Grégoire Montavon

Ping Xiong, Thomas Schnake, Michael Gastegger et al.

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

Johanna Vielhaben, Sebastian Lapuschkin, Grégoire Montavon et al.

The field of eXplainable Artificial Intelligence (XAI) has greatly advanced in recent years, but progress has mainly been made in computer vision and natural language processing. For time series, where the input is often not interpretable, only limited research on XAI is available. In this work, we put forward a virtual inspection layer, that transforms the time series to an interpretable representation and allows to propagate relevance attributions to this representation via local XAI methods like layer-wise relevance propagation (LRP). In this way, we extend the applicability of a family of XAI methods to domains (e.g. speech) where the input is only interpretable after a transformation. Here, we focus on the Fourier transformation which is prominently applied in the interpretation of time series and LRP and refer to our method as DFT-LRP. We demonstrate the usefulness of DFT-LRP in various time series classification settings like audio and electronic health records. We showcase how DFT-LRP reveals differences in the classification strategies of models trained in different domains (e.g., time vs. frequency domain) or helps to discover how models act on spurious correlations in the data.

Alexander Binder, Leander Weber, Sebastian Lapuschkin et al.

While the evaluation of explanations is an important step towards trustworthy models, it needs to be done carefully, and the employed metrics need to be well-understood. Specifically model randomization testing is often overestimated and regarded as a sole criterion for selecting or discarding certain explanation methods. To address shortcomings of this test, we start by observing an experimental gap in the ranking of explanation methods between randomization-based sanity checks [1] and model output faithfulness measures (e.g. [25]). We identify limitations of model-randomization-based sanity checks for the purpose of evaluating explanations. Firstly, we show that uninformative attribution maps created with zero pixel-wise covariance easily achieve high scores in this type of checks. Secondly, we show that top-down model randomization preserves scales of forward pass activations with high probability. That is, channels with large activations have a high probility to contribute strongly to the output, even after randomization of the network on top of them. Hence, explanations after randomization can only be expected to differ to a certain extent. This explains the observed experimental gap. In summary, these results demonstrate the inadequacy of model-randomization-based sanity checks as a criterion to rank attribution methods.

Jacob Kauffmann, Jonas Dippel, Lukas Ruff et al.

Unsupervised learning has become an essential building block of AI systems. The representations it produces, e.g. in foundation models, are critical to a wide variety of downstream applications. It is therefore important to carefully examine unsupervised models to ensure not only that they produce accurate predictions, but also that these predictions are not "right for the wrong reasons", the so-called Clever Hans (CH) effect. Using specially developed Explainable AI techniques, we show for the first time that CH effects are widespread in unsupervised learning. Our empirical findings are enriched by theoretical insights, which interestingly point to inductive biases in the unsupervised learning machine as a primary source of CH effects. Overall, our work sheds light on unexplored risks associated with practical applications of unsupervised learning and suggests ways to make unsupervised learning more robust.

Pattarawat Chormai, Jan Herrmann, Klaus-Robert Müller et al.

Explainable AI aims to overcome the black-box nature of complex ML models like neural networks by generating explanations for their predictions. Explanations often take the form of a heatmap identifying input features (e.g. pixels) that are relevant to the model's decision. These explanations, however, entangle the potentially multiple factors that enter into the overall complex decision strategy. We propose to disentangle explanations by extracting at some intermediate layer of a neural network, subspaces that capture the multiple and distinct activation patterns (e.g. visual concepts) that are relevant to the prediction. To automatically extract these subspaces, we propose two new analyses, extending principles found in PCA or ICA to explanations. These novel analyses, which we call principal relevant component analysis (PRCA) and disentangled relevant subspace analysis (DRSA), maximize relevance instead of e.g. variance or kurtosis. This allows for a much stronger focus of the analysis on what the ML model actually uses for predicting, ignoring activations or concepts to which the model is invariant. Our approach is general enough to work alongside common attribution techniques such as Shapley Value, Integrated Gradients, or LRP. Our proposed methods show to be practically useful and compare favorably to the state of the art as demonstrated on benchmarks and three use cases.

Lorenz Linhardt, Klaus-Robert Müller, Grégoire Montavon

Robustness has become an important consideration in deep learning. With the help of explainable AI, mismatches between an explained model's decision strategy and the user's domain knowledge (e.g. Clever Hans effects) have been identified as a starting point for improving faulty models. However, it is less clear what to do when the user and the explanation agree. In this paper, we demonstrate that acceptance of explanations by the user is not a guarantee for a machine learning model to be robust against Clever Hans effects, which may remain undetected. Such hidden flaws of the model can nevertheless be mitigated, and we demonstrate this by contributing a new method, Explanation-Guided Exposure Minimization (EGEM), that preemptively prunes variations in the ML model that have not been the subject of positive explanation feedback. Experiments demonstrate that our approach leads to models that strongly reduce their reliance on hidden Clever Hans strategies, and consequently achieve higher accuracy on new data.

Thomas Schnake, Farnoush Rezaei Jafari, Jonas Lederer et al.

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.

Sidney Bender, Christopher J. Anders, Pattarawatt Chormai et al.

This paper introduces a novel technique called counterfactual knowledge distillation (CFKD) to detect and remove reliance on confounders in deep learning models with the help of human expert feedback. Confounders are spurious features that models tend to rely on, which can result in unexpected errors in regulated or safety-critical domains. The paper highlights the benefit of CFKD in such domains and shows some advantages of counterfactual explanations over other types of explanations. We propose an experiment scheme to quantitatively evaluate the success of CFKD and different teachers that can give feedback to the model. We also introduce a new metric that is better correlated with true test performance than validation accuracy. The paper demonstrates the effectiveness of CFKD on synthetically augmented datasets and on real-world histopathological datasets.

Oliver Eberle, Jochen Büttner, Hassan El-Hajj et al.

Historical materials are abundant. Yet, piecing together how human knowledge has evolved and spread both diachronically and synchronically remains a challenge that can so far only be very selectively addressed. The vast volume of materials precludes comprehensive studies, given the restricted number of human specialists. However, as large amounts of historical materials are now available in digital form there is a promising opportunity for AI-assisted historical analysis. In this work, we take a pivotal step towards analyzing vast historical corpora by employing innovative machine learning (ML) techniques, enabling in-depth historical insights on a grand scale. Our study centers on the evolution of knowledge within the `Sacrobosco Collection' -- a digitized collection of 359 early modern printed editions of textbooks on astronomy used at European universities between 1472 and 1650 -- roughly 76,000 pages, many of which contain astronomic, computational tables. An ML based analysis of these tables helps to unveil important facets of the spatio-temporal evolution of knowledge and innovation in the field of mathematical astronomy in the period, as taught at European universities.

Ping Xiong, Thomas Schnake, Grégoire Montavon et al.

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.

Yasser Taha, Grégoire Montavon, Nils Körber

While machine learning (ML) architectures have evolved rapidly to account for complex data, loss functions like cross-entropy remain mostly structure-agnostic in many real-world applications. However, the `class-symmetric' nature of these standard losses fundamentally limits the ability of ML models to exploit structural relationships between classes, particularly when facing structured noise. We propose \textsc{Conveyance}, a new classification approach and associated loss function tailored to structured class spaces. It allows users to encode graph-like relations between classes without having to define complex joint distributions or manually tune utility matrices.Technically, our loss function operates by maximizing two separate margins over distinct class partitions, while preserving formal properties such as monotonicity and partial convexity. We demonstrate the versatility and effectiveness of our method by applying it to hierarchical classification, ordinal regression, and multiple instance learning. Across these tasks, \textsc{Conveyance} either matches or exceeds the performance of specialized baselines, thereby offering a unified solution for structured class spaces.

Yasser Taha, Grégoire Montavon, Nils Körber

Modern deep learning faces significant challenges with noisy labels, class ambiguity, as well as the need to robustly reject out-of-distribution or corrupted samples. In this work, we propose a unified framework based on the concept of a "drainage node'' which we add at the output of the network. The node serves to reallocate probability mass toward uncertainty, while preserving desirable properties such as end-to-end training and differentiability. This mechanism provides a natural escape route for highly ambiguous, anomalous, or noisy samples, particularly relevant for instance-dependent and asymmetric label noise. In systematic experiments involving the addition of varying proportions of instance-dependent noise or asymmetric noise to CIFAR-10/100 labels, our drainage formulation achieves an accuracy increase of up to 9\% over existing approaches in the high-noise regime. Our results on real-world datasets, such as mini-WebVision, mini-ImageNet and Clothing-1M, match or surpass existing state-of-the-art methods. Qualitative analysis reveals a denoising effect, where the drainage neuron consistently absorbs corrupt, mislabeled, or outlier data, leading to more stable decision boundaries. Furthermore, our drainage formulation enables applications well beyond classification, with immediate benefits for web-scale, semi-supervised dataset cleaning, and open-set applications.

Pattarawat Chormai, Ali Hashemi, Klaus-Robert Müller et al.

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.

Ping Xiong, Thomas Schnake, Grégoire Montavon et al.

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

Philip Naumann, Jacob Kauffmann, Klaus-Robert Müller et al.

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.

Georgii Mikriukov, Grégoire Montavon, Marina M. -C. Höhne

Post-hoc explanation methods are widely used to interpret black-box predictions, but their generation is often computationally expensive and their reliability is not guaranteed. We propose epistemic uncertainty as a low-cost proxy for explanation reliability: high epistemic uncertainty identifies regions where the decision boundary is poorly defined and where explanations become unstable and unfaithful. This insight enables two complementary use cases: `improving worst-case explanations' (routing samples to cheap or expensive XAI methods based on expected explanation reliability), and `recalling high-quality explanations' (deferring explanation generation for uncertain samples under constrained budget). Across four tabular datasets, five diverse architectures, and four XAI methods, we observe a strong negative correlation between epistemic uncertainty and explanation stability. Further analysis shows that epistemic uncertainty distinguishes not only stable from unstable explanations, but also faithful from unfaithful ones. Experiments on image classification confirm that our findings generalize beyond tabular data.

Elies Gil-Fuster, Jonas R. Naujoks, Grégoire Montavon et al.

A common trait of many machine learning models is that it is often difficult to understand and explain what caused the model to produce the given output. While the explainability of neural networks has been an active field of research in the last years, comparably little is known for quantum machine learning models. Despite a few recent works analyzing some specific aspects of explainability, as of now there is no clear big picture perspective as to what can be expected from quantum learning models in terms of explainability. In this work, we address this issue by identifying promising research avenues in this direction and lining out the expected future results. We additionally propose two explanation methods designed specifically for quantum machine learning models, as first of their kind to the best of our knowledge. Next to our pre-view of the field, we compare both existing and novel methods to explain the predictions of quantum learning models. By studying explainability in quantum machine learning, we can contribute to the sustainable development of the field, preventing trust issues in the future.

Florian Bley, Sebastian Lapuschkin, Wojciech Samek et al.

Explainable AI has brought transparency into complex ML blackboxes, enabling, in particular, to identify which features these models use for their predictions. So far, the question of explaining predictive uncertainty, i.e. why a model 'doubts', has been scarcely studied. Our investigation reveals that predictive uncertainty is dominated by second-order effects, involving single features or product interactions between them. We contribute a new method for explaining predictive uncertainty based on these second-order effects. Computationally, our method reduces to a simple covariance computation over a collection of first-order explanations. Our method is generally applicable, allowing for turning common attribution techniques (LRP, Gradient x Input, etc.) into powerful second-order uncertainty explainers, which we call CovLRP, CovGI, etc. The accuracy of the explanations our method produces is demonstrated through systematic quantitative evaluations, and the overall usefulness of our method is demonstrated via two practical showcases.

Sidney Bender, Jan Herrmann, Klaus-Robert Müller et al.

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.

Sidney Bender, Ole Delzer, Jan Herrmann et al.

Deep learning models remain vulnerable to spurious correlations, leading to so-called Clever Hans predictors that undermine robustness even in large-scale foundation and self-supervised models. Group distributional robustness methods, such as Deep Feature Reweighting (DFR) rely on explicit group labels to upweight underrepresented subgroups, but face key limitations: (1) group labels are often unavailable, (2) low within-group sample sizes hinder coverage of the subgroup distribution, and (3) performance degrades sharply when multiple spurious correlations fragment the data into even smaller groups. We propose Counterfactual Knowledge Distillation (CFKD), a framework that sidesteps these issues by generating diverse counterfactuals, enabling a human annotator to efficiently explore and correct the model's decision boundaries through a knowledge distillation step. Unlike DFR, our method not only reweights the undersampled groups, but it also enriches them with new data points. Our method does not require any confounder labels, achieves effective scaling to multiple confounders, and yields balanced generalization across groups. We demonstrate CFKD's efficacy across five datasets, spanning synthetic tasks to an industrial application, with particularly strong gains in low-data regimes with pronounced spurious correlations. Additionally, we provide an ablation study on the effect of the chosen counterfactual explainer and teacher model, highlighting their impact on robustness.

Simon Letzgus, Klaus-Robert Müller, Grégoire Montavon

In recent years, Explainable AI (XAI) methods have facilitated profound validation and knowledge extraction from ML models. While extensively studied for classification, few XAI solutions have addressed the challenges specific to regression models. In regression, explanations need to be precisely formulated to address specific user queries (e.g.\ distinguishing between `Why is the output above 0?' and `Why is the output above 50?'). They should furthermore reflect the model's behavior on the relevant data sub-manifold. In this paper, we introduce XpertAI, a framework that disentangles the prediction strategy into multiple range-specific sub-strategies and allows the formulation of precise queries about the model (the `explanandum') as a linear combination of those sub-strategies. XpertAI is formulated generally to work alongside popular XAI attribution techniques, based on occlusion, gradient integration, or reverse propagation. Qualitative and quantitative results, demonstrate the benefits of our approach.

Philip Naumann, Jacob Kauffmann, Grégoire Montavon

Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing the corresponding transport map (or coupling) may not be sufficient for understanding what factors contribute to a high or low Wasserstein distance. In this work, we propose a novel solution based on Explainable AI that allows us to efficiently and accurately attribute Wasserstein distances to various data components, including data subgroups, input features, or interpretable subspaces. Our method achieves high accuracy across diverse datasets and Wasserstein distance specifications, and its practical utility is demonstrated in two use cases.

Farnoush Rezaei Jafari, Grégoire Montavon, Klaus-Robert Müller et al.

Recent sequence modeling approaches using selective state space sequence models, referred to as Mamba models, have seen a surge of interest. These models allow efficient processing of long sequences in linear time and are rapidly being adopted in a wide range of applications such as language modeling, demonstrating promising performance. To foster their reliable use in real-world scenarios, it is crucial to augment their transparency. Our work bridges this critical gap by bringing explainability, particularly Layer-wise Relevance Propagation (LRP), to the Mamba architecture. Guided by the axiom of relevance conservation, we identify specific components in the Mamba architecture, which cause unfaithful explanations. To remedy this issue, we propose MambaLRP, a novel algorithm within the LRP framework, which ensures a more stable and reliable relevance propagation through these components. Our proposed method is theoretically sound and excels in achieving state-of-the-art explanation performance across a diverse range of models and datasets. Moreover, MambaLRP facilitates a deeper inspection of Mamba architectures, uncovering various biases and evaluating their significance. It also enables the analysis of previous speculations regarding the long-range capabilities of Mamba models.

Ameen Ali, Thomas Schnake, Oliver Eberle et al.

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.

Simon Letzgus, Patrick Wagner, Jonas Lederer et al.

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.

Siddhant Agarwal, Nicola Tosi, Pan Kessel et al.

Traditionally, 1D models based on scaling laws have been used to parameterized convective heat transfer rocks in the interior of terrestrial planets like Earth, Mars, Mercury and Venus to tackle the computational bottleneck of high-fidelity forward runs in 2D or 3D. However, these are limited in the amount of physics they can model (e.g. depth dependent material properties) and predict only mean quantities such as the mean mantle temperature. We recently showed that feedforward neural networks (FNN) trained using a large number of 2D simulations can overcome this limitation and reliably predict the evolution of entire 1D laterally-averaged temperature profile in time for complex models. We now extend that approach to predict the full 2D temperature field, which contains more information in the form of convection structures such as hot plumes and cold downwellings. Using a dataset of 10,525 two-dimensional simulations of the thermal evolution of the mantle of a Mars-like planet, we show that deep learning techniques can produce reliable parameterized surrogates (i.e. surrogates that predict state variables such as temperature based only on parameters) of the underlying partial differential equations. We first use convolutional autoencoders to compress the temperature fields by a factor of 142 and then use FNN and long-short term memory networks (LSTM) to predict the compressed fields. On average, the FNN predictions are 99.30% and the LSTM predictions are 99.22% accurate with respect to unseen simulations. Proper orthogonal decomposition (POD) of the LSTM and FNN predictions shows that despite a lower mean absolute relative accuracy, LSTMs capture the flow dynamics better than FNNs. When summed, the POD coefficients from FNN predictions and from LSTM predictions amount to 96.51% and 97.66% relative to the coefficients of the original simulations, respectively.

Léo Andeol, Yusei Kawakami, Yuichiro Wada et al.

Domain shifts in the training data are common in practical applications of machine learning; they occur for instance when the data is coming from different sources. Ideally, a ML model should work well independently of these shifts, for example, by learning a domain-invariant representation. However, common ML losses do not give strong guarantees on how consistently the ML model performs for different domains, in particular, whether the model performs well on a domain at the expense of its performance on another domain. In this paper, we build new theoretical foundations for this problem, by contributing a set of mathematical relations between classical losses for supervised ML and the Wasserstein distance in joint space (i.e. representation and output space). We show that classification or regression losses, when combined with a GAN-type discriminator between domains, form an upper-bound to the true Wasserstein distance between domains. This implies a more invariant representation and also more stable prediction performance across domains. Theoretical results are corroborated empirically on several image datasets. Our proposed approach systematically produces the highest minimum classification accuracy across domains, and the most invariant representation.

Jacob Kauffmann, Lukas Ruff, Grégoire Montavon et al.

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.

Thomas Schnake, Oliver Eberle, Jonas Lederer et al.

Graph Neural Networks (GNNs) are a popular approach for predicting graph structured data. As GNNs tightly entangle the input graph into the neural network structure, common explainable AI approaches are not applicable. To a large extent, GNNs have remained black-boxes for the user so far. In this paper, we show that GNNs can in fact be naturally explained using higher-order expansions, i.e. by identifying groups of edges that jointly contribute to the prediction. Practically, we find that such explanations can be extracted using a nested attribution scheme, where existing techniques such as layer-wise relevance propagation (LRP) can be applied at each step. The output is a collection of walks into the input graph that are relevant for the prediction. Our novel explanation method, which we denote by GNN-LRP, is applicable to a broad range of graph neural networks and lets us extract practically relevant insights on sentiment analysis of text data, structure-property relationships in quantum chemistry, and image classification.

Wojciech Samek, Grégoire Montavon, Sebastian Lapuschkin et al.

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.

Oliver Eberle, Jochen Büttner, Florian Kräutli et al.

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.

Jacob Kauffmann, Malte Esders, Lukas Ruff et al.

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.

Maximilian Alber, Sebastian Lapuschkin, Philipp Seegerer et al.

In recent years, deep neural networks have revolutionized many application domains of machine learning and are key components of many critical decision or predictive processes. Therefore, it is crucial that domain specialists can understand and analyze actions and pre- dictions, even of the most complex neural network architectures. Despite these arguments neural networks are often treated as black boxes. In the attempt to alleviate this short- coming many analysis methods were proposed, yet the lack of reference implementations often makes a systematic comparison between the methods a major effort. The presented library iNNvestigate addresses this by providing a common interface and out-of-the- box implementation for many analysis methods, including the reference implementation for PatternNet and PatternAttribution as well as for LRP-methods. To demonstrate the versatility of iNNvestigate, we provide an analysis of image classifications for variety of state-of-the-art neural network architectures.

Jacob Kauffmann, Grégoire Montavon, Luiz Alberto Lima et al.

Detecting and explaining anomalies is a challenging effort. This holds especially true when data exhibits strong dependencies and single measurements need to be assessed and analyzed in their respective context. In this work, we consider scenarios where measurements are non-i.i.d, i.e. where samples are dependent on corresponding discrete latent variables which are connected through some given dependency structure, the contextual information. Our contribution is twofold: (i) Building atop of support vector data description (SVDD), we derive a method able to cope with latent-class dependency structure that can still be optimized efficiently. We further show that our approach neatly generalizes vanilla SVDD as well as k-means and conditional random fields (CRF) and provide a corresponding probabilistic interpretation. (ii) In unsupervised scenarios where it is not possible to quantify the accuracy of an anomaly detector, having an human-interpretable solution is the key to success. Based on deep Taylor decomposition and a reformulation of our trained anomaly detector as a neural network, we are able to backpropagate predictions to pixel-domain and thus identify features and regions of high relevance. We demonstrate the usefulness of our novel approach on toy data with known spatio-temporal structure and successfully validate on synthetic as well as real world off-shore data from the oil industry.

Christopher Anders, Grégoire Montavon, Wojciech Samek et al.

Deep networks are able to learn highly predictive models of video data. Due to video length, a common strategy is to train them on small video snippets. We apply the deep Taylor / LRP technique to understand the deep network's classification decisions, and identify a "border effect": a tendency of the classifier to look mainly at the bordering frames of the input. This effect relates to the step size used to build the video snippet, which we can then tune in order to improve the classifier's accuracy without retraining the model. To our knowledge, this is the the first work to apply the deep Taylor / LRP technique on any video analyzing neural network.

Jacob Kauffmann, Klaus-Robert Müller, Grégoire Montavon

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.

Franziska Horn, Leila Arras, Grégoire Montavon et al.

When dealing with large collections of documents, it is imperative to quickly get an overview of the texts' contents. In this paper we show how this can be achieved by using a clustering algorithm to identify topics in the dataset and then selecting and visualizing relevant words, which distinguish a group of documents from the rest of the texts, to summarize the contents of the documents belonging to each topic. We demonstrate our approach by discovering trending topics in a collection of New York Times article snippets.

Franziska Horn, Leila Arras, Grégoire Montavon et al.

When working with a new dataset, it is important to first explore and familiarize oneself with it, before applying any advanced machine learning algorithms. However, to the best of our knowledge, no tools exist that quickly and reliably give insight into the contents of a selection of documents with respect to what distinguishes them from other documents belonging to different categories. In this paper we propose to extract `relevant words' from a collection of texts, which summarize the contents of documents belonging to a certain class (or discovered cluster in the case of unlabeled datasets), and visualize them in word clouds to allow for a survey of salient features at a glance. We compare three methods for extracting relevant words and demonstrate the usefulness of the resulting word clouds by providing an overview of the classes contained in a dataset of scientific publications as well as by discovering trending topics from recent New York Times article snippets.

Grégoire Montavon, Wojciech Samek, Klaus-Robert Müller

This paper provides an entry point to the problem of interpreting a deep neural network model and explaining its predictions. It is based on a tutorial given at ICASSP 2017. It introduces some recently proposed techniques of interpretation, along with theory, tricks and recommendations, to make most efficient use of these techniques on real data. It also discusses a number of practical applications.

Leila Arras, Grégoire Montavon, Klaus-Robert Müller et al.

Recently, a technique called Layer-wise Relevance Propagation (LRP) was shown to deliver insightful explanations in the form of input space relevances for understanding feed-forward neural network classification decisions. In the present work, we extend the usage of LRP to recurrent neural networks. We propose a specific propagation rule applicable to multiplicative connections as they arise in recurrent network architectures such as LSTMs and GRUs. We apply our technique to a word-based bi-directional LSTM model on a five-class sentiment prediction task, and evaluate the resulting LRP relevances both qualitatively and quantitatively, obtaining better results than a gradient-based related method which was used in previous work.

Leila Arras, Franziska Horn, Grégoire Montavon et al.

Text documents can be described by a number of abstract concepts such as semantic category, writing style, or sentiment. Machine learning (ML) models have been trained to automatically map documents to these abstract concepts, allowing to annotate very large text collections, more than could be processed by a human in a lifetime. Besides predicting the text's category very accurately, it is also highly desirable to understand how and why the categorization process takes place. In this paper, we demonstrate that such understanding can be achieved by tracing the classification decision back to individual words using layer-wise relevance propagation (LRP), a recently developed technique for explaining predictions of complex non-linear classifiers. We train two word-based ML models, a convolutional neural network (CNN) and a bag-of-words SVM classifier, on a topic categorization task and adapt the LRP method to decompose the predictions of these models onto words. Resulting scores indicate how much individual words contribute to the overall classification decision. This enables one to distill relevant information from text documents without an explicit semantic information extraction step. We further use the word-wise relevance scores for generating novel vector-based document representations which capture semantic information. Based on these document vectors, we introduce a measure of model explanatory power and show that, although the SVM and CNN models perform similarly in terms of classification accuracy, the latter exhibits a higher level of explainability which makes it more comprehensible for humans and potentially more useful for other applications.

Wojciech Samek, Grégoire Montavon, Alexander Binder et al.

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.

Leila Arras, Franziska Horn, Grégoire Montavon et al.

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.

Farhad Arbabzadah, Grégoire Montavon, Klaus-Robert Müller et al.

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.

Alexander Binder, Grégoire Montavon, Sebastian Bach et al.

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.

Grégoire Montavon, Sebastian Bach, Alexander Binder et al.

Nonlinear methods such as Deep Neural Networks (DNNs) are the gold standard for various challenging machine learning problems, e.g., image classification, natural language processing or human action recognition. Although these methods perform impressively well, they have a significant disadvantage, the lack of transparency, limiting the interpretability of the solution and thus the scope of application in practice. Especially DNNs act as black boxes due to their multilayer nonlinear structure. In this paper we introduce a novel methodology for interpreting generic multilayer neural networks by decomposing the network classification decision into contributions of its input elements. Although our focus is on image classification, the method is applicable to a broad set of input data, learning tasks and network architectures. Our method is based on deep Taylor decomposition and efficiently utilizes the structure of the network by backpropagating the explanations from the output to the input layer. We evaluate the proposed method empirically on the MNIST and ILSVRC data sets.

Sebastian Bach, Alexander Binder, Grégoire Montavon et al.

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.

Wojciech Samek, Alexander Binder, Grégoire Montavon et al.

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.

Grégoire Montavon, Klaus-Robert Müller, Marco Cuturi

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.

Grégoire Montavon, Klaus-Robert Müller

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.