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Klaus-Robert Müller

Klaus-Robert Müller appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Machine LearningArtificial Intelligencephysics.chem-phComputer Visionphysics.comp-phNeural and Evolutionary Computingcond-mat.mtrl-sciQuantitative MethodsComputation and LanguageComputational Engineering, Finance, and Sciencemath.STStatistics TheoryApplicationsBiomoleculescond-mat.dis-nneess.IVInformation RetrievalMethodologyphysics.data-anPopulations and Evolutionq-fin.PMq-fin.STquant-ph

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Published work

56 published item(s)

preprint2026arXiv

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 performance in 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 - Universtätsmedizin Berlin, LMU Munich, and Mayo Clinic.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

Towards Desiderata-Driven Design of Visual Counterfactual Explainers

Visual counterfactual explainers (VCEs) are a straightforward and promising approach to enhancing the transparency of image classifiers. VCEs complement other types of explanations, such as feature attribution, by revealing the specific data transformations to which a machine learning model responds most strongly. In this paper, we argue that existing VCEs focus too narrowly on optimizing sample quality or change minimality; they fail to consider the more holistic desiderata for an explanation, such as fidelity, understandability, and sufficiency. To address this shortcoming, we explore new mechanisms for counterfactual generation and investigate how they can help fulfill these desiderata. We combine these mechanisms into a novel 'smooth counterfactual explorer' (SCE) algorithm and demonstrate its effectiveness through systematic evaluations on synthetic and real data.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

Analyzing Atomic Interactions in Molecules as Learned by Neural Networks

While machine learning (ML) models have been able to achieve unprecedented accuracies across various prediction tasks in quantum chemistry, it is now apparent that accuracy on a test set alone is not a guarantee for robust chemical modeling such as stable molecular dynamics (MD). To go beyond accuracy, we use explainable artificial intelligence (XAI) techniques to develop a general analysis framework for atomic interactions and apply it to the SchNet and PaiNN neural network models. We compare these interactions with a set of fundamental chemical principles to understand how well the models have learned the underlying physicochemical concepts from the data. We focus on the strength of the interactions for different atomic species, how predictions for intensive and extensive quantum molecular properties are made, and analyze the decay and many-body nature of the interactions with interatomic distance. Models that deviate too far from known physical principles produce unstable MD trajectories, even when they have very high energy and force prediction accuracy. We also suggest further improvements to the ML architectures to better account for the polynomial decay of atomic interactions.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

Towards Symbolic XAI -- Explanation Through Human Understandable Logical Relationships Between Features

Explainable Artificial Intelligence (XAI) plays a crucial role in fostering transparency and trust in AI systems, where traditional XAI approaches typically offer one level of abstraction for explanations, often in the form of heatmaps highlighting single or multiple input features. However, we ask whether abstract reasoning or problem-solving strategies of a model may also be relevant, as these align more closely with how humans approach solutions to problems. We propose a framework, called Symbolic XAI, that attributes relevance to symbolic queries expressing logical relationships between input features, thereby capturing the abstract reasoning behind a model's predictions. The methodology is built upon a simple yet general multi-order decomposition of model predictions. This decomposition can be specified using higher-order propagation-based relevance methods, such as GNN-LRP, or perturbation-based explanation methods commonly used in XAI. The effectiveness of our framework is demonstrated in the domains of natural language processing (NLP), vision, and quantum chemistry (QC), where abstract symbolic domain knowledge is abundant and of significant interest to users. The Symbolic XAI framework provides an understanding of the model's decision-making process that is both flexible for customization by the user and human-readable through logical formulas.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems

The application of machine learning methods in quantum chemistry has enabled the study of numerous chemical phenomena, which are computationally intractable with traditional ab-initio methods. However, some quantum mechanical properties of molecules and materials depend on non-local electronic effects, which are often neglected due to the difficulty of modeling them efficiently. This work proposes a modified attention mechanism adapted to the underlying physics, which allows to recover the relevant non-local effects. Namely, we introduce spherical harmonic coordinates (SPHCs) to reflect higher-order geometric information for each atom in a molecule, enabling a non-local formulation of attention in the SPHC space. Our proposed model So3krates - a self-attention based message passing neural network - uncouples geometric information from atomic features, making them independently amenable to attention mechanisms. Thereby we construct spherical filters, which extend the concept of continuous filters in Euclidean space to SPHC space and serve as foundation for a spherical self-attention mechanism. We show that in contrast to other published methods, So3krates is able to describe non-local quantum mechanical effects over arbitrary length scales. Further, we find evidence that the inclusion of higher-order geometric correlations increases data efficiency and improves generalization. So3krates matches or exceeds state-of-the-art performance on popular benchmarks, notably, requiring a significantly lower number of parameters (0.25 - 0.4x) while at the same time giving a substantial speedup (6 - 14x for training and 2 - 11x for inference) compared to other models.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Toward Explainable AI for Regression Models

In addition to the impressive predictive power of machine learning (ML) models, more recently, explanation methods have emerged that enable an interpretation of complex non-linear learning models such as deep neural networks. Gaining a better understanding is especially important e.g. for safety-critical ML applications or medical diagnostics etc. While such Explainable AI (XAI) techniques have reached significant popularity for classifiers, so far little attention has been devoted to XAI for regression models (XAIR). In this review, we clarify the fundamental conceptual differences of XAI for regression and classification tasks, establish novel theoretical insights and analysis for XAIR, provide demonstrations of XAIR on genuine practical regression problems, and finally discuss the challenges remaining for the field.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Accurate Machine Learned Quantum-Mechanical Force Fields for Biomolecular Simulations

Molecular dynamics (MD) simulations allow atomistic insights into chemical and biological processes. Accurate MD simulations require computationally demanding quantum-mechanical calculations, being practically limited to short timescales and few atoms. For larger systems, efficient, but much less reliable empirical force fields are used. Recently, machine learned force fields (MLFFs) emerged as an alternative means to execute MD simulations, offering similar accuracy as ab initio methods at orders-of-magnitude speedup. Until now, MLFFs mainly capture short-range interactions in small molecules or periodic materials, due to the increased complexity of constructing models and obtaining reliable reference data for large molecules, where long-ranged many-body effects become important. This work proposes a general approach to constructing accurate MLFFs for large-scale molecular simulations (GEMS) by training on "bottom-up" and "top-down" molecular fragments of varying size, from which the relevant physicochemical interactions can be learned. GEMS is applied to study the dynamics of alanine-based peptides and the 46-residue protein crambin in aqueous solution, allowing nanosecond-scale MD simulations of >25k atoms at essentially ab initio quality. Our findings suggest that structural motifs in peptides and proteins are more flexible than previously thought, indicating that simulations at ab initio accuracy might be necessary to understand dynamic biomolecular processes such as protein (mis)folding, drug-protein binding, or allosteric regulation.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Automated Dissipation Control for Turbulence Simulation with Shell Models

The application of machine learning (ML) techniques, especially neural networks, has seen tremendous success at processing images and language. This is because we often lack formal models to understand visual and audio input, so here neural networks can unfold their abilities as they can model solely from data. In the field of physics we typically have models that describe natural processes reasonably well on a formal level. Nonetheless, in recent years, ML has also proven useful in these realms, be it by speeding up numerical simulations or by improving accuracy. One important and so far unsolved problem in classical physics is understanding turbulent fluid motion. In this work we construct a strongly simplified representation of turbulence by using the Gledzer-Ohkitani-Yamada (GOY) shell model. With this system we intend to investigate the potential of ML-supported and physics-constrained small-scale turbulence modelling. Instead of standard supervised learning we propose an approach that aims to reconstruct statistical properties of turbulence such as the self-similar inertial-range scaling, where we could achieve encouraging experimental results. Furthermore we discuss pitfalls when combining machine learning with differential equations.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Diffeomorphic Counterfactuals with Generative Models

Counterfactuals can explain classification decisions of neural networks in a human interpretable way. We propose a simple but effective method to generate such counterfactuals. More specifically, we perform a suitable diffeomorphic coordinate transformation and then perform gradient ascent in these coordinates to find counterfactuals which are classified with great confidence as a specified target class. We propose two methods to leverage generative models to construct such suitable coordinate systems that are either exactly or approximately diffeomorphic. We analyze the generation process theoretically using Riemannian differential geometry and validate the quality of the generated counterfactuals using various qualitative and quantitative measures.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Super-resolution in Molecular Dynamics Trajectory Reconstruction with Bi-Directional Neural Networks

Molecular dynamics simulations are a cornerstone in science, allowing to investigate from the system's thermodynamics to analyse intricate molecular interactions. In general, to create extended molecular trajectories can be a computationally expensive process, for example, when running $ab-initio$ simulations. Hence, repeating such calculations to either obtain more accurate thermodynamics or to get a higher resolution in the dynamics generated by a fine-grained quantum interaction can be time- and computationally-consuming. In this work, we explore different machine learning (ML) methodologies to increase the resolution of molecular dynamics trajectories on-demand within a post-processing step. As a proof of concept, we analyse the performance of bi-directional neural networks such as neural ODEs, Hamiltonian networks, recurrent neural networks and LSTMs, as well as the uni-directional variants as a reference, for molecular dynamics simulations (here: the MD17 dataset). We have found that Bi-LSTMs are the best performing models; by utilizing the local time-symmetry of thermostated trajectories they can even learn long-range correlations and display high robustness to noisy dynamics across molecular complexity. Our models can reach accuracies of up to 10$^{-4}$ angstroms in trajectory interpolation, while faithfully reconstructing several full cycles of unseen intricate high-frequency molecular vibrations, rendering the comparison between the learned and reference trajectories indistinguishable. The results reported in this work can serve (1) as a baseline for larger systems, as well as (2) for the construction of better MD integrators.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

XAI for Transformers: Better Explanations through Conservative Propagation

Transformers have become an important workhorse of machine learning, with numerous applications. This necessitates the development of reliable methods for increasing their transparency. Multiple interpretability methods, often based on gradient information, have been proposed. We show that the gradient in a Transformer reflects the function only locally, and thus fails to reliably identify the contribution of input features to the prediction. We identify Attention Heads and LayerNorm as main reasons for such unreliable explanations and propose a more stable way for propagation through these layers. Our proposal, which can be seen as a proper extension of the well-established LRP method to Transformers, is shown both theoretically and empirically to overcome the deficiency of a simple gradient-based approach, and achieves state-of-the-art explanation performance on a broad range of Transformer models and datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

A Unifying Review of Deep and Shallow Anomaly Detection

Deep learning approaches to anomaly detection have recently improved the state of the art in detection performance on complex datasets such as large collections of images or text. These results have sparked a renewed interest in the anomaly detection problem and led to the introduction of a great variety of new methods. With the emergence of numerous such methods, including approaches based on generative models, one-class classification, and reconstruction, there is a growing need to bring methods of this field into a systematic and unified perspective. In this review we aim to identify the common underlying principles as well as the assumptions that are often made implicitly by various methods. In particular, we draw connections between classic 'shallow' and novel deep approaches and show how this relation might cross-fertilize or extend both directions. We further provide an empirical assessment of major existing methods that is enriched by the use of recent explainability techniques, and present specific worked-through examples together with practical advice. Finally, we outline critical open challenges and identify specific paths for future research in anomaly detection.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

BIGDML: Towards Exact Machine Learning Force Fields for Materials

Machine-learning force fields (MLFF) should be accurate, computationally and data efficient, and applicable to molecules, materials, and interfaces thereof. Currently, MLFFs often introduce tradeoffs that restrict their practical applicability to small subsets of chemical space or require exhaustive datasets for training. Here, we introduce the Bravais-Inspired Gradient-Domain Machine Learning (BIGDML) approach and demonstrate its ability to construct reliable force fields using a training set with just 10-200 geometries for materials including pristine and defect-containing 2D and 3D semiconductors and metals, as well as chemisorbed and physisorbed atomic and molecular adsorbates on surfaces. The BIGDML model employs the full relevant symmetry group for a given material, does not assume artificial atom types or localization of atomic interactions and exhibits high data efficiency and state-of-the-art energy accuracies (errors substantially below 1 meV per atom) for an extended set of materials. Extensive path-integral molecular dynamics carried out with BIGDML models demonstrate the counterintuitive localization of benzene--graphene dynamics induced by nuclear quantum effects and allow to rationalize the Arrhenius behavior of hydrogen diffusion coefficient in a Pd crystal for a wide range of temperatures.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Explaining Deep Neural Networks and Beyond: A Review of Methods and Applications

With the broader and highly successful usage of machine learning in industry and the sciences, there has been a growing demand for Explainable AI. Interpretability and explanation methods for gaining a better understanding about the problem solving abilities and strategies of nonlinear Machine Learning, in particular, deep neural networks, are therefore receiving increased attention. In this work we aim to (1) provide a timely overview of this active emerging field, with a focus on 'post-hoc' explanations, and explain its theoretical foundations, (2) put interpretability algorithms to a test both from a theory and comparative evaluation perspective using extensive simulations, (3) outline best practice aspects i.e. how to best include interpretation methods into the standard usage of machine learning and (4) demonstrate successful usage of explainable AI in a representative selection of application scenarios. Finally, we discuss challenges and possible future directions of this exciting foundational field of machine learning.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

From Clustering to Cluster Explanations via Neural Networks

A recent trend in machine learning has been to enrich learned models with the ability to explain their own predictions. The emerging field of Explainable AI (XAI) has so far mainly focused on supervised learning, in particular, deep neural network classifiers. In many practical problems however, label information is not given and the goal is instead to discover the underlying structure of the data, for example, its clusters. While powerful methods exist for extracting the cluster structure in data, they typically do not answer the question why a certain data point has been assigned to a given cluster. We propose a new framework that can, for the first time, explain cluster assignments in terms of input features in an efficient and reliable manner. It is based on the novel insight that clustering models can be rewritten as neural networks - or 'neuralized'. Cluster predictions of the obtained networks can then be quickly and accurately attributed to the input features. Several showcases demonstrate the ability of our method to assess the quality of learned clusters and to extract novel insights from the analyzed data and representations.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects

Machine-learned force fields (ML-FFs) combine the accuracy of ab initio methods with the efficiency of conventional force fields. However, current ML-FFs typically ignore electronic degrees of freedom, such as the total charge or spin state, and assume chemical locality, which is problematic when molecules have inconsistent electronic states, or when nonlocal effects play a significant role. This work introduces SpookyNet, a deep neural network for constructing ML-FFs with explicit treatment of electronic degrees of freedom and quantum nonlocality. Chemically meaningful inductive biases and analytical corrections built into the network architecture allow it to properly model physical limits. SpookyNet improves upon the current state-of-the-art (or achieves similar performance) on popular quantum chemistry data sets. Notably, it is able to generalize across chemical and conformational space and can leverage the learned chemical insights, e.g. by predicting unknown spin states, thus helping to close a further important remaining gap for today's machine learning models in quantum chemistry.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Building and Interpreting Deep Similarity Models

Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on the concept of 'distance' or 'similarity'. Before similarities are used for training an actual machine learning model, we would like to verify that they are bound to meaningful patterns in the data. In this paper, we propose to make similarities interpretable by augmenting them with an explanation in terms of input features. We develop BiLRP, a scalable and theoretically founded method to systematically decompose similarity scores on pairs of input features. Our method can be expressed as a composition of LRP explanations, which were shown in previous works to scale to highly nonlinear functions. Through an extensive set of experiments, we demonstrate that BiLRP robustly explains complex similarity models, e.g. built on VGG-16 deep neural network features. Additionally, we apply our method to an open problem in digital humanities: detailed assessment of similarity between historical documents such as astronomical tables. Here again, BiLRP provides insight and brings verifiability into a highly engineered and problem-specific similarity model.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Deep Semi-Supervised Anomaly Detection

Deep approaches to anomaly detection have recently shown promising results over shallow methods on large and complex datasets. Typically anomaly detection is treated as an unsupervised learning problem. In practice however, one may have---in addition to a large set of unlabeled samples---access to a small pool of labeled samples, e.g. a subset verified by some domain expert as being normal or anomalous. Semi-supervised approaches to anomaly detection aim to utilize such labeled samples, but most proposed methods are limited to merely including labeled normal samples. Only a few methods take advantage of labeled anomalies, with existing deep approaches being domain-specific. In this work we present Deep SAD, an end-to-end deep methodology for general semi-supervised anomaly detection. We further introduce an information-theoretic framework for deep anomaly detection based on the idea that the entropy of the latent distribution for normal data should be lower than the entropy of the anomalous distribution, which can serve as a theoretical interpretation for our method. In extensive experiments on MNIST, Fashion-MNIST, and CIFAR-10, along with other anomaly detection benchmark datasets, we demonstrate that our method is on par or outperforms shallow, hybrid, and deep competitors, yielding appreciable performance improvements even when provided with only little labeled data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Ensemble Learning of Coarse-Grained Molecular Dynamics Force Fields with a Kernel Approach

Gradient-domain machine learning (GDML) is an accurate and efficient approach to learn a molecular potential and associated force field based on the kernel ridge regression algorithm. Here, we demonstrate its application to learn an effective coarse-grained (CG) model from all-atom simulation data in a sample efficient manner. The coarse-grained force field is learned by following the thermodynamic consistency principle, here by minimizing the error between the predicted coarse-grained force and the all-atom mean force in the coarse-grained coordinates. Solving this problem by GDML directly is impossible because coarse-graining requires averaging over many training data points, resulting in impractical memory requirements for storing the kernel matrices. In this work, we propose a data-efficient and memory-saving alternative. Using ensemble learning and stratified sampling, we propose a 2-layer training scheme that enables GDML to learn an effective coarse-grained model. We illustrate our method on a simple biomolecular system, alanine dipeptide, by reconstructing the free energy landscape of a coarse-grained variant of this molecule. Our novel GDML training scheme yields a smaller free energy error than neural networks when the training set is small, and a comparably high accuracy when the training set is sufficiently large.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Fairwashing Explanations with Off-Manifold Detergent

Explanation methods promise to make black-box classifiers more transparent. As a result, it is hoped that they can act as proof for a sensible, fair and trustworthy decision-making process of the algorithm and thereby increase its acceptance by the end-users. In this paper, we show both theoretically and experimentally that these hopes are presently unfounded. Specifically, we show that, for any classifier $g$, one can always construct another classifier $\tilde{g}$ which has the same behavior on the data (same train, validation, and test error) but has arbitrarily manipulated explanation maps. We derive this statement theoretically using differential geometry and demonstrate it experimentally for various explanation methods, architectures, and datasets. Motivated by our theoretical insights, we then propose a modification of existing explanation methods which makes them significantly more robust.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

How Much Can I Trust You? -- Quantifying Uncertainties in Explaining Neural Networks

Explainable AI (XAI) aims to provide interpretations for predictions made by learning machines, such as deep neural networks, in order to make the machines more transparent for the user and furthermore trustworthy also for applications in e.g. safety-critical areas. So far, however, no methods for quantifying uncertainties of explanations have been conceived, which is problematic in domains where a high confidence in explanations is a prerequisite. We therefore contribute by proposing a new framework that allows to convert any arbitrary explanation method for neural networks into an explanation method for Bayesian neural networks, with an in-built modeling of uncertainties. Within the Bayesian framework a network's weights follow a distribution that extends standard single explanation scores and heatmaps to distributions thereof, in this manner translating the intrinsic network model uncertainties into a quantification of explanation uncertainties. This allows us for the first time to carve out uncertainties associated with a model explanation and subsequently gauge the appropriate level of explanation confidence for a user (using percentiles). We demonstrate the effectiveness and usefulness of our approach extensively in various experiments, both qualitatively and quantitatively.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Langevin Cooling for Domain Translation

Domain translation is the task of finding correspondence between two domains. Several Deep Neural Network (DNN) models, e.g., CycleGAN and cross-lingual language models, have shown remarkable successes on this task under the unsupervised setting---the mappings between the domains are learned from two independent sets of training data in both domains (without paired samples). However, those methods typically do not perform well on a significant proportion of test samples. In this paper, we hypothesize that many of such unsuccessful samples lie at the fringe---relatively low-density areas---of data distribution, where the DNN was not trained very well, and propose to perform Langevin dynamics to bring such fringe samples towards high density areas. We demonstrate qualitatively and quantitatively that our strategy, called Langevin Cooling (L-Cool), enhances state-of-the-art methods in image translation and language translation tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Resolving challenges in deep learning-based analyses of histopathological images using explanation methods

Deep learning has recently gained popularity in digital pathology due to its high prediction quality. However, the medical domain requires explanation and insight for a better understanding beyond standard quantitative performance evaluation. Recently, explanation methods have emerged, which are so far still rarely used in medicine. This work shows their application to generate heatmaps that allow to resolve common challenges encountered in deep learning-based digital histopathology analyses. These challenges comprise biases typically inherent to histopathology data. We study binary classification tasks of tumor tissue discrimination in publicly available haematoxylin and eosin slides of various tumor entities and investigate three types of biases: (1) biases which affect the entire dataset, (2) biases which are by chance correlated with class labels and (3) sampling biases. While standard analyses focus on patch-level evaluation, we advocate pixel-wise heatmaps, which offer a more precise and versatile diagnostic instrument and furthermore help to reveal biases in the data. This insight is shown to not only detect but also to be helpful to remove the effects of common hidden biases, which improves generalization within and across datasets. For example, we could see a trend of improved area under the receiver operating characteristic curve by 5% when reducing a labeling bias. Explanation techniques are thus demonstrated to be a helpful and highly relevant tool for the development and the deployment phases within the life cycle of real-world applications in digital pathology.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Risk Estimation of SARS-CoV-2 Transmission from Bluetooth Low Energy Measurements

Digital contact tracing approaches based on Bluetooth low energy (BLE) have the potential to efficiently contain and delay outbreaks of infectious diseases such as the ongoing SARS-CoV-2 pandemic. In this work we propose a novel machine learning based approach to reliably detect subjects that have spent enough time in close proximity to be at risk of being infected. Our study is an important proof of concept that will aid the battery of epidemiological policies aiming to slow down the rapid spread of COVID-19.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The Clever Hans Effect in Anomaly Detection

The 'Clever Hans' effect occurs when the learned model produces correct predictions based on the 'wrong' features. This effect which undermines the generalization capability of an ML model and goes undetected by standard validation techniques has been frequently observed for supervised learning where the training algorithm leverages spurious correlations in the data. The question whether Clever Hans also occurs in unsupervised learning, and in which form, has received so far almost no attention. Therefore, this paper will contribute an explainable AI (XAI) procedure that can highlight the relevant features used by popular anomaly detection models of different type. Our analysis reveals that the Clever Hans effect is widespread in anomaly detection and occurs in many (unexpected) forms. Interestingly, the observed Clever Hans effects are in this case not so much due to the data, but due to the anomaly detection models themselves whose structure makes them unable to detect the truly relevant features, even though vast amounts of data points are available. Overall, our work contributes a warning against an unrestrained use of existing anomaly detection models in practical applications, but it also points at a possible way out of the Clever Hans dilemma, specifically, by allowing multiple anomaly models to mutually cancel their individual structural weaknesses to jointly produce a better and more trustworthy anomaly detector.

0 citations0 reviewsNo code linkedOpen access
preprint2018arXiv

Towards Explaining Anomalies: A Deep Taylor Decomposition of One-Class Models

A common machine learning task is to discriminate between normal and anomalous data points. In practice, it is not always sufficient to reach high accuracy at this task, one also would like to understand why a given data point has been predicted in a certain way. We present a new principled approach for one-class SVMs that decomposes outlier predictions in terms of input variables. The method first recomposes the one-class model as a neural network with distance functions and min-pooling, and then performs a deep Taylor decomposition (DTD) of the model output. The proposed One-Class DTD is applicable to a number of common distance-based SVM kernels and is able to reliably explain a wide set of data anomalies. Furthermore, it outperforms baselines such as sensitivity analysis, nearest neighbor, or simple edge detection.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Controlling Explanatory Heatmap Resolution and Semantics via Decomposition Depth

We present an application of the Layer-wise Relevance Propagation (LRP) algorithm to state of the art deep convolutional neural networks and Fisher Vector classifiers to compare the image perception and prediction strategies of both classifiers with the use of visualized heatmaps. Layer-wise Relevance Propagation (LRP) is a method to compute scores for individual components of an input image, denoting their contribution to the prediction of the classifier for one particular test point. We demonstrate the impact of different choices of decomposition cut-off points during the LRP-process, controlling the resolution and semantics of the heatmap on test images from the PASCAL VOC 2007 test data set.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Explaining Predictions of Non-Linear Classifiers in NLP

Layer-wise relevance propagation (LRP) is a recently proposed technique for explaining predictions of complex non-linear classifiers in terms of input variables. In this paper, we apply LRP for the first time to natural language processing (NLP). More precisely, we use it to explain the predictions of a convolutional neural network (CNN) trained on a topic categorization task. Our analysis highlights which words are relevant for a specific prediction of the CNN. We compare our technique to standard sensitivity analysis, both qualitatively and quantitatively, using a "word deleting" perturbation experiment, a PCA analysis, and various visualizations. All experiments validate the suitability of LRP for explaining the CNN predictions, which is also in line with results reported in recent image classification studies.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Feature Importance Measure for Non-linear Learning Algorithms

Complex problems may require sophisticated, non-linear learning methods such as kernel machines or deep neural networks to achieve state of the art prediction accuracies. However, high prediction accuracies are not the only objective to consider when solving problems using machine learning. Instead, particular scientific applications require some explanation of the learned prediction function. Unfortunately, most methods do not come with out of the box straight forward interpretation. Even linear prediction functions are not straight forward to explain if features exhibit complex correlation structure. In this paper, we propose the Measure of Feature Importance (MFI). MFI is general and can be applied to any arbitrary learning machine (including kernel machines and deep learning). MFI is intrinsically non-linear and can detect features that by itself are inconspicuous and only impact the prediction function through their interaction with other features. Lastly, MFI can be used for both --- model-based feature importance and instance-based feature importance (i.e, measuring the importance of a feature for a particular data point).

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preprint2016arXiv

Identifying individual facial expressions by deconstructing a neural network

This paper focuses on the problem of explaining predictions of psychological attributes such as attractiveness, happiness, confidence and intelligence from face photographs using deep neural networks. Since psychological attribute datasets typically suffer from small sample sizes, we apply transfer learning with two base models to avoid overfitting. These models were trained on an age and gender prediction task, respectively. Using a novel explanation method we extract heatmaps that highlight the parts of the image most responsible for the prediction. We further observe that the explanation method provides important insights into the nature of features of the base model, which allow one to assess the aptitude of the base model for a given transfer learning task. Finally, we observe that the multiclass model is more feature rich than its binary counterpart. The experimental evaluation is performed on the 2222 images from the 10k US faces dataset containing psychological attribute labels as well as on a subset of KDEF images.

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preprint2016arXiv

Interpretable Deep Neural Networks for Single-Trial EEG Classification

Background: In cognitive neuroscience the potential of Deep Neural Networks (DNNs) for solving complex classification tasks is yet to be fully exploited. The most limiting factor is that DNNs as notorious 'black boxes' do not provide insight into neurophysiological phenomena underlying a decision. Layer-wise Relevance Propagation (LRP) has been introduced as a novel method to explain individual network decisions. New Method: We propose the application of DNNs with LRP for the first time for EEG data analysis. Through LRP the single-trial DNN decisions are transformed into heatmaps indicating each data point's relevance for the outcome of the decision. Results: DNN achieves classification accuracies comparable to those of CSP-LDA. In subjects with low performance subject-to-subject transfer of trained DNNs can improve the results. The single-trial LRP heatmaps reveal neurophysiologically plausible patterns, resembling CSP-derived scalp maps. Critically, while CSP patterns represent class-wise aggregated information, LRP heatmaps pinpoint neural patterns to single time points in single trials. Comparison with Existing Method(s): We compare the classification performance of DNNs to that of linear CSP-LDA on two data sets related to motor-imaginery BCI. Conclusion: We have demonstrated that DNN is a powerful non-linear tool for EEG analysis. With LRP a new quality of high-resolution assessment of neural activity can be reached. LRP is a potential remedy for the lack of interpretability of DNNs that has limited their utility in neuroscientific applications. The extreme specificity of the LRP-derived heatmaps opens up new avenues for investigating neural activity underlying complex perception or decision-related processes.

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preprint2016arXiv

Interpreting the Predictions of Complex ML Models by Layer-wise Relevance Propagation

Complex nonlinear models such as deep neural network (DNNs) have become an important tool for image classification, speech recognition, natural language processing, and many other fields of application. These models however lack transparency due to their complex nonlinear structure and to the complex data distributions to which they typically apply. As a result, it is difficult to fully characterize what makes these models reach a particular decision for a given input. This lack of transparency can be a drawback, especially in the context of sensitive applications such as medical analysis or security. In this short paper, we summarize a recent technique introduced by Bach et al. [1] that explains predictions by decomposing the classification decision of DNN models in terms of input variables.

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preprint2016arXiv

Investigating the influence of noise and distractors on the interpretation of neural networks

Understanding neural networks is becoming increasingly important. Over the last few years different types of visualisation and explanation methods have been proposed. However, none of them explicitly considered the behaviour in the presence of noise and distracting elements. In this work, we will show how noise and distracting dimensions can influence the result of an explanation model. This gives a new theoretical insights to aid selection of the most appropriate explanation model within the deep-Taylor decomposition framework.

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preprint2016arXiv

Language Detection For Short Text Messages In Social Media

With the constant growth of the World Wide Web and the number of documents in different languages accordingly, the need for reliable language detection tools has increased as well. Platforms such as Twitter with predominantly short texts are becoming important information resources, which additionally imposes the need for short texts language detection algorithms. In this paper, we show how incorporating personalized user-specific information into the language detection algorithm leads to an important improvement of detection results. To choose the best algorithm for language detection for short text messages, we investigate several machine learning approaches. These approaches include the use of the well-known classifiers such as SVM and logistic regression, a dictionary based approach, and a probabilistic model based on modified Kneser-Ney smoothing. Furthermore, the extension of the probabilistic model to include additional user-specific information such as evidence accumulation per user and user interface language is explored, with the goal of improving the classification performance. The proposed approaches are evaluated on randomly collected Twitter data containing Latin as well as non-Latin alphabet languages and the quality of the obtained results is compared, followed by the selection of the best performing algorithm. This algorithm is then evaluated against two already existing general language detection tools: Chromium Compact Language Detector 2 (CLD2) and langid, where our method significantly outperforms the results achieved by both of the mentioned methods. Additionally, a preview of benefits and possible applications of having a reliable language detection algorithm is given.

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preprint2016arXiv

Layer-wise Relevance Propagation for Neural Networks with Local Renormalization Layers

Layer-wise relevance propagation is a framework which allows to decompose the prediction of a deep neural network computed over a sample, e.g. an image, down to relevance scores for the single input dimensions of the sample such as subpixels of an image. While this approach can be applied directly to generalized linear mappings, product type non-linearities are not covered. This paper proposes an approach to extend layer-wise relevance propagation to neural networks with local renormalization layers, which is a very common product-type non-linearity in convolutional neural networks. We evaluate the proposed method for local renormalization layers on the CIFAR-10, Imagenet and MIT Places datasets.

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preprint2016arXiv

Validity of time reversal for testing Granger causality

Inferring causal interactions from observed data is a challenging problem, especially in the presence of measurement noise. To alleviate the problem of spurious causality, Haufe et al. (2013) proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time-reversed data. They show that this procedure, time-reversed Granger causality (TRGC), robustly rejects causal interpretations on mixtures of independent signals. While promising results have been achieved in simulations, it was so far unknown whether time reversal leads to valid measures of information flow in the presence of true interaction. Here we prove that, for linear finite-order autoregressive processes with unidirectional information flow, the application of time reversal for testing Granger causality indeed leads to correct estimates of information flow and its directionality. Using simulations, we further show that TRGC is able to infer correct directionality with similar statistical power as the net Granger causality between two variables, while being much more robust to the presence of measurement noise.

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preprint2015arXiv

Analyzing Classifiers: Fisher Vectors and Deep Neural Networks

Fisher Vector classifiers and Deep Neural Networks (DNNs) are popular and successful algorithms for solving image classification problems. However, both are generally considered `black box' predictors as the non-linear transformations involved have so far prevented transparent and interpretable reasoning. Recently, a principled technique, Layer-wise Relevance Propagation (LRP), has been developed in order to better comprehend the inherent structured reasoning of complex nonlinear classification models such as Bag of Feature models or DNNs. In this paper we (1) extend the LRP framework also for Fisher Vector classifiers and then use it as analysis tool to (2) quantify the importance of context for classification, (3) qualitatively compare DNNs against FV classifiers in terms of important image regions and (4) detect potential flaws and biases in data. All experiments are performed on the PASCAL VOC 2007 data set.

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preprint2015arXiv

Evaluating the visualization of what a Deep Neural Network has learned

Deep Neural Networks (DNNs) have demonstrated impressive performance in complex machine learning tasks such as image classification or speech recognition. However, due to their multi-layer nonlinear structure, they are not transparent, i.e., it is hard to grasp what makes them arrive at a particular classification or recognition decision given a new unseen data sample. Recently, several approaches have been proposed enabling one to understand and interpret the reasoning embodied in a DNN for a single test image. These methods quantify the ''importance'' of individual pixels wrt the classification decision and allow a visualization in terms of a heatmap in pixel/input space. While the usefulness of heatmaps can be judged subjectively by a human, an objective quality measure is missing. In this paper we present a general methodology based on region perturbation for evaluating ordered collections of pixels such as heatmaps. We compare heatmaps computed by three different methods on the SUN397, ILSVRC2012 and MIT Places data sets. Our main result is that the recently proposed Layer-wise Relevance Propagation (LRP) algorithm qualitatively and quantitatively provides a better explanation of what made a DNN arrive at a particular classification decision than the sensitivity-based approach or the deconvolution method. We provide theoretical arguments to explain this result and discuss its practical implications. Finally, we investigate the use of heatmaps for unsupervised assessment of neural network performance.

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preprint2015arXiv

Understanding Kernel Ridge Regression: Common behaviors from simple functions to density functionals

Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on hyperparameters. We find universal features of the behavior in extreme limits, including both very small and very large length scales, and the noise-free limit. We show how such features arise in ML models of density functionals.

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preprint2015arXiv

Wasserstein Training of Boltzmann Machines

The Boltzmann machine provides a useful framework to learn highly complex, multimodal and multiscale data distributions that occur in the real world. The default method to learn its parameters consists of minimizing the Kullback-Leibler (KL) divergence from training samples to the Boltzmann model. We propose in this work a novel approach for Boltzmann training which assumes that a meaningful metric between observations is given. This metric can be represented by the Wasserstein distance between distributions, for which we derive a gradient with respect to the model parameters. Minimization of this new Wasserstein objective leads to generative models that are better when considering the metric and that have a cluster-like structure. We demonstrate the practical potential of these models for data completion and denoising, for which the metric between observations plays a crucial role.

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preprint2014arXiv

Learning with Algebraic Invariances, and the Invariant Kernel Trick

When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase independence, scaling etc. can be included easily by essentially performing the kernel trick twice. We demonstrate the usefulness of our theory in simulations on selected applications such as sign-invariant spectral clustering and underdetermined ICA.

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preprint2014arXiv

Multi-Target Shrinkage

Stein showed that the multivariate sample mean is outperformed by "shrinking" to a constant target vector. Ledoit and Wolf extended this approach to the sample covariance matrix and proposed a multiple of the identity as shrinkage target. In a general framework, independent of a specific estimator, we extend the shrinkage concept by allowing simultaneous shrinkage to a set of targets. Application scenarios include settings with (A) additional data sets from potentially similar distributions, (B) non-stationarity, (C) a natural grouping of the data or (D) multiple alternative estimators which could serve as targets. We show that this Multi-Target Shrinkage can be translated into a quadratic program and derive conditions under which the estimation of the shrinkage intensities yields optimal expected squared error in the limit. For the sample mean and the sample covariance as specific instances, we derive conditions under which the optimality of MTS is applicable. We consider two asymptotic settings: the large dimensional limit (LDL), where the dimensionality and the number of observations go to infinity at the same rate, and the finite observations large dimensional limit (FOLDL), where only the dimensionality goes to infinity while the number of observations remains constant. We then show the effectiveness in extensive simulations and on real world data.

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preprint2014arXiv

Understanding Machine-learned Density Functionals

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and highly accurate energies are achieved. Accurate {\em constrained optimal densities} are found via a modified Euler-Lagrange constrained minimization of the total energy. A projected gradient descent algorithm is derived using local principal component analysis. Additionally, a sparse grid representation of the density can be used without degrading the performance of the methods. The implications for machine-learned density functional approximations are discussed.

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preprint2013arXiv

Machine Learning of Molecular Electronic Properties in Chemical Compound Space

The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property relationships. Such relationships enable high-throughput screening for relevant properties in an exponentially growing pool of virtual compounds that are synthetically accessible. Here, we present a machine learning (ML) model, trained on a data base of \textit{ab initio} calculation results for thousands of organic molecules, that simultaneously predicts multiple electronic ground- and excited-state properties. The properties include atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity, and excitation energies. The ML model is based on a deep multi-task artificial neural network, exploiting underlying correlations between various molecular properties. The input is identical to \emph{ab initio} methods, \emph{i.e.} nuclear charges and Cartesian coordinates of all atoms. For small organic molecules the accuracy of such a "Quantum Machine" is similar, and sometimes superior, to modern quantum-chemical methods---at negligible computational cost.

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preprint2013arXiv

Multiple Kernel Learning for Brain-Computer Interfacing

Combining information from different sources is a common way to improve classification accuracy in Brain-Computer Interfacing (BCI). For instance, in small sample settings it is useful to integrate data from other subjects or sessions in order to improve the estimation quality of the spatial filters or the classifier. Since data from different subjects may show large variability, it is crucial to weight the contributions according to importance. Many multi-subject learning algorithms determine the optimal weighting in a separate step by using heuristics, however, without ensuring that the selected weights are optimal with respect to classification. In this work we apply Multiple Kernel Learning (MKL) to this problem. MKL has been widely used for feature fusion in computer vision and allows to simultaneously learn the classifier and the optimal weighting. We compare the MKL method to two baseline approaches and investigate the reasons for performance improvement.

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preprint2013arXiv

Regression for sets of polynomial equations

We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal regression directly without resorting to numerical optimization. Ideal regression is useful whenever the solution to a learning problem can be described by a system of polynomial equations. As an example, we demonstrate how to formulate Stationary Subspace Analysis (SSA), a source separation problem, in terms of ideal regression, which also yields a consistent estimator for SSA. We then compare this estimator in simulations with previous optimization-based approaches for SSA.

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preprint2012arXiv

Directional Variance Adjustment: improving covariance estimates for high-dimensional portfolio optimization

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on Factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong market we show that our proposed method leads to improved portfolio allocation.

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preprint2012arXiv

Learning Feature Hierarchies with Centered Deep Boltzmann Machines

Deep Boltzmann machines are in principle powerful models for extracting the hierarchical structure of data. Unfortunately, attempts to train layers jointly (without greedy layer-wise pretraining) have been largely unsuccessful. We propose a modification of the learning algorithm that initially recenters the output of the activation functions to zero. This modification leads to a better conditioned Hessian and thus makes learning easier. We test the algorithm on real data and demonstrate that our suggestion, the centered deep Boltzmann machine, learns a hierarchy of increasingly abstract representations and a better generative model of data.

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preprint2011arXiv

Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schrödinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross-validation over more than seven thousand small organic molecules yields a mean absolute error of ~10 kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves.

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preprint2011arXiv

Feature Extraction for Change-Point Detection using Stationary Subspace Analysis

Detecting changes in high-dimensional time series is difficult because it involves the comparison of probability densities that need to be estimated from finite samples. In this paper, we present the first feature extraction method tailored to change point detection, which is based on an extended version of Stationary Subspace Analysis. We reduce the dimensionality of the data to the most non-stationary directions, which are most informative for detecting state changes in the time series. In extensive simulations on synthetic data we show that the accuracy of three change point detection algorithms is significantly increased by a prior feature extraction step. These findings are confirmed in an application to industrial fault monitoring.

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preprint2011arXiv

Finding Density Functionals with Machine Learning

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is within the interpolation region. Via principal component analysis, a projected functional derivative finds highly accurate self-consistent densities. Challenges for application of our method to real electronic structure problems are discussed.

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preprint2011arXiv

Insights from Classifying Visual Concepts with Multiple Kernel Learning

Combining information from various image features has become a standard technique in concept recognition tasks. However, the optimal way of fusing the resulting kernel functions is usually unknown in practical applications. Multiple kernel learning (MKL) techniques allow to determine an optimal linear combination of such similarity matrices. Classical approaches to MKL promote sparse mixtures. Unfortunately, so-called 1-norm MKL variants are often observed to be outperformed by an unweighted sum kernel. The contribution of this paper is twofold: We apply a recently developed non-sparse MKL variant to state-of-the-art concept recognition tasks within computer vision. We provide insights on benefits and limits of non-sparse MKL and compare it against its direct competitors, the sum kernel SVM and the sparse MKL. We report empirical results for the PASCAL VOC 2009 Classification and ImageCLEF2010 Photo Annotation challenge data sets. About to be submitted to PLoS ONE.

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