through all event-associated variables. Our method is built upon the recent Normalized Relevance Measure (NRM) framework, which enables explicit quantification of information flow originating from event embeddings as well as information flow passing through event-induced variables. It also ensures comparability of latent variables across layers, and supports higher-order analysis of interactions between events. To handle the architectural complexity of ETGNNs, we extend the NRM framework with a modular decomposition procedure that facilitates the systematic construction of relevance structure for complex neural architectures. We evaluate our approach on two synthetic datasets for epidemic tracing and social dynamics, as well as a real-world dataset of political event networks. Our qualitative and quantitative experiments show that our method consistently outperforms existing explanation approaches while producing more human-interpretable explanations.

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arXiv2026

Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics

Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the mean phase-space evolution over a chosen time span, enabling stable large-timestep updates far beyond the stability limits of classical integrators. To this end, we impose a Mean Flow consistency condition for time-averaged Hamiltonian dynamics. Unlike prior approaches, this allows training on independent phase-space samples without access to future states, avoiding expensive trajectory generation. Validated across diverse Hamiltonian systems, our method in particular improves upon molecular dynamics simulations using machine-learned force fields (MLFF). Our models maintain comparable training and inference cost, but support significantly larger integration timesteps while trained directly on widely-available trajectory-free MLFF datasets.

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arXiv2026

ReactionAtlas: Ab origine exploration of chemical reaction networks with machine learning

Mapping a chemical reaction network, the graph of minima and transition states (TS) and the elementary reactions connecting them, is the natural language of chemistry, from catalysis to combustion to the origin of life. Constructing such a reaction network for a given chemistry has been impractical: it requires finding and characterizing tens of thousands of TS, a task for which traditional methods such as density functional theory (DFT) are typically prohibitively slow and require reactant and product as input. We introduce ReactionAtlas, which builds a reaction network $\textit{ab origine}$ from a handful of seed molecules and without hand-crafted rules. Specifically, our machine-learned generative model proposes reactions from kinetically sampled candidate compounds and a DFT-trained machine learned force field (MLFF) filters them to valid TS, the resulting products of which enter the search as new seeds. Starting from eight pre-biotic seeds (CH$_2$O, H$_2$O, OH$^-$, H$_3$O$^+$, CO$_2$, H$_2$CO$_3$, HCO$_3^-$, H), ReactionAtlas discovers $\sim$47,000 reactions among $\sim$12,000 compounds. The MLFF TSs match the PBE0 references within 0.5 Å RMSD in 85% of the cases and can be easily brought to the PBE0 level. Thus, ReactionAtlas maps small carbohydrate chemistry up to C$_4$H$_8$O$_4$ at unprecedented scale and accuracy, including charge and stereo information. It enables novel insights into many well-studied reaction paths, including the formose cycle, which we highlight for its centrality to the chemical origins of life. Notably, our framework also allows establishing alternative reaction pathways for formose chemistry.

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arXiv2026

Symb-xMIL: Symbolic Explanations for Multiple Instance Learning in Digital Pathology

Explanations of multiple instance learning (MIL) models are widely used for validation and discovery in digital histopathology. Existing methods primarily rely on heatmaps that highlight influential regions but do not explain how evidence from different tissue regions is combined to produce a prediction. This limits interpretability, especially when decisions depend on interactions between tissue features. We introduce Symbolic explainable MIL (Symb-xMIL), a post-hoc explanation framework that quantifies how a MIL model's behavior aligns with human-readable decision rules, expressed as logical relationships (e.g., AND, OR, NOT) between input features. These alignment scores reveal semantic patterns underlying the model's predictions. We evaluate Symb-xMIL on synthetic and real-world histopathology datasets. On synthetic MIL data, Symb-xMIL reliably recovers ground-truth logical rules. In a clinical tumor detection task, the best-aligned rules uncover heterogeneous decision patterns and expose hidden model errors. On an HPV-prediction task on TCGA-HNSCC, a cohort of head and neck cancer, our framework refines patient survival stratification beyond HPV status with potential clinical relevance. Overall, Symb-xMIL extends MIL explainability beyond visual attribution toward structured, rule-based reasoning, enabling more transparent and semantically grounded interpretation of model predictions.

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arXiv2026

Normalized Relevance Measure as a Unifying Framework to Explain Neural Network Latent Structures

To understand how a neural network (NN) functions and makes predictions, it has become increasingly clear that analyzing only the input domain is insufficient -- one must also examine its internal inference mechanisms to capture the complete picture. To explain the internal inference mechanisms of such models, it is essential to analyze the importance of latent representations for a given task. In this paper, we propose the \emph{normalized relevance measure} (NRM) framework -- a novel general explanation procedure that attributes relevance to \emph{arbitrary sets of neurons across layers of arbitrary architectures}. In the NRM framework, relevance of selected neurons is explicitly defined as a normalized signed measure, constructed using simple operations -- marginalization and conditioning based on additive and multiplicative laws -- in analogy to the probability measures. The normalization property further guarantees comparability across layers. The NRM framework subsumes existing propagation-based explanation algorithms by explicitly identifying the underlying quantity being computed. We demonstrate the utility of the framework in computer vision applications, where joint relevance analysis across multiple layers reveals key information flows in VGG16 networks. Overall, the NRM framework provides a general, mathematically grounded approach to understanding how modern NNs propagate information, offering a versatile and broadly applicable foundation for explainable artificial intelligence.

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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.

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