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 plan (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 three use cases.

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 tend to focus too narrowly on optimizing sample quality or change minimality; they do not 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.

Distance-based classifiers, such as k-nearest neighbors and support vector machines, continue to be a workhorse of machine learning, widely used in science and industry. In practice, to derive insights from these models, it is also important to ensure that their predictions are explainable. While the field of Explainable AI has supplied methods that are in principle applicable to any model, it has also emphasized the usefulness of latent structures (e.g. the sequence of layers in a neural network) to produce explanations. In this paper, we contribute by uncovering a hidden neural network structure in distance-based classifiers (consisting of linear detection units combined with nonlinear pooling layers) upon which Explainable AI techniques such as layer-wise relevance propagation (LRP) become applicable. Through quantitative evaluations, we demonstrate the advantage of our novel explanation approach over several baselines. We also show the overall usefulness of explaining distance-based models through two practical use cases.

Deep learning models have made significant advances in histological prediction tasks in recent years. However, for adaptation in clinical practice, their lack of robustness to varying conditions such as staining, scanner, hospital, and demographics is still a limiting factor: if trained on overrepresented subpopulations, models regularly struggle with less frequent patterns, leading to shortcut learning and biased predictions. Large-scale foundation models have not fully eliminated this issue. Therefore, we propose a novel approach explicitly modeling such metadata into a Me tadata-guided generative Di ffusion model framework (MeDi). MeDi allows for a targeted augmentation of underrepresented subpopulations with synthetic data, which balances limited training data and mitigates biases in downstream models. We experimentally show that MeDi generates high-quality histopathology images for unseen subpopulations in TCGA, boosts the overall fidelity of the generated images, and enables improvements in performance for downstream classifiers on datasets with subpopulation shifts. Our work is a proof-of-concept towards better mitigating data biases with generative models.

Explainable AI has brought transparency to complex ML black boxes, enabling us, in particular, to identify which features these models use to make predictions. So far, the question of how to explain 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 × 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 through two practical showcases. • Explaining the predictive uncertainty of an ML model is practically relevant. • Second-order effects are found to be dominant in uncertainty estimates. • An efficient method for attributing uncertainty to input features is proposed. • Evaluations and showcases demonstrate the accuracy and usefulness of the method.

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.

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.

The field of eXplainable Artificial Intelligence (XAI) has witnessed significant advancements in recent years. However, the majority of progress has been concentrated in the domains of computer vision and natural language processing. For time series data, where the input itself is often not interpretable, dedicated XAI research is scarce. In this work, we put forward a virtual inspection layer for transforming the time series to an interpretable representation and allows to propagate relevance attributions to this representation via local XAI methods. In this way, we extend the applicability of XAI methods to domains (e.g. speech) where the input is only interpretable after a transformation. In this work, we focus on the Fourier transformation which, is prominently applied in the preprocessing of time series, with Layer-wise Relevance Propagation (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.

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, the 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.

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 can be overinterpreted if regarded as a primary criterion for selecting or discarding 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. [20]). 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.

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 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 exponential computational complexity with respect to the network depth, which we will remedy in this paper. Specifically, we propose 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 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 github.com/xiong-ping/rel_walk_gnnlrp.

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.

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.

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.

Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on distances or similarities. 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. We develop BiLRP, a scalable and theoretically founded method to systematically decompose the output of an already trained deep similarity model 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 models. 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.

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.

Deep learning approaches to anomaly detection (AD) have recently improved the state of the art in detection performance on complex data sets, such as large collections of images or text. These results have sparked a renewed interest in the AD 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 and 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 are 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 AD.

With the broader and highly successful usage of machine learning (ML) in industry and the sciences, there has been a growing demand for explainable artificial intelligence (XAI). Interpretability and explanation methods for gaining a better understanding of the problem-solving abilities and strategies of nonlinear ML, 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 ML; and 4) demonstrate successful usage of XAI in a representative selection of application scenarios. Finally, we discuss challenges and possible future directions of this exciting foundational field of ML.

Detecting anomalies in the data is a common machine learning task, with numerous applications in the sciences and industry. In practice, it is not always sufficient to reach high detection accuracy, one would also like to be able to understand why a given data point has been predicted to be anomalous. We propose a principled approach for one-class SVMs (OC-SVM), that draws on the novel insight that these models can be rewritten as distance/pooling neural networks. This ‘neuralization’ step lets us apply deep Taylor decomposition (DTD), a methodology that leverages the model structure in order to quickly and reliably explain decisions in terms of input features. The proposed method (called ‘OC-DTD’) is applicable to a number of common distance-based kernel functions, and it outperforms baselines such as sensitivity analysis, distance to nearest neighbor, or edge detection.

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 predictions, 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 shortcoming 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.

Nonlinear methods such as Deep Neural Networks (DNNs) are the gold standard for various challenging machine learning problems such as image 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 called deep Taylor decomposition 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.

Deep neural networks (DNNs) have demonstrated impressive performance in complex machine learning tasks such as image classification or speech recognition. However, due to their multilayer 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 with respect to 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 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 the neural network performance.

Fisher vector (FV) 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 and ILSVRC 2012 data sets.

Boltzmann machines are able to learn highly complex, multimodal, structured and multiscale real-world data distributions. Parameters of the model are usually learned by minimizing the Kullback-Leibler (KL) divergence from training samples to the learned model. We propose in this work a novel approach for Boltzmann machine training which assumes that a meaningful metric between observations is known. This metric between observations can then be used to define the Wasserstein distance between the distribution induced by the Boltzmann machine on the one hand, and that given by the training sample on the other hand. We derive a gradient of that distance with respect to the model parameters. Minimization of this new objective leads to generative models with different statistical properties. We demonstrate their practical potential on data completion and denoising, for which the metric between observations plays a crucial role.

The Layer-wise Relevance Propagation (LRP) algorithm explains a classifier's prediction specific to a given data point by attributing relevance scores to important components of the input by using the topology of the learned model itself. With the LRP Toolbox we provide platform-agnostic implementations for explaining the predictions of pre-trained state of the art Caffe networks and stand-alone implementations for fully connected Neural Network models. The implementations for Matlab and python shall serve as a playing field to familiarize oneself with the LRP algorithm and are implemented with readability and transparency in mind. Models and data can be imported and exported using raw text formats, Matlab's .mat files and the .npy format for numpy or plain text.

The accurate prediction of molecular energetics in chemical compound space is a crucial ingredient for rational compound design. The inherently graph-like, non-vectorial nature of molecular data gives rise to a unique and difficult machine learning problem. In this paper, we adopt a learning-from-scratch approach where quantum-mechanical molecular energies are predicted directly from the raw molecular geometry. The study suggests a benefit from setting flexible priors and enforcing invariance stochastically rather than structurally. Our results improve the state-of-the-art by a factor of almost three, bringing statistical methods one step closer to the holy grail of ''chemical accuracy''.

Deep networks can potentially express a learning problem more efficiently than local learning machines. While deep networks outperform local learning machines on some problems, it is still unclear how their nice representation emerges from their complex structure. We present an analysis based on Gaussian kernels that measures how the representation of the learning problem evolves layer after layer as the deep network builds higher-level abstract representations of the input. We use this analysis to show empirically that deep networks build progressively better representations of the learning problem and that the best representations are obtained when the deep network discriminates only in the last layers.