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.Index Terms-graph neural networks, higher-order explanations, layer-wise relevance propagation, explainable machine learning. ! INTRODUCTIONMany interesting structures found in scientific and industrial applications can be expressed as graphs. Examples are lattices in fluid modeling, molecular geometry, biological interaction networks, or social / historical networks. Graph neural networks (GNNs) [1], [2] have been proposed as a method to learn from observations in general graph structures and have found use in an ever growing number of applications [3]-[8]. While GNNs make useful predictions, they typically act as black-boxes, and it has neither been directly possible (1) to extract novel insight from the learned model nor (2) to verify that the model has made the intended use of the graph structure, e.g. that it has avoided Clever Hans phenomena [9].Explainable AI (XAI) is an emerging research area that aims to extract interpretable insights from trained ML models [10], [11]. So far, research has focused, for example, on full black-box models [12], [13], self-explainable models [14], [15], or deep neural networks [16], where in all cases, the prediction can be attributed to the input features. For a GNN, however, the graph being received as input is deeply

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.

The Sphere project stands at the intersection of the humanities and information sciences. The project aims to better understand the evolution of knowledge in the early modern period by studying a collection of 359 textbook editions published between 1472 and 1650 which were used to teach geocentric cosmology and astronomy at European universities. The relatively large size of the corpus at hand presents a challenge for traditional historical approaches, but provides a great opportunity to explore such a large collection of historical data using computational approaches. In this paper, we present a review of the different computational approaches, used in this project over the period of the last three years, that led to a better understanding of the dynamics of knowledge transfer and transformation in the early modern period.

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.

Learned self-attention functions in state-of-theart NLP models often correlate with human attention. We investigate whether self-attention in large-scale pre-trained language models is as predictive of human eye fixation patterns during task-reading as classical cognitive models of human attention. We compare attention functions across two task-specific reading datasets for sentiment analysis and relation extraction. We find the predictiveness of large-scale pretrained self-attention for human attention depends on 'what is in the tail', e.g., the syntactic nature of rare contexts. Further, we observe that task-specific fine-tuning does not increase the correlation with human task-specific reading. Through an input reduction experiment we give complementary insights on the sparsity and fidelity trade-off, showing that lowerentropy attention vectors are more faithful.