Original: MEGAN: Multi Explanation Graph Attention Network
Revised: MEGAN: Multi Explanation Graph Attention Network

Original: Abstract
Revised: Abstract

Original: Besides increasing trust in the human-AI relationship, XAI methods have thepotential to promote new scientific insight.
Revised: Besides increasing trust in the human-AI relationship, XAI methods have the potential to promote new scientific insight.

Original: Graph neural networks (GNNs) haverecently established themselves as a valuable tool in chemistry and material sciences.
Revised: Graph neural networks (GNNs) have recently established themselves as a valuable tool in chemistry and material sciences.

Original: Various XAI methods have already been applied to gain new understandingof real-world scientific questions in these application domains.
Revised: Various XAI methods have already been applied to gain new understanding of real-world scientific questions in these application domains.

Original: To that end wepropose MEGAN, a multi-explanation graph attention network.
Revised: To that end we propose MEGAN, a multi-explanation graph attention network.

Original: Unlike commonpost-hoc XAI methods, our model is self-explaining and features multiple explanation channels, which can be chosen independent of the task specifications.
Revised: Unlike common post-hoc XAI methods, our model is self-explaining and features multiple explanation channels, which can be chosen independent of the task specifications.

Original: Wefirst validate our model on a synthetic graph regression dataset.
Revised: We first validate our model on a synthetic graph regression dataset.

Original: We then apply ourmodel to the prediction of water solubility for chemical compounds.
Revised: We then apply our model to the prediction of water solubility, as well as the single-triplet energy gap.

Original: We find thatour model learns to produce explanations consistent with human intuition, openingthe way to learning from our model in less well-understood tasks.
Revised: The explanations generated by our model reproduce commonly known rules of thumb, supports previously hypothesized explanations and proposes novel explanatory motifs.

Original:  Introduction
Revised:  Introduction

Original: Explainable AI (XAI) methods aim to provide additional explanations for a model’s predictionsto make it’s complex inner workings more transparent to humans with the intention to improvetrust within the human-AI relationship, provide tools for model analysis, and comply with antidiscrimination laws (Doshi-Velez and Kim, 2017).
Revised: Explainable AI (XAI) methods aim to provide additional explanations for a model’s predictions to make it’s complex inner workings more transparent to humans with the intention to improve trust within the human-AI relationship, provide tools for model analysis, and comply with antidiscrimination laws (Doshi-Velez and Kim, 2017).

Original: One important subclass of XAI methods areattention-based models, which usually derive an attributional explanation from the internal attentionweights.
Revised: One important subclass of XAI methods are attention-based models, which usually derive an attributional explanation from the internal attention weights.

Original: In contrast to most post-hoc explainability procedures, the differentiable nature of attentionmodels offers the potential for explanation supervised training.
Revised: In contrast to most post-hoc explainability procedures, the differentiable nature of attention models offers the potential for explanation supervised training.

Original: Here the explanations generatedby the model are trained to match a given reference alongside the main prediction value.
Revised: Here the explanations generated by the model are trained to match a given reference alongside the main prediction value.

Original: Recentlyseveral successes for explanation supervision have been reported in the domains of natural languageprocessing (Fernandes et al., 2022;
Revised: Recently several successes for explanation supervision have been reported in the domains of natural language processing (Fernandes et al., 2022;

Original: Stacey et al., 2022) and image processing (Linsley et al., 2019;
Revised: Stacey et al., 2022) and image processing (Linsley et al., 2019;

Original: Qiao et al., 2018).
Revised: Qiao et al., 2018).

Original: Attention is increasingly applied to graph neural networks as well (Veliˇckovi´c et al., 2018; Brodyet al., 2022; Pan et al., 2022).
Revised: Attention is increasingly applied to graph neural networks as well (Veliˇckovi´c et al., 2018; Brody et al., 2022; Pan et al., 2022).

Original: However, its potential to be used in explainable models is not fullyexploited yet, when compared to other state-of-the-art graph XAI methods such as GNNExplainer(Ying et al., 2019) or Grad-CAM (Pope et al., 2019).
Revised: However, its potential to be used in explainable models is not fully exploited yet, when compared to other state-of-the-art graph XAI methods such as GNNExplainer (Ying et al., 2019) or Grad-CAM (Pope et al., 2019).

Original: We hypothesize that this is partly due to thelimited expressiveness of attention-derived explanations.
Revised: We hypothesize that this is partly due to the limited expressiveness of attention-derived explanations.

Original: While Grad-CAM for example can generateattributional explanations which feature positive and negative values for each output of a modelseparately, attention-based models usually can only generate a single explanation with values in the[0 , 1] range.
Revised: While Grad-CAM for example can generate attributional explanations which feature positive and negative values for each output of a model separately, attention-based models usually can only generate a single explanation with values in the [0 , 1] range.

Original: Considering a typical node attribution explanation for a regression model, which assignseach node an importance value between 0 and 1: It highlights which nodes were important for themodel to make a given prediction, but it does not explain how the node correlates with the actualnumerical prediction.
Revised: Considering a typical node attribution explanation for a regression model, which assigns each node an importance value between 0 and 1: It highlights which nodes were important for the model to make a given prediction, but it does not explain how the node correlates with the actual numerical prediction.

Original: We show in this paper that a substantial gain in interpretability can be achievedwhen using attention to generate multi-channel explanations.
Revised: We show in this paper that a substantial gain in interpretability can be achieved when using attention to generate multi-channel explanations.

Original: We propose the multi-explanation graph attention network (MEGAN) architecture, which allows thenumber of explanation channels to be chosen as an independent parameter.
Revised: We propose the multi-explanation graph attention network (MEGAN) architecture, which allows the number of explanation channels to be chosen as an independent parameter.

Original: The network generatesmultiple channels of node and edge attribution explanations, building on the recently proposed GATv2layer (Brody et al., 2022) for edge explanations and a weighted global pooling operation for thenode explanations.
Revised: The network generates multiple channels of node and edge attribution explanations, building on the recently proposed GATv2 layer (Brody et al., 2022) for edge explanations and a weighted global pooling operation for the node explanations.

Original: While the number of explanation channels is a free parameter, in this work wefirst investigate the special choice of two explanation channels for regression tasks. This amountsto a linear interpretation of the problem, where one channel is providing positive explanations andthe other negative explanations with respect to a chosen reference value. For the classification case,we choose the number of explanation channels the same as the number of classes.
Revised: While the number of explanation channels is a free parameter, in this work we first investigate the simple choice of two explanation channels for regression tasks: One channel to capture positive evidence that points towards higher target values and another to capture the negative evidence.

Original: To promote thechannels to behave according to these intended interpretations, we introducea modified trainingprocedure where each training step is split into an explanation-only step first and a prediction stepafterward.
Revised: To promote the channels to behave according to these intended interpretations, we introduce an explanation co-training loss that tries to approximately solve the task by using only the explanation channels.

Original: We validate the functionality of our model on a synthetic graph regression dataset as well as realworld datasets.
Revised: We validate the functionality of our model on a synthetic graph regression dataset as well as realworld datasets.

Original: We firstly show that the special single-explanation case of our model producesexplanations with quality similar to GNNExplainer.
Revised: We firstly show that the special single-explanation case of our model produces explanations with quality similar to GNNExplainer.

Original: Switching to two explanations significantlyimproves prediction performance and interpretability of explanations.
Revised: Switching to two explanations significantly improves prediction performance and interpretability of explanations.

Original: We furthermore show thatexplanation-supervised training produces explanations with the highest similarity to the ground truthexplanations as well as fidelity w.r.t.
Revised: We furthermore show that explanation-supervised training produces explanations with the highest similarity to the ground truth explanations as well as fidelity w.r.t.

Original: the intended interpretations of the respective channels.
Revised: the intended interpretations of the respective channels.

Original: Atlast, we demonstrate our model for two real-world datasets, namely the water solubility predictionfor molecular graphs and sentiment classification for movie reviews.
Revised: At last, we demonstrate our model for two material science datasets, namely prediction of water solubility for molecular graphs and the prediction of singlet-triplet energy splittings reported by the TADF dataset Gómez-Bombarelli et al.

Original: We can show that our modelproduces explanations consistent with human intuition for these tasks, potentially opening the way tolearning from our model in less well-understood real-world tasks related to chemistry and materialsciences (see Appendix D).
Revised: Our model reproduces commonly known rules of thumb about these tasks. Additionally, for the energy splittings task it provides supporting evidence for explanations previously hypothesized by Friederich et al. and generates new hypotheses for novel explanatory motifs.

Original:  Related Work
Revised:  Related Work

Original: Graph explanations.
Revised: Graph explanations.

Original: Yuan et al.
Revised: Yuan et al.

Original: (2022) provides an overview of XAI methods that were eitheradopted or specifically designed for graph neural networks (GNNs).
Revised: (2022) provides an overview of XAI methods that were either adopted or specifically designed for graph neural networks (GNNs).

Original: Notable ones include GradCAM(Pope et al., 2019), GraphLIME (Huang et al., 2022) and GNNExplainer (Ying et al., 2019).
Revised: Notable ones include GradCAM (Pope et al., 2019), GraphLIME (Huang et al., 2022) and GNNExplainer (Ying et al., 2019).

Original: JiménezLuna et al.
Revised: JiménezLuna et al.

Original: (2020) presents another overview of XAI methods used for the application domain ofdrug discovery.
Revised: (2020) presents another overview of XAI methods used for the application domain of drug discovery.

Original: (Sanchez-Lengeling et al., 2020) evaluate many common graph XAI methods fortasks of chemical property prediction.
Revised: (Sanchez-Lengeling et al., 2020) evaluate many common graph XAI methods for tasks of chemical property prediction.

Original: Henderson et al.
Revised: Henderson et al.

Original: (2021) for example introduce regularizationterms to improve GradCAM generated explanations for chemical property prediction.
Revised: (2021) for example introduce regularization terms to improve GradCAM generated explanations for chemical property prediction.

Original: Most of theapproaches presented here are classified as post-hoc methods, which aim to explain the decision ofof existing models in hindsight.
Revised: Most of the approaches presented here are classified as post-hoc methods, which aim to explain the decision of of existing models in hindsight.

Original: Our model on the other hand is self-explaining , as Jiménez-Lunaet al.
Revised: Our model on the other hand is self-explaining , as Jiménez-Luna et al.

Original: (2020) describe it.
Revised: (2020) describe it.

Original: Due to being based on an attention mechanism, this provides the potentialfor explanation-supervised training.
Revised: Due to being based on an attention mechanism, this provides the potential for explanation-supervised training.

Original: Explanation supervision.
Revised: Explanation supervision.

Original: During explanation-supervised training, the explanations generated bythe model are trained to match a given dataset of usually human-generated explanations alongside themain prediction task.
Revised: During explanation-supervised training, the explanations generated by the model are trained to match a given dataset of usually human-generated explanations alongside the main prediction task.

Original: Linsley et al.
Revised: Linsley et al.

Original: , Qiao et al.
Revised: , Qiao et al.

Original: (2018) and Boyd et al.
Revised: (2018) and Boyd et al.

Original: (2022) for example havedemonstrated promising results for explanation supervision in the image processing domain.
Revised: (2022) for example have demonstrated promising results for explanation supervision in the image processing domain.

Original: Likewise,
Revised: Likewise,

Original: Fernandes et al.
Revised: Fernandes et al.

Original: , Pruthi et al.
Revised: , Pruthi et al.

Original: (2022) and Stacey et al.
Revised: (2022) and Stacey et al.

Original: (2022) for example demonstrate thisfor the language processing domain.
Revised: (2022) for example demonstrate this for the language processing domain.

Original: Recently, Gao et al.
Revised: Recently, Gao et al.

Original: (2021) demonstrated a method to perform
Revised: (2021) demonstrated a method to perform

Original: GNN explanation supervision for GradCAM explanations.
Revised: GNN explanation supervision for GradCAM explanations.

Original: However, their implementation currentlydoes not support batching and the extent of the explanation is coupled to the task specifications.
Revised: However, their implementation currently does not support batching and the extent of the explanation is coupled to the task specifications.

Original: Incontrary, our MEGAN architecture supports batching and features a choice of explanation channelsindependent of task specifications. 
Revised: In contrary, our MEGAN architecture supports batching and features a choice of explanation channels independent of task specifications. Scientific insight through XAI. Roscher et al.

Revised: (2020) present a recent literature survey about the emerging role of XAI for the development of new scientific insight in various application domains.

Revised: For the domain of material sciences specifically, Kailkhura et al.

Original: Multi-Explanation Graph Attention Network3.1 Task Description
Revised: (2019) for example use an ensemble method of many simple and interpretable regression models instead of a more complex black box model. This way they are able to provide explanations as well as asssess the uncertainty of each prediction. Friederich et al. (2021) employ an interpretable decision tree approach on molecular fingerprints to generate hypotheses for the influence of certain sub graph motifs on several molecular properties.

Revised: The explanations generated by our proposed model are able to reproduce commonly known rules of thumb for two molecular properties, provide supporting evidence for previously proposed hypotheses and suggest potentially novel explanatory sub graph motifs.

Revised:  Multi-Explanation Graph Attention Network 3.1 Task Description

Original: We assume a directed graph G =
Revised: We assume a directed graph G =

Original: ( V , E ) is represented by a set of node indices V ⊂ N V and a setof edges E ⊆
Revised: ( V , E ) is represented by a set of node indices V ⊂ N V and a set of edges E ⊆

Original: V × V ⊂ R E , where a tuple ( i,
Revised: V × V ⊂ R E , where a tuple ( i,

Original: j ) ∈
Revised: j ) ∈

Original: E denotes an edge from node i to node j .
Revised: E denotes an edge from node i to node j .

Original: Everynode i is associated with a vector of initial node features h (0) i ∈
Revised: Every node i is associated with a vector of initial node features h (0) i ∈

Original: R N 0 , combining into the initial nodefeature tensor H (0)
Revised: R N 0 , combining into the initial node feature tensor H (0)

Original: ∈
Revised: ∈

Original: R V × N 0 .
Revised: R V × N 0 .

Original: Each edge is associated with a feature vector u i ∈ R M , combininginto the edge feature tensor U ∈ R E × M .
Revised: Each edge is associated with a feature vector u i ∈ R M , combining into the edge feature tensor U ∈ R E × M .

Original: We consider the problems of graphclassification and graph regression, i.e.output vectors y class ∈ { 0 , 1 } C (with | y class | = 1 , such that the highest value of thatvector identifies the class ˆ c = c y class c ) or single real output values y reg ∈ R , respectively.
Revised: We consider the problem of graph regression, i.e. real output values y reg ∈ R .

Original: In addition, MEGAN outputs node and edge attribution explanations alongside each prediction.
Revised: In addition, MEGAN outputs node and edge attribution explanations alongside each prediction.

Original: We define explanations as priority masks by assigning [0 , 1] values to each node and each edge,representing the importance of the corresponding element towards the outcome of the prediction.
Revised: We define explanations as priority masks by assigning [0 , 1] values to each node and each edge, representing the importance of the corresponding element towards the outcome of the prediction.

Original: We generally assume that any prediction may be explained by K individual importance channels.
Revised: We generally assume that any prediction may be explained by K individual importance channels.

Original: The node explanations are given as the node importance tensor V im ∈ [0 , 1] V × K and the edgeexplanations are given as the edge importance tensor E im ∈
Revised: The node explanations are given as the node importance tensor V im ∈ [0 , 1] V × K and the edge explanations are given as the edge importance tensor E im ∈

Original: [0 , 1] E × K .
Revised: [0 , 1] E × K .

Original: 3.2 Architecture Overview
Revised: 3.2 Architecture Overview

Original: To solve the previously defined task we propose the following multi-explanation graph attentionnetwork (MEGAN) architecture.
Revised: To solve the previously defined task we propose the following multi-explanation graph attention network (MEGAN) architecture.

Original: Figure 1 provides a visual overview of this architecture.
Revised: Figure 1 provides a visual overview of this architecture.

Original: The networkconsists of L attention layers, where the number of layers L and the hidden units of each layer arehyperparameters.
Revised: The network consists of L attention layers, where the number of layers L and the hidden units of each layer are hyperparameters.

Original: Each of these layers consists of K individual, yet structurally identical GATv2(Brody et al., 2022) attention heads, one for each of the K expected explanation channels.
Revised: Each of these layers consists of K individual, yet structurally identical GATv (Brody et al., 2022) attention heads, one for each of the K expected explanation channels.

Original: Assumingthe attention heads in the l -th layer have N l hidden units, then each attention head produces it’sown node embeddings H ( l,k ) , where k ∈ { 1 , . . 
Revised: Assuming the attention heads in the l -th layer have N l hidden units, then each attention head produces it’s own node embeddings H ( l,k ) , where k ∈ { 1 , . . .

Original: , K } is the head index.
Revised: , K } is the head index.

Original: The final node embeddings
Revised: The final node embeddings

Original: H ( l ) ∈ R V × N l · K of layer l are then produced by concatenating all these individual matrices alongthe feature dimension:
Revised: H ( l ) ∈ R V × N l · K of layer l are then produced by concatenating all these individual matrices along the feature dimension:

Original: [Equation]
Revised: [Equation]

Original: This node embedding tensor will then be used as the input to each of the K attention heads of layerl + 1 .
Revised: This node embedding tensor will then be used as the input to each of the K attention heads of layer l + 1 .

Original: Aside from the node embeddings, each attention head also produces 
Revised: Aside from the node embeddings, each attention head also produces a vector A ( l,k ) ∈

Original: a vector A ( l,k ) ∈ R E ofattention logits which are used to calculate the attention weights
Revised: R E of attention logits which are used to calculate the attention weights

Original: [Equation]
Revised: [Equation]

Original: ) of the k -the attention head in the l -th layer.
Revised: of the k -the attention head in the l -th layer.

Original: The edge importance tensor E im ∈ [0 , 1] E × K is calculatedfrom the concatenation of these attention logit tensors in the feature dimension and summed up overthe number of layers:
Revised: The edge importance tensor E im ∈ [0 , 1] E × K is calculated from the concatenation of these attention logit tensors in the feature dimension and summed up over the number of layers:

Original: [Equation]
Revised: [Equation]

Original: Based on this, a local pooling operation is used to derive the pooled edge importance tensor E p ∈[0 , 1] V × K for the nodes of the graph.
Revised: Based on this, a local pooling operation is used to derive the pooled edge importance tensor E p ∈ [0 , 1] V × K for the nodes of the graph.

Original: The final node embeddings H ( L ) are then used as the input to a dense network, whose final layeris set to have K hidden units, producing the node importance embeddings ˜ V 
Revised: The final node embeddings H ( L ) are then used as the input to a dense network, whose final layer is set to have K hidden units, producing the node importance embeddings ˜ V im ∈

Original: im ∈ [0 , 1] V × K .
Revised: [0 , 1] V × K .

Original: Thenode importance tensor is then calculated as the product of those node importance embeddings˜ V
Revised: The node importance tensor is then calculated as the product of those node importance embeddings ˜

Original:  im ∈ [0 , 1] V × K and the pooled edge importance tensor E p ∈ [0 , 1] V × K :
Revised: V im ∈ [0 , 1] V × K and the pooled edge importance tensor E p ∈ [0 , 1] V × K :

Original: [Equation]
Revised: [Equation]

Original: The mask M introduced in Fig.
Revised: The mask M introduced in Fig.

Original: 1 is needed to compute the fidelity metric, which will be discussedlater.
Revised: 1 is needed to compute the fidelity metric, which will be discussed later.

Original: At this point the edge and node importance matrices, which represent the explanations generated bythe network, are already accounted for, which leaves only the primary prediction to be explained.
Revised: At this point the edge and node importance matrices, which represent the explanations generated by the network, are already accounted for, which leaves only the primary prediction to be explained.

Original: Thefirst remaining step is a global sum pooling operation which turns the node embedding tensor H ( L )into vector of global graph embeddings.
Revised: The first remaining step is a global sum pooling operation which turns the node embedding tensor H ( L ) into vector of global graph embeddings.

Original: For this, K separate weighted global sum pooling operationsare performed, one for each explanation channel.
Revised: For this, K separate weighted global sum pooling operations are performed, one for each explanation channel.

Original: Each of these pooling operations uses the samenode embeddings H ( L ) as input, but a different slice V im : ,k of the node importance matrix as weights.
Revised: Each of these pooling operations uses the same node embeddings H ( L ) as input, but a different slice V im : ,k of the node importance matrix as weights.

Original: In that way, K separate graph embedding vectors
Revised: In that way, K separate graph embedding vectors

Original: [Equation]
Revised: [Equation]

Original: are created, which are then concatenated into a single graph embedding vector
Revised: are created, which are then concatenated into a single graph embedding vector

Original: [Equation]
Revised: [Equation]

Original: ) where h ∈ R N L · K 2 .
Revised: where h ∈ R N L · K 2 .

Original: This graph embedding vector is then passed through a generic MLP whose finallayer either has linear activation for graph regression or softmax activation for graph classification tocreate an appropriate output
Revised: This graph embedding vector is then passed through a generic MLP whose final layer either has linear activation for graph regression or softmax activation for graph classification to create an appropriate output

Original: [Equation]
Revised: [Equation]

Original: 3.3 Explanation Co-Training
Revised: 3.3 Explanation Co-Training

Original: With the architecture as is it is up to this point, there is no mechanism to ensure that individualexplanation channels learn the appropriate explanations according to their intended interpretation.
Revised: With the architecture as is it is up to this point, there is no mechanism to ensure that individual explanation channels learn the appropriate explanations according to their intended interpretation.

Original: We use a modified training procedure to ensure that each channel learns the appropriate explanations.
Revised: We use a special explanation-only loss to ensure that each channel learns the appropriate explanations.

Original: This is illustrated in Figure 2.
Revised: This is illustrated in Figure 2.

Original: Each overall train step of the model is split into two parts: Theexplanation step and the prediction step.
Revised: Each overall train step of the model is split into two parts: The explanation step and the prediction step.

Original: The explanation step is based only on the node importancesproduced by the network.
Revised: The explanation step is based only on the node importances produced by the network.

Original: A global sum pooling operation is used to turn the importance values ofeach separate channel into a single alternate output tensor
Revised: A global sum pooling operation is used to turn the importance values of each separate channel into a single alternate output tensor

Original: ˆ Y ∈ R B × K , where B is the training batchsize.
Revised: ˆ Y ∈ R B × K , where B is the training batch size.

Original: This alternate output tensor is then used to solve an approximation of the original predictionproblem.
Revised: This alternate output tensor is then used to solve an approximation of the original prediction problem.

Original: This can be seen as a reduction of the problem into a set of K separate subgraph countingproblems, where each of those only uses the subset of training batch samples that aligns with therespective channel’s intended interpretation.
Revised: This can be seen as a reduction of the problem into a set of K separate subgraph counting problems, where each of those only uses the subset of training batch samples that aligns with the respective channel’s intended interpretation.

Original: Regression For regression, we assume K = 2 , where the first channel represents the negative andthe second channel the positive influences relative to the reference value y c .
Revised: Regression For regression, we assume K = 2 , where the first channel represents the negative and the second channel the positive influences relative to the reference value y c .

Original: We select all samplesof the current training batch lesser and greater than the reference value and use these to calculate amean squared error (MSE) loss:[Equation]
Revised: We select all samples of the current training batch lesser and greater than the reference value and use these to calculate a mean squared error (MSE) loss:

Original: Classification We assume the number of channels K = C is equal to the number of possible outputclasses C .

Original: We use the alternate output channel to compute an individual binary cross entropy (BCE)loss for each channel:

Original: [Equation]
Revised: [Equation]

Original: For regression as well as classification, the total loss during the explanation step consists of thesetask-specific terms and an additional term for explanation sparsity:
Revised: The total loss during each training step consists of a term for the main network prediction, the special explanation term and an additional term for explanation sparsity:

Original: [Equation]
Revised: [Equation]

Original: where  γ and β are hyperparameters of the training process.
Revised: where the coefficients γ and β are hyperparameters of the training process.

Original: Explanation sparsity L sparsity is calculatedas L1 regularization over the node importance tensor.
Revised: Explanation sparsity L sparsity is calculated as L1 regularization over the node importance tensor.

Original: Based on this loss the gradients are calculatedand the model weights are updated.
Revised: Based on this loss the gradients are calculated and the model weights are updated.

Original: After the explanation step, a normal prediction step is executed as well, which uses the main modeloutput and the entirety of the training batch to perform another weight update.

Original: 3.4 Implementation
Revised: 3.4 Implementation

Original: The model is implemented using KGCNN framework (Reiser et al., 2021) which implements graphneural networks in TensorFlow and Keras.
Revised: The model is implemented using KGCNN framework (Reiser et al., 2021) which implements graph neural networks in TensorFlow and Keras.

Original: The source code is publicly available and can be found athttps://github.com/awa59kst120df/graph_attention_student .
Revised: The source code is publicly available and can be found at https://github.com/aimat-lab/graph_attention_student .

Original:  Computational Experiments
Revised:  Computational Experiments

Original: In this section we only give a brief overview of the used datasets and experiments.
Revised: In this section we only give a brief overview of the used datasets and experiments.

Original: For more detailedinformation, we refer to Appendix A and Appendix B, respectively.
Revised: For more detailed information, we refer to Appendix A and Appendix B, respectively.

Original: 4.1 Datasets
Revised: 4.1 Datasets

Original: RbMotifs.
Revised: RbMotifs.

Original: We create a synthetic graph regression dataset consisting of 5000 randomly generatedgraphs, where each node has three node features representing a RGB color value.
Revised: We create a synthetic graph regression dataset consisting of 5000 randomly generated graphs, where each node has three node features representing a RGB color value.

Original: Edges are undirectedand unweighted.
Revised: Edges are undirected and unweighted.

Original: Some of these randomly generated colored graphs are additionally seeded withspecific subgraph motifs, which consist of pre-defined color combinations and are associated with aconstant value.
Revised: Some of these randomly generated colored graphs are additionally seeded with specific subgraph motifs, which consist of pre-defined color combinations and are associated with a constant value.

Original: When a motif appears in a graph, the associated value is added to that graph’s overallvalue.
Revised: When a motif appears in a graph, the associated value is added to that graph’s overall value.

Original: Solubility.
Revised: Solubility.

Original: Approx.
Revised: Approx.

Original: 8000 molecular graphs of the AqSolDB dataset (Sorkun et al., 2019).
Revised: 8000 molecular graphs of the AqSolDB dataset (Sorkun et al., 2019).

Original: The targetvalue for each graph is the measured logS value representing water solubility of the correspondingchemical compound.
Revised: The target value for each graph is the measured logS value representing water solubility of the corresponding chemical compound.

Original: Node and edge features are generated by RDKit (Landrum, 2010).
Revised: Node and edge features are generated by RDKit (Landrum, 2010).

Revised: Singlet-Triplet Energy Splittings.

Original: MovieReviews.
Revised: Approx.

Original: A dataset of2000 movie reviews, classified by sentiments "positive" and "negative". Originally a text-based dataset from the ERASER benchmark (DeYoung et al., 2020), we preprocessed it into a graph dataset by representing each word as a node and connecting adjacent nodesby undirected and unweighted edges using a sliding window of size 2 as it was done by Rathee et al.(2022).
Revised: 500000 molecular graphs of the TADF dataset GómezBombarelli et al. We use the singlet-triplet energy splittings ∆ E ST as target value, which is one of two primary parameters to assess thermally activated delayed fluorescence (TADF) properties of molecules. Molecules with such TADF character are promising candidates for a novel, low-cost

Original: Node features for each node were generated by using a pre-trained GLOVE (Penningtonet al., 2014) model with 50 dimensions.
Revised: OLED materials Endo et al. (2011); Zhang et al.

Original: 4.2 Metrics
Revised: 4.2 Metrics

Original: We measure similarity to the ground truth explanations using AUROC, as it is done by McCloskeyet al.
Revised: We measure similarity to the ground truth explanations using AUROC, as it is done by McCloskey et al.

Original: We measure sparsity on binarized explanations, which are generated by thresholding the model’s continuous attributions.
Revised: We measure sparsity on binarized explanations, which are generated by thresholding the model’s continuous attributions.

Original: We also measure explanation fidelity as described in Yuan et al.(2022) and additionally provide the fidelity of random explanations for comparison.
Revised: We also measure explanation fidelity as described in Yuan et al. (2022) and additionally provide the fidelity of random explanations for comparison.

Original: More details canbe found in Appendix B.2.
Revised: More details can be found in Appendix B.2.

Original: For the multi-explanation models, we define the Fidelity ∗ metric:
Revised: For the multi-explanation models, we define the Fidelity ∗ metric:

Original: Considering regression as anexample, we argue that the positive explanation channel is faithful to the predicted output, exactly ifthe model output becomes significantly more negative when the positive channel is withheld from themodel, as it is then missing all supposedly positive information about the graph.
Revised: Considering regression as an example, we argue that the positive explanation channel is faithful to the predicted output, exactly if the model output becomes significantly more negative when the positive channel is withheld from the model, as it is then missing all supposedly positive information about the graph.

Original: The same appliesfor the negative channel, which when withheld, should produce a more positive output.
Revised: The same applies for the negative channel, which when withheld, should produce a more positive output.

Original: In this sensewe calculate a deviation ∆ y k for each channel by supplying a corresponding binary importancemask M k (see Figure 1) which completely blocks channel k .
Revised: In this sense we calculate a deviation ∆ y k for each channel by supplying a corresponding binary importance mask M k (see Figure 1) which completely blocks channel k .

Original: A channel’s deviation then contributespositively to the overall value if that deviation is along the expected direction as defined before:
Revised: A channel’s deviation then contributes positively to the overall value if that deviation is along the expected direction as defined before:

Original: [Equation]
Revised: [Equation]

Revised: if direction of deviation as expected for channel k

Revised: [Equation]

Original:  Consequently, positive values of Fidelity* show good alignment of explanations with their respectivechannel’s intended interpretation, while low and negative values indicate misalignment.
Revised: direction of deviation not as expected for channel k [Equation] Consequently, positive values of Fidelity* show good alignment of explanations with their respective channel’s intended interpretation, while low and negative values indicate misalignment.

Original: 4.3 Synthetic Dataset - Single Explanations
Revised: 4.3 Synthetic Dataset - Single Explanations

Original: We demonstrate the base capabilities of our model for the special single-explanation ( K = 1 ) case.
Revised: We demonstrate the base capabilities of our model for the special single-explanation ( K = 1 ) case.

Original: The experiment is conducted on the synthetic RbMotifs graph regression dataset. 
Revised: The experiment is conducted on the synthetic RbMotifs graph regression dataset. We compare [Table]

Original: We compareexplanations of a baseline MEGAN K =1 γ =0 .
Revised: [Table] [Table] [Table] explanations of a baseline MEGAN K =1 γ =0 .

Original: 0 model, an explanation-supervised MEGAN K [-=1 , (S) γ =
-]
Revised: 0 model, an explanation-supervised MEGAN K [-=1 , (S) γ =
-]= [Table]

Original: .modeland the explanations of GNNExplainer based on a simple GCN network with similar layer structure.
Revised: model and the explanations of GNNExplainer based on a simple GCN network with similar layer structure.

Original: The experiment is repeated independently 50 times, where a new random dataset split is chosen eachtime.
Revised: The experiment is repeated independently 50 times, where a new random dataset split is chosen each time.

Original: We report our results in Table 1 and show examples in Figure 3.
Revised: We report our results in Table 1 and show examples in Figure 3.

Original: The results show that both MEGAN models greatly outperform the GCN baseline in terms of themain predictions (MSE, R 2 ).
Revised: The results show that both MEGAN models greatly outperform the GCN baseline in terms of the main predictions (MSE, R 2 ).

Original: The baseline MEGAN 10 . 0 and GNNExplainer perform comparably interms of similarity to ground truth, while the explanation-supervised MEGAN 10 . 0 clearly outperformsboth, nearly achieving a perfect match.We also point out, that explanations of MEGAN models show [Table]
Revised: The baseline MEGAN 10 . 0 and GNNExplainer perform comparably in terms of similarity to ground truth, while the explanation-supervised MEGAN 10 . 0 clearly outperforms both, nearly achieving a perfect match.

Original: [Table] [Table] [Table] noticeably larger median fidelity than the random baseline, while explanations of GNNExplainerdon’t, indicating that explanations produced by MEGAN actually faithfully reflect the model’s predictive behavior.
Revised: We also point out, that explanations of MEGAN models show noticeably larger median fidelity than the random baseline, while explanations of GNNExplainer don’t, indicating that explanations produced by MEGAN actually faithfully reflect the model’s predictive behavior.

Original: Generally, in the single-explanation case, we often observe that that with samples where the graphcontains two opposing motifs (red and blue) the explanations of baseline MEGAN 10 . 0 and GNNExplainer usually focus only on either of the motifs, as it can be seen in Figure 3(a).
Revised: Generally, in the single-explanation case, we often observe that that with samples where the graph contains two opposing motifs (red and blue) the explanations of baseline MEGAN 10 . 0 and GNNExplainer usually focus only on either of the motifs, as it can be seen in Figure 3(a).

Original: Only theexplanation-supervised MEGAN 1 , (S) 0 . {+
+}
Revised: Only the explanation-supervised MEGAN 1 , (S) 0 . {+
+}

Original: 0 correctly highlights both motifs.
Revised: correctly highlights both motifs.

Original: 4.4 Synthetic Dataset - Multi Explanations
Revised: 4.4 Synthetic Dataset - Multi Explanations

Original: In the second experiment, we demonstrate our model’s capability to learn dual explanations ( K = 2 ).
Revised: In the second experiment, we demonstrate our model’s capability to learn dual explanations ( K = 2 ).

Original: The experiment is conducted on the synthetic RbMotifs graph regression dataset.
Revised: The experiment is conducted on the synthetic RbMotifs graph regression dataset.

Original: We comparemultiple architecturally identical MEGAN Kγ models and vary the value of the explanation traininghyperparameter γ , including a baseline model with γ = 0 , which performs no additional explanationtraining step at all, and an explanation-supervised version MEGAN 2 , (S) 0 .[-
-]
Revised: We compare multiple architecturally identical MEGAN Kγ models and vary the value of the explanation training hyperparameter γ , including a baseline model with γ = 0 , which performs no additional explanation training step at all, and an explanation-supervised version MEGAN 2 , (S) 0 .[-
-]

Original: Each experiment is independently repeated 50 times, where a new random dataset split is choseneach time.
Revised: Each experiment is independently repeated 50 times, where a new random dataset split is chosen each time.

Original: We report our results in Table 1 and show an example in Figure 3.
Revised: We report our results in Table 1 and show an example in Figure 3.

Original: The results show that the baseline MEGAN 20 . 0 model achieves the lowest similarity to the groundtruth explanations, with MEGAN 2 , (S) 0 . 

Revised: The results show that the baseline MEGAN 20 . 0 model achieves the lowest similarity to the ground truth explanations, with MEGAN 2 , (S) 0 .

Original: showing the highest value, achieving a near perfect matchfor nodes and edges.
Revised: showing the highest value, achieving a near perfect match for nodes and edges.

Original: For the prediction performance on the other hand there is no clear differencebetween the models, all of them achieving nearly identical R 2 values.
Revised: For the prediction performance on the other hand there is no clear difference between the models, all of them achieving nearly identical R 2 values.

Original: The Fidelity ∗ is also the highestfor the explanation-supervised model MEGAN 2 , (S) 0 . 0 , while the models with γ ̸ = 0 result in similarlyhigh median values, although the distributions show higher deviation for lower values of γ .
Revised: The Fidelity ∗ is also the highest for the explanation-supervised model MEGAN 2 , (S) 0 . 0 , while the models with γ ̸ = 0 result in similarly high median values, although the distributions show higher deviation for lower values of γ .

Original: Thebaseline model MEGAN 20 . 0 shows the lowest median Fidelity ∗ value with the highest fluctuations.
Revised: The baseline model MEGAN 20 . 0 shows the lowest median Fidelity ∗ value with the highest fluctuations.

Revised: higher predicted importance values.

Revised: Examples generally show an association of long carbon chains and carbon rings with low water solubility

Revised: Groups including nitrogen and oxygen are associated with higher solubility

Original: We firstly conclude that explanation-supervision can be applied effectively to train a MEGAN modelto emulate pre-defined explanations.
Revised: We firstly conclude that explanation-supervision can be applied effectively to train a MEGAN model to emulate pre-defined explanations.

Original: Secondly, the proposed modified training procedure also leadsto the development of explanations which have high similarity to ground truth and are faithful to theintended channel interpretations when compared to the baseline.
Revised: Secondly, the proposed modified training procedure also leads to the development of explanations which have high similarity to ground truth and are faithful to the intended channel interpretations when compared to the baseline.

Original: In this context it is also important tonote that the baseline model MEGAN 20 . 0 does not perform significantly differently on the predictiontask.
Revised: In this context it is also important to note that the baseline model MEGAN 20 . 0 does not perform significantly differently on the prediction task.

Original: In fact, we generally observe that this model learns the correct explanations as well, butwithout any additional guidance the alignment of these explanations with the two available channelsis arbitrary.
Revised: In fact, we generally observe that this model learns the correct explanations as well, but without any additional guidance the alignment of these explanations with the two available channels is arbitrary.

Original: This often leads the correct explanations to develop in the wrong channels (w.r.t theirintended interpretation) as it can be seen in Figure 3.
Revised: This often leads the correct explanations to develop in the wrong channels (w.r.t their intended interpretation) as it can be seen in Figure 3.

Original: 4.5 Real-World Datasets
Revised: 4.5 Real-World Datasets

Original: In addition to the synthetic datasets, we conduct experiments with real world datasets, namely theprediction of water solubilityfor molecular graphs and sentiment classification for movie reviews.
Revised: In addition to the synthetic datasets, we conduct experiments with real world datasets, namely the prediction of water solubility and the prediction of singlet-triplet energy splittings for molecular graphs.

Original: For more details on hyperparameter configurations in both cases, we refer to Appendix B.
Revised: For more details on hyperparameter configurations in both cases, we refer to Appendix B.

Original: For the solubility dataset, some illustrated examples can be found in Figure 4 (more in Appendix C.1).
Revised: For the solubility dataset, some illustrated examples can be found in Figure 4 (more in Appendix C.1).

Original: The overall predictivity is high ( r 2 correlation coefficient of 0.91 on test set).
Revised: The overall predictivity is high ( r 2 correlation coefficient of 0.91 on test set).

Original: We observe that thenegative channel usually highlights long chains of carbon atoms and carbon rings, while the positivechannel is usually associated with functional groups including oxygen and nitrogen atoms.
Revised: We observe that the negative channel usually highlights large carbon structures, while the positive channel is usually associated with functional groups including oxygen and nitrogen atoms.

Original: This is consistent with chemistry knowledge, as non-polar carbon chains and rings are associatedwith low water solubility, while polar chemical groups including O and N atoms increase watersolubility.
Revised: This is consistent with chemistry intuition, as non-polar carbon chains and rings are associated with low water solubility, while polar chemical groups including O and N atoms increase water solubility.

Original: Overall, the models explanations are surprisingly convincing, opening the possibility toobtain non-trivial insight into data sets where little prior knowledge exists. For  the movie reviews dataset we show one example in Table 2 (more in Appendix C.2).
Revised: Examples for the singlet-triplet dataset are illustrated in Figure 5. For this task the model also achieves high predictivity ( r 2 correlation coefficient of 0.90 on test set).

Original: In generalwe observe that the positive channel foremost tends to highlight positive adjectives and thenegativechannel highlights negative adjectives respectively. This leads to the fact that in some cases theclassification result of  the network can be guessed by looking at the importance activation map dueto the fact that positive reviews tend to contain a lot of positive adjectives and negative reviewsaccordingly. However, the explanations of our model are unable to grasp the concepts of sarcasm and negations.
Revised: We firstly observe that the model is able to reproduce chemical knowledge, one example being triphenylamines consistently highlighted in the negative explanation channel as indicative of low singlet triplet gaps. These triarylamine bridges cause the necessary twist angles between the fragments, decoupling electron donating and electron accepting parts of a molecule to reduce the exchange interaction between the frontier orbitals which would otherwise lower the triplet state compared to the singlet state, thus preventing undesired singlet triplet splittings.

Original: [Table] some of the movies i had to sit through to get here were not worth it some of the early mcu movies and series leading up to this finale i found rather bland unfunny and sometimes just downright bad but this movie was one of the best movies i have seen in a while overall avengers endgame was a remarkable movie and a worthy culmination of the mcu up to this point there were some genuinely heartbreaking moments and breathtaking action sequences but to be honest some of the movies i had to sit through to get here were not worth it some of the early mcu movies and series leading up to this finale i found rather bland unfunny and sometimes just downright bad but this movie was one of the best movies i have seen in a while
Revised: Additionally, we find evidence for hypotheses about structure property relationships previously suggested by Friederich et al.

Original: Even if positive adjectives are negated they are still in the positive explanation channel and the same istrue for sarcastic remarks.
Revised: One example is conjugated bridges consistently highlighted as a positive influence in our model, as they have hypothesized as well.

Original: We believe that this is part of the reason why our model does not reach thebenchmark classification accuracy provided by DeYoung et al. (2020) usually achieved by languagemodels.
Revised: Furthermore, by analyzing samples of the test set and identifying repeating patterns within the respective explanation channels, we propose new hypotheses for structure-property relationships shown in Figure 5(c). For example we find silane groups and phosphine oxides to be consistently highlighted as positive influence on ∆ E st across all independent training repetitions.

Original: However, our model’s accuracy is consistent with that achieved by other GNNS as reportedby Rathee et al.
Revised: We provide more examples for a total of 5 new hypothesized explanatory motifs in Appendix C.2.

Original:  Limitations
Revised:  Limitations

Original: Despite the encouraging experimental results, there are limitations to the proposed MEGAN architecture:
Revised: Despite the encouraging experimental results, there are limitations to the proposed MEGAN architecture:

Original: Firstly, there is no guarantee that each channel’s explanations align correctly accordingto their predetermined interpretations.
Revised: Firstly, there is no guarantee that each channel’s explanations align correctly according to their predetermined interpretations.

Original: This alignment is mainly promoted through an additionaltraining step, whose influence on the network is dependent on the hyperparameter γ .
Revised: This alignment is mainly promoted through an additional loss term during training, whose influence on the network is dependent on the hyperparameter γ .

Original: We observed"explanation leakage" and "explanation flipping" on rare occasions even with reasonable valuesof γ .
Revised: We observed "explanation leakage" and "explanation flipping" on rare occasions even with reasonable values of γ .

Original: In those cases explanations of one channel may faintly appear in the opposite channel or aparticularly disadvantageous initialization of the network causes explanations to develop in the exactopposite channel relative to their assigned interpretation.
Revised: In those cases explanations of one channel may faintly appear in the opposite channel or a particularly disadvantageous initialization of the network causes explanations to develop in the exact opposite channel relative to their assigned interpretation.

Original: The second limitation is in the designof the explanation training step itself, whichuses only the importance values of each channel toapproximately solve an augmentation of the main prediction task. This process essentially amountsto reducing the problem to a subgraph detection / counting task.
Revised: The second limitation is in the design of the explanation co-training procedure itself, which essentially amounts to reducing the problem to a subgraph detection / counting task.

Original: While there are important real-worldapplications that can be approximated as such, it still presents an important limit to the expressivenessof our model.
Revised: While there are important real-world applications that can be approximated as such, it still presents an important limit to the expressiveness of our model.

Original:  Conclusion
Revised:  Conclusion

Original: In this paper we present MEGAN, a multi-explanation graph attention network architecture.
Revised: In this paper we present MEGAN, a multi-explanation graph attention network architecture.

Original: Ourmodel uses attention mechanisms to produce node and edge attribution explanations along multiplechannels for graphclassification and regression tasks.
Revised: Our model uses attention mechanisms to produce node and edge attribution explanations along multiple channels for graph regression tasks.

Original: Thereby, the number of explanations canbe chosen independently of the task specifications.
Revised: Thereby, the number of explanations can be chosen independently of the task specifications.

Original: This may be an important step in developingricher and more interpretable explanations for graph neural networks in the future.
Revised: This may be an important step in developing richer and more interpretable explanations for graph neural networks in the future.

Original: In this work, weinvestigate one specific choice of explanation channels first: For graph regression tasks we use twoexplanation channels to capture explanations that explain positive and negative influences relativeto a value of reference.
Revised: In this work, we investigate one specific choice of explanation channels first: For graph regression tasks we use two explanation channels to capture explanations that explain positive and negative influences relative to a value of reference.

Original: For classification tasks we choose the number of explanation channels tobe equal to the number of classes, such that each class receives its own explanation.

Original: We promotethe individual explanation channels to behave according to those predetermined interpretations byapplying a modified training procedure which includes an additional self-supervised explanation-onlytraining step in each iteration.
Revised: We promote the individual explanation channels to behave according to those predetermined interpretations by applying a modified training procedure which includes an additional self-supervised explanation-only training step in each iteration.

Original: We validate our model on a synthetic graph regression dataset and show that it produces explanationswith quality similar to GNNExplainer for the single-explanation case.
Revised: We validate our model on a synthetic graph regression dataset and show that it produces explanations with quality similar to GNNExplainer for the single-explanation case.

Original: When switching to the dualexplanation case, we argue that explanations become more interpretable.

Original: Furthermore, we showthat when using the additional explanation training step, explanations become more faithful withrespect to the outcome of the network. Furthermore, we can show thatan explanation-supervisedversion of our model achieves the highest similarity toexplanation ground truth as well as fidelityw.r.t.
Revised: We furthermore demonstrate that our model can successfully be used for explanation supervision to achieve superior results for similarity to ground truth and faithfulnes w.r.t to the prediction value.

Original: to the respective channel’s intended interpretation. Finally, we demonstrate the capabilitiesof our model on two real-world datasets: Prediction of water solubility  for molecular graphs andsentiment classification for movie reviews.
Revised: Finally, we demonstrate the capabilities of our model on two real-world datasets: The prediction of water solubility and the prediction of singlet-triplet energy splittings for molecular graphs.

Original: We show that the explanations generated by our modelare coherent with human intuition for both tasks.
Revised: We show that the explanations generated by our model are coherent with human intuition for both tasks.

Original: Inspired by the recent successes of explanation supervision (Linsley et al., 2019; Fernandes et al.

Original: ,2022) we intend to leverage the differentiability of our model, in order to investigate thepotentialbenefits of explanation supervision using human-generated explanations for more complex real-worldgraph related tasks.
Revised: Additionally, we are able to propose new hypotheses for explanatory sub-graph motifs for the singlet-triplet task based on the explanations of our model.

Original: A Dataset Details 
Revised: A Dataset Details A.1 RbMotifs

Original: [Figure] RbMotifs (red & blue motifs) is a synthetic graph regression dataset.
Revised: RbMotifs (red & blue motifs) is a synthetic graph regression dataset.

Original: It consits of 5000 randomlygenerated graphs with node counts between 10 and 40.
Revised: It consits of 5000 randomly generated graphs with node counts between 10 and 40.

Original: Each node is associated with three nodefeature values in the range [0 , 1] , which represent RGB color values.
Revised: Each node is associated with three node feature values in the range [0 , 1] , which represent RGB color values.

Original: Node colors are randomlysampled from a predefined set of 7 colors.
Revised: Node colors are randomly sampled from a predefined set of 7 colors.

Original: Edges are undirected and unweighted.
Revised: Edges are undirected and unweighted.

Original: Additionally tothe random nodes, graphs may be seeded with one of four subgraph motifs, each associated with aconstant value.
Revised: Additionally to the random nodes, graphs may be seeded with one of four subgraph motifs, each associated with a constant value.

Original: The target value for each graph is then calculated as the sum of all the motif-specificvalues of all motifs which are contained in the graph and a random component δ ∼ U ( − 0 .[Equation]
Revised: The target value for each graph is then calculated as the sum of all the motif-specific values of all motifs which are contained in the graph and a random component δ ∼ U ( − 0 .

Original: [Equation]
Revised: [Equation]

Original: where y m is the constant value associated with the m -th motif contained in the graph.
Revised: where y m is the constant value associated with the m -th motif contained in the graph.

Original: The foursubgraph motifs consist of specifc combinations of colored nodes, where two motifs form a similarpair, whose nodes are either dominated by red or blue nodes.
Revised: The four subgraph motifs consist of specifc combinations of colored nodes, where two motifs form a similar pair, whose nodes are either dominated by red or blue nodes.

Original: This means there are two possible redmotifs and two blue motifs.
Revised: This means there are two possible red motifs and two blue motifs.

Original: The red motifs are associated with a positive constant value, while theblue motifs are associated with negative values.
Revised: The red motifs are associated with a positive constant value, while the blue motifs are associated with negative values.

Original: Figure 5 illustrates this and shows some examplesgraphs from the dataset.
Revised: Figure 6 illustrates this and shows some examples graphs from the dataset.

Original: Figure 6 shows the distribution of color values as well as the distribution ofhow many motifs are contained within the graphs.
Revised: Figure 7 shows the distribution of color values as well as the distribution of how many motifs are contained within the graphs.

Original: [Figure]
Revised: [Figure]

Original: A.2 Solubility
Revised: A.2 Solubility

Original: We use the AqSolDB dataset introduced by Sorkun et al.
Revised: We use the AqSolDB dataset introduced by Sorkun et al.

Original: (2019), which consists of 9982 chemicalcompounds, annotated with measurements of water solubility (logS) at room temperature.
Revised: (2019), which consists of 9982 chemical compounds, annotated with measurements of water solubility (logS) at room temperature.

Original: The datasetwas created by merging multiple existing datasets.
Revised: The dataset was created by merging multiple existing datasets.

Original: We follow the instructions in (Sorkun et al. , 2021)and and use all of the 1290 compounds originally contained within the so-called Huuskonen dataset(Huuskonen, 2000) as the test set for all experiments.
Revised: We follow the instructions in (Sorkun et al., 2021) and and use all of the 1290 compounds originally contained within the so-called Huuskonen dataset (Huuskonen, 2000) as the test set for all experiments.

Original: For the remaining elements we apply the samepre-processing steps:
Revised: For the remaining elements we apply the same pre-processing steps:

Original: • Remove all compounds which do not contain a carbon atom • Remove adjoined mixtures• Remove compounds that contain charged atoms
Revised: • Remove all compounds which do not contain a carbon atom • Remove adjoined mixtures • Remove compounds that contain charged atoms

Original: After the application of these pre-processing steps, that leaves approx.
Revised: After the application of these pre-processing steps, that leaves approx.

Original: 7000 molecules in the trainingdataest.
Revised: 7000 molecules in the training dataest.

Original: We process all of the SMILES strings into molecular graphs using RDKit (Landrum, 2010).
Revised: We process all of the SMILES strings into molecular graphs using RDKit (Landrum, 2010).

Original: A.3 MovieReviews
Revised: A.3 MovieReviews

Original: MovieReviews is a real world text classification datasets consisting of 2000 movie reviews from
Revised: MovieReviews is a real world text classification datasets consisting of 2000 movie reviews from

Original: IMDB.
Revised: IMDB.

Original: Each movie review is to be classified into one of the two sentiment classes "positive" and"negative".
Revised: Each movie review is to be classified into one of the two sentiment classes "positive" and "negative".

Original: Within the dataset, both classes are represented equally.
Revised: Within the dataset, both classes are represented equally.

Original: We take this dataset from the
Revised: We take this dataset from the

Original: ERASER benchmark (DeYoung et al., 2020) and process it in a similar way as it was done in Ratheeet al. (2022) as well.
Revised: ERASER benchmark (DeYoung et al., 2020) and process it in a similar way as it was done in Rathee et al. (2022) as well.

Original: First, the strings are converted into token lists, where tokens are individual words and other sentenceelements such as punctuation.
Revised: First, the strings are converted into token lists, where tokens are individual words and other sentence elements such as punctuation.

Original: In this step we remove punctuation and capitalization.
Revised: In this step we remove punctuation and capitalization.

Original: The stringtokens are then converted into a 50 dimensional numeric feature vector by using a pre-trained GLOVE(Pennington et al., 2014) model.
Revised: The string tokens are then converted into a 50 dimensional numeric feature vector by using a pre-trained GLOVE (Pennington et al., 2014) model.

Original: We convert the token lists into graphs by interpreting every tokenas a graph node and connecting each node with it’s neighboring nodes (according to the order ofthe token list / sentence order) using a sliding window of size 2.
Revised: We convert the token lists into graphs by interpreting every token as a graph node and connecting each node with it’s neighboring nodes (according to the order of the token list / sentence order) using a sliding window of size 2.

Original: This means that every word isconnected to the 2 neighboring words in both directions.
Revised: This means that every word is connected to the 2 neighboring words in both directions.

Original: Edges are undirected and unweighted.
Revised: Edges are undirected and unweighted.

Original: Forall experiments we use the canonical train-test split as defined by DeYoung et al.
Revised: For all experiments we use the canonical train-test split as defined by DeYoung et al.

Original: B Experiment Details
Revised: A.4 Singlet Triplet Energy Splittings

Revised: The datasets consists of approx. 500000 molecular graphs. Annotations were created during a high-throughput virtual screening experiment conducted by Gómez-Bombarelli et al.

Revised: (2016) with the objective to discover novel materials for an application in OLED technology.

Revised: Specifically, the authors aimed to discover materials which show a specific characteristic of thermally activated delayed fluorescence (TADF).

Revised: This class of materials are a promising approach to avoid the high cost of typically used phosphorescent OLED materials (Endo et al., 2011; Zhang et al., 2012).

Revised: In their work the authors use a virtual screening approach to identify particularly promising candidates.

Revised: From an initial library of almost 2 million compounds they use a neural network to predict an estimate for the delayed fluorescent rate constant ( k TADF ).

Revised: Candidates with especially promising values were subjected to quantum chemical simulations to obtain more accurate values.

Revised: Through this process approx.

Revised: 500000 compounds were annotated with the results from quantum chemical simulations.

Revised: In the end, the top results were presented to human experts which selectedmolecules that were experimentally assessed.

Revised: Along the delayed fluorescent rate constant property k TADF , the dataset also contains annotations for the singlet-triplet gap ∆ E st and the oscillator strength f , which are the main properties from which k TADF is calculated.

Original:  B.1 Explanation Pre-processing
Revised: In our work we train our network to predict the singlet-triplet energy gap ∆ E st because there already exists some chemical knowledge about some structure-property relationships regarding it. Moreover, previous work by Friederich et al. (2021) already investigates this property using an interpretable decision tree approach. B Experiment Details B.1 Explanation Pre-processing

Original: We pre-process all explanations of MEGAN an GNNExplainer by normalizing the attribution valuesto a [0 , 1] value range.
Revised: We pre-process all explanations of MEGAN an GNNExplainer by normalizing the attribution values to a [0 , 1] value range.

Original: This is done w.r.t to all explanation channels, which means that the relativedifferences between the explanation channels remain the same.
Revised: This is done w.r.t to all explanation channels, which means that the relative differences between the explanation channels remain the same.

Original: B.2 Evaluation Metrics
Revised: B.2 Evaluation Metrics

Original: Explanation Accuracy.
Revised: Explanation Accuracy.

Original: For cases where definite ground truth explanations are available, wemeasure the accuracy of the generated explanations by computing the are under the ROC curve(AUROC), as it is done in McCloskey et al.
Revised: For cases where definite ground truth explanations are available, we measure the accuracy of the generated explanations by computing the are under the ROC curve (AUROC), as it is done in McCloskey et al.

Original: (2019), for the entire validation set.
Revised: (2019), for the entire validation set.

Original: The AUROC value isin range [0 , 1] , where 1 . 0 indicates a perfect classifier and 0 .
Revised: The AUROC value is in range [0 , 1] , where 1 . 0 indicates a perfect classifier and 0 .

Original: 5 indicates a random classifier.
Revised: 5 indicates a random classifier.

Original: Sparsity.
Revised: Sparsity.

Original: We calculate the sparsity as the percentage of nodes / edges contained in the binaryversion of the predicted node / edge importance vector.
Revised: We calculate the sparsity as the percentage of nodes / edges contained in the binary version of the predicted node / edge importance vector.

Original: The binary version of these vectors iscalculated with a threshold at 0 . 5 .
Revised: The binary version of these vectors is calculated with a threshold at 0 . 5 .

Original: Fidelity.
Revised: Fidelity.

Original: For single-explanation cases, we calculate Fidelity as described in Yuan et al.
Revised: For single-explanation cases, we calculate Fidelity as described in Yuan et al.

Original: The
Revised: The

Original: Fidelity value is the deviation of the predicted output when the given binary explanation is removedfrom the input of a particular sample.
Revised: Fidelity value is the deviation of the predicted output when the given binary explanation is removed from the input of a particular sample.

Original: In this case removal means setting all the feature values of thecorresponding input elements to zero.
Revised: In this case removal means setting all the feature values of the corresponding input elements to zero.

Original: The binary version of the explanation vectors is calculatedwith a simple threshold at 0 . 5 .
Revised: The binary version of the explanation vectors is calculated with a simple threshold at 0 . 5 .

Original: Since changes in a regressed value are harder to put into context than for a normalized classificationoutput, which is always in the [0 , 1] value range, we also provide Fidelity rand as a reference.
Revised: Since changes in a regressed value are harder to put into context than for a normalized classification output, which is always in the [0 , 1] value range, we also provide Fidelity rand as a reference.

Original: This is the Fidelity value which results from a randomly generated explanation mask, which has thesame sparsity value as the original explanation mask.
Revised: This is the Fidelity value which results from a randomly generated explanation mask, which has the same sparsity value as the original explanation mask.

Original: Consequently, regression explanations can beconsidered faithful if their Fidelity values are significantly higher than the Fidelity rand baseline.
Revised: Consequently, regression explanations can be considered faithful if their Fidelity values are significantly higher than the Fidelity rand baseline.

Original: B.3 Synthetic Dataset Experiments
Revised: B.3 Synthetic Dataset Experiments

Original: The first experiment on the RbMotifs dataset compares GNNExplainer with MEGAN models, whichonly use a single explanation channel ( K = 1 ).
Revised: The first experiment on the RbMotifs dataset compares GNNExplainer with MEGAN models, which only use a single explanation channel ( K = 1 ).

Original: In this experiment, the ground truth explanations areconsidered to consist of the union of all subgraph motifs that appear in the respective graph.
Revised: In this experiment, the ground truth explanations are considered to consist of the union of all subgraph motifs that appear in the respective graph.

Original: Theindividual model and training parameters are reported in Table 3.
Revised: The individual model and training parameters are reported in Table 2.

Original: The GNNExplainer explanations are based on a standard multi-layer GCN (Kipf and Welling, 2017)network.
Revised: The GNNExplainer explanations are based on a standard multi-layer GCN (Kipf and Welling, 2017) network.

Original: The GCN network is trained on the same train set as the MEGAN models.
Revised: The GCN network is trained on the same train set as the MEGAN models.

Original: Afterwards a
Revised: Afterwards a

Original: GNNExplainer optimization is performed for each element of the test set to obtain the explanations.
Revised: GNNExplainer optimization is performed for each element of the test set to obtain the explanations.

Original: We note that we use a slightly modified implementation of GNNExplainer contained in KGCNNlibrary Reiser et al.
Revised: We note that we use a slightly modified implementation of GNNExplainer contained in KGCNN library Reiser et al.

Original: The MEGAN models used in this first experiment use only the one explanation channel.
Revised: The MEGAN models used in this first experiment use only the one explanation channel.

Original: Since the
Revised: Since the

Original: K = 1 case is not covered in Section 3.3, these models do not use any additional explanation step atall ( γ = 0 ).
Revised: K = 1 case is not covered in Section 3.3, these models do not use any additional explanation step at all ( γ = 0 ).

Original: The second experiment compares different MEGAN configurations for the dual-explanation case
Revised: The second experiment compares different MEGAN configurations for the dual-explanation case

Original: K
Revised: K

Original: = 2 .
Revised: = 2 .

Original: In this case, ground truth explanations are split into two channels.
Revised: In this case, ground truth explanations are split into two channels.

Original: The first channel containsall blue (negative) motifs that appear in the graph and the second channel contains all red (positive)motifs.
Revised: The first channel contains all blue (negative) motifs that appear in the graph and the second channel contains all red (positive) motifs.

Original: The individual model and training parameters are reported in Table 3.
Revised: The individual model and training parameters are reported in Table 2.

Original: The results of 50 independent repetitions of these experiments can be found in Table 1.[Table] [Table]
Revised: The results of 50 independent repetitions of these experiments can be found in Table 1.

Original: B.4 Real-World Dataset Experiments
Revised: B.4 Real-World Dataset Experiments

Original: Additional to the experiments for the synthetic dataset we also perform experiments with tworeal-world datasets: The prediction of water solubility for chemical compounds and the sentimentclassification of movie reviews.
Revised: Additional to the experiments for the synthetic dataset we also perform experiments with two real-world datasets: The prediction of water solubility for chemical compounds and the sentiment classification of movie reviews.

Original: For both experiments we only report one configuration of the MEGANarchitecture.
Revised: For both experiments we only report one configuration of the MEGAN architecture.

Original: The model and training parameters can be found in Table 4.
Revised: The model and training parameters can be found in Table 3.

Original: For each experiment webriefly optimize the hyperparameters manually.
Revised: For each experiment we briefly optimize the hyperparameters manually.

Original: Most importantly, we find that dropout regularizationproves increasingly useful for increasing numbers of node features and layers.
Revised: Most importantly, we find that dropout regularization [Table] [Table] proves increasingly useful for increasing numbers of node features and layers.

Original: The given dropoutpercentages are applied after each layer.
Revised: The given dropout percentages are applied after each layer.

Original: The results of 50 independent repetitions of the solubility experiment can be found in Table 5.
Revised: The results of 50 independent repetitions of the solubility experiment can be found in Table 4.

Original: Wealso report the results of Sorkun et al.
Revised: We also report the results of Sorkun et al.

Original: (2021) for the same test set.
Revised: (2021) for the same test set.

Original: Over all repetitions, our model performs consistently well in terms of predictivity ( R 2 = 0 . 91 ),although the results are slightly worse than those achieved by the consensus model employed by
Revised: Over all repetitions, our model performs consistently well in terms of predictivity ( R 2 = 0 . 91 ), although the results are slightly worse than those achieved by the consensus model employed by

Original: Sorkun et al.
Revised: Sorkun et al.

Original: However, we especially point out the high Fidelity ∗ value for our model.
Revised: However, we especially point out the high Fidelity ∗ value for our model.

Original: On theone hand this indicates that the explanation train step effectively promotes the learned explanations toremain truthful to the intended interpretations of the respective channels.
Revised: On the one hand this indicates that the explanation train step effectively promotes the learned explanations to remain truthful to the intended interpretations of the respective channels.

Original: On the other hand this alsoindicates that the explanations which are found by the model can indeed be interpreted as positiveand negative influences for the concept of solubility in general.
Revised: On the other hand this also indicates that the explanations which are found by the model can indeed be interpreted as positive and negative influences for the concept of solubility in general.

Original: [Table]
Revised: [Table]

Original: The results of 50 independent repetitions of the MovieReviews experiment can be found in Table 6.
Revised: The results of 50 independent repetitions of the MovieReviews experiment can be found in Table 5.

Original: We also report the results of DeYoung et al.
Revised: We also report the results of DeYoung et al.

Original: (2020), who use a BERT encoder and LSTM network,and Rathee et al.
Revised: (2020), who use a BERT encoder and LSTM network, and Rathee et al.

Original: (2022), who use the same pre-processing steps to provide a baseline for a simple
Revised: (2022), who use the same pre-processing steps to provide a baseline for a simple

Original: GCN network.
Revised: GCN network.

Original: Overall, DeYoung et al.
Revised: Overall, DeYoung et al.

Original: (2020) clearly show the best classification performance.
Revised: (2020) clearly show the best classification performance.

Original: We believe this is dueto their usage of a state-of-the art BERT language model, which has recently proven very powerfulfor multiple language processing tasks.
Revised: We believe this is due to their usage of a state-of-the art BERT language model, which has recently proven very powerful for multiple language processing tasks.

Original: To our surprise however, our results are only marginallybetter than those of a GCN baseline model reported by Rathee et al.
Revised: To our surprise however, our results are only marginally better than those of a GCN baseline model reported by Rathee et al.

Original: We hypothesize that thisis due to our usage of a 50 dimensional GLOVE model instead of the full 300 dimensional versionused by Rathee et al.
Revised: We hypothesize that this is due to our usage of a 50 dimensional GLOVE model instead of the full 300 dimensional version used by Rathee et al.

Original: In the future, we want to investigate different language encoder modelsin junction with our model.
Revised: In the future, we want to investigate different language encoder models in junction with our model.

Original: [Table]
Revised: [Table]

Original: C Additional Examples
Revised: The results of 3 independent repetitions of the TADF experiment can be found in Table 6. For this experiment we conducted only 3 independent repetitions due to the drastically increased computation time for the larger dataset. We are not able to provide a direct comparison from the literature because the original authors Gómez-Bombarelli et al. (2016) only publish their results for the prediction of the k TADF property.

Revised: Using a neural network they achieve R 2 = 0 .

Revised: 92 for the prediction of k TADF .

Original: [Figure]
Revised: In regards to our own results, we can summarize that we are able to achieve overall good predictivity for the main prediction task as well. The network generates explanations which are sparse and faithful to the respective channel’s intended interpretation, as it can be seed by the positive value of Fidelity ∗ . One thing of note is that the Fidelity ∗ value is much lower when compared to the solubility experiment (see Table 4).

Original: C.2 Movie Reviews
Revised: This is most likely due to the overall different value ranges of the two tasks. While the effective target value range of the solubility dataset is [ − 16 , 2] the value range for the singlet-triplet energy gap is much smaller with [0 , 3] . Thus, deviations caused by masking individual importance channels are generally expected to have smaller absolute values.

Original: [Table]
Revised: [Table]

Original: a couple of criminals mario van
Revised: C.3 Movie Reviews

Original: [Table]
Revised: [Table]

Original:  and loretta devine move into a rich family house in hopes of conning them out of their jewels however someone else steals the jewels before they are able to get to them writer mario van peebles delivers a clever script with several unexpected plot twists but director mario van peebles undermines his own high points with haphazard camera work editing and pacing it felt as though the film should have been wrapping up at the hour mark
Revised: a couple of criminals mario van peebles and loretta devine move into a rich family house in hopes of conning them out of their jewels however someone else steals the jewels before they are able to get to them writer mario van peebles delivers a clever script with several unexpected plot twists but director mario van peebles undermines his own high points with haphazard camera work editing and pacing it felt as though the film should have been wrapping up at the hour mark

Original: but alas there was still 35 more minutes to go daniel baldwin i ca n’t believe i ’m about to type this gives the best performance in the film outshining the other talented members of the cast a couple of criminals mario van peebles and loretta devine move into a rich family house in hopes of conning them out of their jewels however someone else steals the jewels before they are able to get to them writer mario van peebles delivers a clever script with several unexpected plot twists but director mario van peebles undermines his own high points with haphazard camera work editing and pacing it felt as though the film should have been wrapping up at the hour mark
Revised: but alas there was still 35 more minutes to go daniel baldwin i ca n’t believe i ’m about to type this gives the best performance in the film outshining the other talented members of the cast a couple of criminals mario van peebles and loretta devine move into a rich family house in hopes of conning them out of their jewels however someone else steals the jewels before they are able to get to them writer mario van peebles delivers a clever script with several unexpected plot twists but director mario van peebles undermines his own high points with haphazard camera work editing and pacing it felt as though the film should have been wrapping up at the hour mark

Original: but alas there was still 35 more minutes to go daniel baldwin i ca n’t believe i ’m about to type this gives the best performance in the film outshining the other talented members of the cast
Revised: but alas there was still 35 more minutes to go daniel baldwin i ca n’t believe i ’m about to type this gives the best performance in the film outshining the other talented members of the cast

Original: [Table]
Revised: [Table]

Original: this three hour movie opens up with a view of singer guitar player musician composer frank zappa rehearsing with his fellow band members all the rest displays a compilation of footage mostly from the concert at the palladium in new york city halloween 1979 other footage shows backstage foolishness and amazing clay animation by bruce bickford the performance of titties and beer played in this movie is very entertaining with drummer terry bozzio supplying the voice of the devil frank guitar solos outdo any van halen
Revised: this three hour movie opens up with a view of singer guitar player musician composer frank zappa rehearsing with his fellow band members all the rest displays a compilation of footage mostly from the concert at the palladium in new york city halloween 1979 other footage shows backstage foolishness and amazing clay animation by bruce bickford the performance of titties and beer played in this movie is very entertaining with drummer terry bozzio supplying the voice of the devil frank guitar solos outdo any van halen

Original: or hendrix i ’ve ever heard bruce bickford outlandish clay animation is that beyond belief with zooms morphings etc
Revised: or hendrix i ’ve ever heard bruce bickford outlandish clay animation is that beyond belief with zooms morphings etc

Original: and actually it does n’t even look like clay it looks like meat this three hour movie opens up with a view of singer guitar player musician composer frank zappa rehearsing with his fellow band members all the rest displays a compilation of footage mostly from the concert at the palladium in new york city halloween 1979 other footage shows backstage foolishness and amazing clay animation by bruce bickford the performance of titties and beer played in this movie is very entertaining with drummer terry bozzio supplying the voice of the devil frank guitar solos outdo any van halen
Revised: and actually it does n’t even look like clay it looks like meat this three hour movie opens up with a view of singer guitar player musician composer frank zappa rehearsing with his fellow band members all the rest displays a compilation of footage mostly from the concert at the palladium in new york city halloween 1979 other footage shows backstage foolishness and amazing clay animation by bruce bickford the performance of titties and beer played in this movie is very entertaining with drummer terry bozzio supplying the voice of the devil frank guitar solos outdo any van halen

Original: or hendrix i ’ve ever heard bruce bickford outlandish clay animation is that beyond belief with zooms morphings etc
Revised: or hendrix i ’ve ever heard bruce bickford outlandish clay animation is that beyond belief with zooms morphings etc

Original: and actually it does n’t even look like clay it looks like meat partial sentence "never a bad thing in the middle of the is praise features is meant sarcastically, but is still sorted into the
Revised: and actually it does n’t even look like clay it looks like meat partial sentence "never a bad thing in the middle of the is praise features is meant sarcastically, but is still sorted into the

Original: [Table]
Revised: [Table]

Original: burnt money is the perfect festival film it will show once or twice and then no one thankfully will ever have to hear from it again this film from the seattle international film festival 2001 emerging masters series is easily one of the year worst billed as a gay ‘ bonnie and clyde this gritty film from director marcelo pi eyro has its only highlight in a well designed title sequence two gay lovers get involved in a bank robbery that makes a gang leader whose plan they screwed up angry this causes the gang leader to send his boys out to get the gay guys one of whom may not actually be gay hiding out in a prostitute apartment the two men must fight off police and gang members in a very long showdown for the movie conclusion if caught they risk losing all the money and their love as an added emotional bonus one of the gay men is dying or something like that everything that happens is so quick and confusing i was completely lost clarity is n’t exactly this movie striving virtue so it was a little hard to pick up not much could have really happened though the main events in this long two hour film are explicit homosexual and heterosexual sex graphic drug use extreme violence and strong language lots of explicit material is never a bad thing when there a reason but there no purpose to anything in this film most of the sex and violence scenes come off as silly while the heavy drug use comes off as ridiculous and depressing it appears pi eyro who co wrote with marcelo figueras from a novel by ricardo piglia purposefully adds more blood and lovemaking for his own amusement he makes the actors as sweaty and dirty as possible makes them snort cocaine gives them guns and condoms and lets them go burnt money is pointless the performances are bad it tries to thrill and shock but only causes boredom god forbid it will ever get a distributor another disappointing film from this year so called emerging masters series pass on by burnt money is the perfect festival film it will show once or twice and then no one thankfully will ever have to hear from it again this film from the seattle international film festival 2001 emerging masters series is easily one of the year worst billed as a gay ‘ bonnie and clyde this gritty film from director marcelo pi eyro has its only highlight in a well designed title sequence two gay lovers get involved in a bank robbery that makes a gang leader whose plan they screwed up angry this causes the gang leader to send his boys out to get the gay guys one of whom may not actually be gay hiding out in a prostitute apartment the two men must fight off police and gang members in a very long showdown for the movie conclusion if caught they risk losing all the money and their love as an added emotional bonus one of the gay men is dying or something like that everything that happens is so quick and confusing i was completely lost clarity is n’t exactly this movie striving virtue so it was a little hard to pick up not much could have really happened though the main events in this long two hour film are explicit homosexual and heterosexual sex graphic drug use extreme violence and strong language lots of explicit material is never a bad thing when there a reason but there no purpose to anything in this film most of the sex and violence scenes come off as silly while the heavy drug use comes off as ridiculous and depressing it appears pi eyro who co wrote with marcelo figueras from a novel by ricardo piglia purposefully adds more blood and lovemaking for his own amusement he makes the actors as sweaty and dirty as possible makes them snort cocaine gives them guns and condoms and lets them go burnt money is pointless the performances are bad it tries to thrill and shock but only causes boredom god forbid it will ever get a distributor another disappointing film from this year so called emerging masters series pass on byD Relevance to Material Sciences XAI methods aim to improve trust within the human-AI relationship and thus promote a morewidespread adoption of powerful AI solutions into every facet of human society. Beyond this factorof trust in a researcher-AI relationship, we believe that further development of XAI methodology willeventually be able to directly support the process of scientific discovery itself.
Revised: burnt money is the perfect festival film it will show once or twice and then no one thankfully will ever have to hear from it again this film from the seattle international film festival 2001 emerging masters series is easily one of the year worst billed as a gay ‘ bonnie and clyde this gritty film from director marcelo pi eyro has its only highlight in a well designed title sequence two gay lovers get involved in a bank robbery that makes a gang leader whose plan they screwed up angry this causes the gang leader to send his boys out to get the gay guys one of whom may not actually be gay hiding out in a prostitute apartment the two men must fight off police and gang members in a very long showdown for the movie conclusion if caught they risk losing all the money and their love as an added emotional bonus one of the gay men is dying or something like that everything that happens is so quick and confusing i was completely lost clarity is n’t exactly this movie striving virtue so it was a little hard to pick up not much could have really happened though the main events in this long two hour film are explicit homosexual and heterosexual sex graphic drug use extreme violence and strong language lots of explicit material is never a bad thing when there a reason but there no purpose to anything in this film most of the sex and violence scenes come off as silly while the heavy drug use comes off as ridiculous and depressing it appears pi eyro who co wrote with marcelo figueras from a novel by ricardo piglia purposefully adds more blood and lovemaking for his own amusement he makes the actors as sweaty and dirty as possible makes them snort cocaine gives them guns and condoms and lets them go burnt money is pointless the performances are bad it tries to thrill and shock but only causes boredom god forbid it will ever get a distributor another disappointing film from this year so called emerging masters series pass on by burnt money is the perfect festival film it will show once or twice and then no one thankfully will ever have to hear from it again this film from the seattle international film festival 2001 emerging masters series is easily one of the year worst billed as a gay ‘ bonnie and clyde this gritty film from director marcelo pi eyro has its only highlight in a well designed title sequence two gay lovers get involved in a bank robbery that makes a gang leader whose plan they screwed up angry this causes the gang leader to send his boys out to get the gay guys one of whom may not actually be gay hiding out in a prostitute apartment the two men must fight off police and gang members in a very long showdown for the movie conclusion if caught they risk losing all the money and their love as an added emotional bonus one of the gay men is dying or something like that everything that happens is so quick and confusing i was completely lost clarity is n’t exactly this movie striving virtue so it was a little hard to pick up not much could have really happened though the main events in this long two hour film are explicit homosexual and heterosexual sex graphic drug use extreme violence and strong language lots of explicit material is never a bad thing when there a reason but there no purpose to anything in this film most of the sex and violence scenes come off as silly while the heavy drug use comes off as ridiculous and depressing it appears pi eyro who co wrote with marcelo figueras from a novel by ricardo piglia purposefully adds more blood and lovemaking for his own amusement he makes the actors as sweaty and dirty as possible makes them snort cocaine gives them guns and condoms and lets them go burnt money is pointless the performances are bad it tries to thrill and shock but only causes boredom god forbid it will ever get a distributor another disappointing film from this year so called emerging masters series pass on by

Original: This is because humanresearchers and computational models possess very complementary strengths.

Original: While humans providethe required creativity and the ability to theorize on higher levels of abstraction, methods of machinelearning have an unparalleled capability to learn the hidden relationships within vast amounts of data.

Original: Nowadays, the top AI models are able to perform highly complex tasks on a level similar or above tothat of average humans.

Original: This ranges from the proficiency of playing highly complex games (Silveret al., 2016;

Original: Vinyals et al., 2019) to image recognition and generation (Ramesh et al., 2021; OpenAI,2022), natural language processing (Radford et al., 2018; Lewis et al., 2020) and even various taskswithin the natural sciences (Boobier et al., 2017).

Original: We argue that if such highly capable AI modelswere able to communicate their learned knowledge effectively and efficiently to an audience of humanresearchers that this could provide a valuable tool in the pursuit of new scientific insight (Friederichet al., 2021; Krenn et al., 2022).

Original: Especially in the domain of material sciences, a model trained toaccurately predict a complex material property could teach us it’s hidden structural causality, helpingin turn to accelerate the discovery and synthesis of new materials.

Original: We propose our MEGAN architecture as a first step towards this goal.

Original: Our model mainly aims toexpand the explanatory capabilities of the GNN approach.

Original: Unlike the common post-hoc explanabilitymethods our model is self-explaining as it is coined by Jiménez-Luna et al.

Original: This meansthat the explanation mechanism is built into the network architecture itself, where the explanationsthemselves are being directly involved in the calculation of the network’s main prediction.

Original: For onething, this results in explanations which are more faithful in describing the model’s actual behavior.

Original: Additionally, we design our architecture to have the number of explanation channels be independentof the task specifications.

Original: We argue that such an increased flexibility will be important for thedevelopment of more expressive and granular forms of explanation in the future.

Original: Encouraged by theresults obtained for the prediction of water solubility, we specifically plan to investigate methodsto meaningfully expand this approach to different choices of explanation channels than the onespresented in this work.

Original: We believe that this has the potential to reveal even more fine-grained insightsabout the structure property relationship of real-world problems in chemistry and material science.

Original: Checklist

Original: For all authors...

Original: (a) Do the main claims made in the abstract and introduction accurately reflect the paper’s

Original: contributions and scope?

Original: [Yes] The abstract however focuses more on the relevance to

Original: the context of material sciences than the original submission.

Original: (b) Did you describe the limitations of your work?

Original: [Yes] See Section

Original: (c) Did you discuss any potential negative societal impacts of your work?

Original: [No] We cannot

Original: conceive of any immediate negative social impacts of our work.

Original: (d) Have you read the ethics review guidelines and ensured that your paper conforms to

Original: them?

Original: [Yes]

Original: If you are including theoretical results...

Original: (a) Did you state the full set of assumptions of all theoretical results?

Original: [N/A]

Original: (b) Did you include complete proofs of all theoretical results?

Original: [N/A]

Original: If you ran experiments...

Original: (a) Did you include the code, data, and instructions needed to reproduce the main experi-

Original: mental results (either in the supplemental material or as a URL)?

Original: [Yes] See Section 3.

Original: (b) Did you specify all the training details (e.g., data splits, hyperparameters,

Original: how they

Original: were chosen)?

Original: [Yes] See Appendix

Original: (c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?

Original: [Yes] Our experimental results are reported in the form of the

Original: median as well as the 25th and 75th percentile of the distribution

Original: (d) Did you include the total amount of compute and the type of resources used (e.g., typeof GPUs, internal cluster, or cloud provider)?

Original: [No] Computational experiments do

Original: not have any out-of-the-ordinary requirments, they were all executed on a personalcomputer.

Original: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...

Original: (a) If your work uses existing assets, did you cite the creators?

Original: [Yes] The origin of all used

Original: datasets is cited as well as the main software library used for the implementation.

Original: (b) Did you mention the license of the assets?

Original: [No]

Original: (c) Did you include any new assets either in the supplemental material or as a URL?

Original: [No]

Original: (d) Did you discuss whether and how consent was obtained from people whose data you’reusing/curating?

Original: [No] All used datasets are publicly available

Original: (e) Did you discuss whether the data you are using/curating contains personally identifiable

Original: information or offensive content?

Original: [No]

Original: If you used crowdsourcing or conducted research with human subjects...

Original: (a) Did you include the full text of instructions given to participants and screenshots, if

Original: applicable?

Original: [N/A]

Original: (b) Did you describe any potential participant risks, with links to Institutional Review

Original: Board (IRB) approvals, if applicable?

Original: [N/A]

Original: (c) Did you include the estimated hourly wage paid to participants and the total amount

Original: spent on participant compensation?

Original: [N/A]