MEGAN: Multi Explanation Graph Attention Network
Authors: Jonas Teufel
Luca Torresi
Patrick Nicholas Reiser
Pascal Friederich
Venue: Submitted to ICLR 2023 (2023)
Keywords: explainable artificial intelligence
interpretable machine learning
graph neural networks
attention network
graph regression
graph classification

Abstract: Explainable artificial intelligence (XAI) methods are expected to improve trust during human-AI interactions, provide tools for model analysis and extend human understanding of complex problems. Attention-based models are an important subclass of XAI methods, partly due to their full differentiability and the potential to improve explanations by means of explanation-supervised training. We propose the novel multi-explanation graph attention network (MEGAN). Our graph regression and classification model features multiple explanation channels, which can be chosen independently of the task specifications. We first validate our model on a synthetic graph regression dataset, where our model produces single-channel explanations with quality similar to GNNExplainer. Furthermore, we demonstrate the advantages of multi-channel explanations on one synthetic and two real-world datasets: The prediction of water solubility of molecular graphs and sentiment classification of movie reviews. We find that our model produces explanations consistent with human intuition, opening the way to learning from our model in less well-understood tasks.

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MEGAN: MULTI-EXPLANATION GRAPH ATTENTION NETWORK
Anonymous authors Paper under double-blind review
ABSTRACT
Explainable artificial intelligence (XAI) methods are expected to improve trust during human-Al interactions, provide tools for model analysis and extend human understanding of complex problems. Explanation Explanatioo-supprriised training allows improve explanation quality by training self-explaining XAI models on ground truth or aumann-geneaated explanations. However, existing explanation methods have limited expressiveness and interoperability due to the fact that only single explanations in form of node and edge importance are generated. To that end we propose the novel multi-explanation graph attention network (MEGAN). Our fully differentiable, attention based model features multiple explanation channels, which can be chosen independently of the task specifications. We first validate our model on a synthetic graph regression dataset. We show that for the spe- cial single explanation case, our model significantly outperforms existing post- baseline methods. Furthermore, we demonstrate
hoc and significant advantages when using two explanations, both in quantitative expla- nation measures as well as in human interpretability. Finally, we demonstrate our model's capabilities on multiple real-world datasets. We find that our model produces sparse high-fidelity explanations consistent with human intuition about those tasks and at the same time matches state-of-the-arr art graph neural networks predictive performance, indicating that explanations and accuracy are not neces- sarily a trade-off.
INTRODUCTION
Explainable AI (XAI) methods aim to provide explanations complementing a model's predictions to make it's complex inner workings more transparent to humans with the intention to improve trust and reliability, provide tools for model analysis, and comply with anti citt-diserimination laws (Doshi- Velez & Kim 2017). Many explainability methods have already been proposed for graph neural networks (GNNs), as Yuan et al. (202)) demonstrate in their literature survey. However, the ma- jority of work is focused post-hoe hoc XAI methods that aim provide explanations for already existing models through external analysis procedures. In contrast to that, we demonstrate signifi- cant advantages of methods which Jiménez-Luna al. (2020) call self-explaining methods. This class of models directly generates explanations alongside each prediction. One inherent advantage training. In explana-
of many self-explaining models their capability for spplanation-suprvvii tion supervision the explanations are trained alongside the main prediction task to match known explanations, improving explanation quality in the explanation ground truth human-generate ooplanation-supervisionn process. Recently, impressive successes of explanation supervision have been reported in the do- mains of image processing (Linsley al. 2019 Qiao al.) 2018 Boyd et al. (022) and natural language processing (Fernandes et al.) 2022 Pruthi et al. 2020 Stacey et al. 2022). In the graph domain, explanation supervision very sparsely explored yet (Gao al.) 2021 Magister et al.) 2022). Inspired by the explanation-ssperviiite by attention-basee models, we propose our novel, self-cxplaining multiiexpllnattion graph atten- tion network (MEGAN) enable effective aaplanation-superiisse training for graph regression and classification problems.
successes demonstrated in other domains, especially
We specifically want to emphasize focus graph regression tasks, which have been ignored by previous work on explanation supervision. However, we argue that graph regression problems are becoming especially important topic due to their high relevance in chemistry and material sci-

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ence applications. Typical graph XAI methods and existing work explanation supervision provide single-channer attributional explanations, which means that each input element (nodes and edges) associated with single [0, I] value to denote their importance. We argue that explanations merely indicating importance are hardly interpretable for regression tasks, as it remains unknown for what such explanations provide evidence: The exact predicted value, certain value range or an especially high/low value? Due to this fact, we design our model to support an arbitrary number of explanation channels, independent of task specifications. For regression tasks, we choose chan- nels: One positive channel which indicates evidence of high target values, and one negative channel which contains evidence of low target values. We introduce a special explanation co-training routine to promote channels to behave according to those interpretations. Using synthetic and real-world datasets, we illustrate how multi-channel explanations help to improve interpretability, especially for graph regression problems.
We first validate our model on a synthetic graph regression dataset. We show that even in the single-channel case, our model outperforms existing post-hoc and explanation supervision baseline methods significantly, not only in accuracy of explanations but also in terms of prediction perfor- mance. In general, we find that our proposed model shows surprisingly good prediction performance independent from the aspect of explainability. In Appendix D we provide a benchmark comparison with numerous recent GNN architectures which shows that our model achieves state-of-the-ar per- formance for graph regression tasks.
Moving to multi-channel explanations we show that our model creates explanations that are accu- rate, sparse, and faithful to predicted values. On the three real-world datasets about movie review sentiment analysis and the prediction of solubility and photophysical properties of molecular graphs, we show that our model creates explanations consistent with human intuition and knowledge. Fur- thermore, we show that our model reproduces known structure- propprrry relationships for the non- trivial singlet-triplet task, supports previously hypothesized explanations, and even produces new hypotheses for explanatory motifs.
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RELATED WORK
Graph explanations. Yuan et al. 2002) provides an overview of XAI methods that were ei- ther adopted or specifically designed for graph neural networks (GNNs). Notable ones include GradCAM (Pope et al.] 2019). GraphLIME (Huang et al. 2022) and GNNExplainer (Ying et al.) 2019). Jiménez-Luna et al. (2020) presents another overview of XAI methods used for the appli- cation domain of drug discovery. Sanchez-Lengeling et al. (2020) evaluate many common graph XAI methods for tasks of chemical property prediction. Henderson et al. (202T) for example in- troduce regularization terms to improve GradCAM --gneerated explanations for chemical property prediction. Most of the approaches presented here are classified as post-hoc methods, which aim to explain the decision of existing models in hindsight. Few prior works explore the class of GNNs which Jiménez- Luna et al. (2020) describe as self-explaining. Notably, Magister et al. (2022) intro- duce a self-explaining graph-concept network and Zhang al. (2022) outline a prototype-leaming approach for graphs where internal prototypes act as natural explanations.
Explanation supervision. During explanation-sspervvn the model are trained to match a given dataset of usually human-generatedd explanations alongside the main prediction task. [insley al. (2019), Qiao al. (2018) and LndBooyd et al./ (2022) for example have demonstrated promising results for explanation supervision in the image processing domain. Likewise, Fernandes et al. (2022), Pruthi et al. (2022) and (Stacey et al. (2022) ) for example demon- strate this for the language processing domain. Recently, [ao et al. (202T) introduce GNES, method to perform GNN explanation supervision using
training, the explanations generated by
explanations. In our work, we show that MEGAN is able to significantly improve explanation-supervissee
capabilities when compared to GNES. Additionally, Magister et al. (2022) emphasize that their method supports explanation supervision with buman-generaun explanations, however, the concept-based explana- tions generated by their approach are not empirically comparable to the attributional explanations produced by model.
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3 MULTI-EXPLANATION GRAPH ATTENTION NETWORK
3.1 TASK DESCRIPTION
We assume directed graph 9 = (V.E) is represented by set of node indices V C NV and set of edges & S V C R where a tuple (i.j) denotes an edge from node to node j. Every node i is associated with a vector of initial node features ( E R N2,o combining into the initial node feature tensor o E RV x Each edge associated with a feature vector u; RM, combining into the edge feature tensor U E -
We consider the problems of graph classification and graph regression, i.e. output vectors 1, such that the highest value of that vector identifies the class
yelass {0,1} 1) (with yydl arg max, yolas) or single real output values y ε R, respectively.
In addition, MEGAN outputs node and edge attributional explanations alongside each prediction. 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. We generally assume that any prediction may be explained by K individual importance channels, where K hyperparameter of the model. The node explanations are given as the node impor- tance tensor Vim E [0, 1] and the edge explanations are given as the edge importance tensor Eim [0, 1]EXK
3.2 ARCHITECTURE OVERVIEW
To solve the previously defined task we propose the following multi-explanation graph attention network (MEGAN) architecture. Figure work consists of L attention layers, where the number of layers L and the hidden units of each layer are hyperparameters. Each of these layers consists of individual, yet structurally identical GATv2 (Boody al. 2022) attention heads, one for each of the K expected explanation channels. Assum- ing the attention heads in the [-th layer have N₁ hidden units, then each attention head produces its own node embeddings ([..k), where E (1,..., . K} is the head index. The final node embeddings ( R V of layer are then produced by concatenating these individual matrices along the feature dimension:
visual overview this architecture. The net-
H H (1.)
H (.2)
||....| H (..)
Multi head attention hevers with atteadoon leads each
sepazate poaling oprations wsing loti ingortaance chanmel
Taput
GLOBAL POOLING
WEICHTED
G
GarV2
CUNCAT
MLP
Outprtt
(D)
H(L)
(9)
(V
K
y
DENSE LAYER R UNITS
A (1)
A (L) (8
Vim
Music
(R.R)
SEGMOOID
(P.K)
Vio (V.K)
Vin
E (V.K)
POOLING EDGES
Σ A
Fi
Figure 1: Multi-explanation graph attention network (MEGAN) architecture overview. Rectangle boxes represent layers; arrows indicate layer interconnections. Rounded boxes represent tensors. Intermediate tensors are also named annotated arrows. Tuples beneath variable names indicate the tensor shape, with batch dimension omitted, but implicitly assumed as first dimension for all.
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This node embedding tensor will then be used as the input each of the K attention heads of layer I + 1. Aside from the node embeddings, each attention head also produces a vector A (1.k) E R of attention logits which are used to calculate the attention weights
(1.R) softmax(A ((AA)
(2)
of the te-the attention head in the 1-th layer. The edge importance tensor E 1] is calcu- lated from the concatenation of these attention logit tensors in the feature dimension and summed up over the number of layers:
L Σ
E
((A)))
(ADD))
A
|| A4x))
(3)
Based on this, local pooling operation is used to derive the pooled edge importance tensor Eº E [0, 1] for the nodes of the graph.
(L)) are then used the input dense network, whose final layer set have K hidden units, producing the node importance embeddings Viim E [0, 1] The node importance tensor is then calculated as the product of those node importance embeddings Vim E [0, 1jj* and the pooled edge importance tensor EP E [0, 1]v:
The final node embeddings
Vin
Vii E M.
(4)
The mask M introduced in Fig. is only optionally used to compute the fidelity metric, which introduced in Section 4.2
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. The first remaining step a global sum pooling operation which turns the node embedding tensor (LL) into a vector of global graph embeddings. For this, K separate weighted global sum pooling operations are performed, one for each explanation channel. Fach of these pooling operations uses the same node embeddings
(L) as input, but different slice Vilm of the node importance matrix as weights. In that way, K separate graph embedding vectors
h
H
Vim
(5)
created, which are then concatenated into a single graph embedding vector
h
(K)
(6)
where h E k2 This graph embedding vector is then passed through a generic MLP whose final layer either has linear activation for graph regression softmax activation for graph classification to create an appropriate output
= MLP(h)
3.3 EXPLANATION CO-TRAINING
With the architecture as explained up to this point, there no mechanism yet to ensure that individual explanation channels learn the appropriate explanations according their intended interpretation (for example positive/negative evidence). We use a special explanation co-training procedure to guide explanations develop according pre-determined interpretations. This illustrated in Figure For this purpose, the loss function consists of two parts: The prediction and the explanation part. The explanation part based only on the node importances produced by the network. global sum pooling operation is used to turn the importance values of each separate channel into a single alternate output tensor Y E BxX where B is the training batch size. This alternate output tensor then used to solve an approximation of the original prediction problem: This can be seen as a reduction of the problem into 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.
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Regression For regression, assume K 2, where the first channel represents the negative and the second channel the positive influences relative to the reference value ye- which is hyperparam- eter of the model and usually set the arithmetic mean of the target value distribution in the train set. We select all samples of the current training batch lesser and greater than the reference value and use these calculate mean squared error (MSE) loss:
B
Y 6.0 ye g if B ye oY
Lexp B b=1
(8)
Ye Y if Y Y/
We assume the number of channels K is equal the number of possible output classes C. We use the alternate output channel to compute an individual binary cross entropy (BCE) loss for each channel:
Classification
Lexp LBCE (Y . (Y))
For regression as well as classification, the total loss during model training consists of these task- specific terms and an additional term for explanation sparsity:
Listal = Lred + Teup + B
(10)
where 7 and 3 are hyperparameters of the training process. Explanation sparsity Espariiry is calculated as regularization over the node importance tensor. Based on this loss the gradients are calculated and the model weights are updated.
4 COMPUTATIONAL EXPERIMENTS
In this section, we only give brief overview of the used datasets and experiments, Details about the datasets can be found in Appendix A Details on hyperparameters and empirical results for experiments are listed in Appendix B
4.1 DATASETS
RbMotifs. We create a synthetic graph regression dataset consisting of 5000 randomly generated graphs, where each node has three node features representing an RGB color value. Edges undi- rected and unweighted. Some of these randomly generated colored graphs are additionally seeded with specific subgraph motifs, which consist of pre-defined color combinations and associated with a constant value. When motif appears in a graph, the associated value is added to that graph's 's overall value.
Solubility. Approx. 8000 molecular graphs of the AqSolDB dataset (Sorkun et al. 2019 The target value for each graph is the value of the measured log representing the water solubility of the corresponding chemical compound. Node and edge features are generated by RDKit Landruu 2010
Juput Graphs
Explanation Step
Ground Truth Labels You
Vinue
GLOBAL POOLING
Yoas
Yiue
MEGAN
U. H
gin
ytrue
Expanett
Low
Prodiction Step
Epeed
Ecarpppes
Figure 2: Illustration of the split training procedure for the regression case. The explanation-only train step attempts to find approximate solution to the main prediction task, by using only globally pooled node importance tensor. After the weight update for the explanation step was applied to the model, the prediction step performs another weight update based on the actual output of the model and the ground truth labels.
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GNNExpliues
GNESS
MECANOS
MPGAN
MEGANA
Bood
Negative Chouaul
Poenive Channel
Groun
Single Explonations
Mulsi Explanations
Figure 3: Examples for explanations generated for element of the RbMotifs dataset using lected methods. We point out that in this instance GNNExplainer fails to discover the second rel- evant explanatory motif. Even though GNES and single-channel MEGAN correctly highlight both motifs, the single-channel explanations fail to capture the fact that both motifs represent opposing evidence. Only the multi-channel methods correctly capture the polarity of influence for both motifs, increasing the interpretability of the explanations.
MovieReviews. dataset of 2000 movie reviews, classified by sentiments "positive" and "neg- ative". Originally text-based dataset from the ERASER benchmark (De et al. (020)), pre-processed it into a graph dataset by representing each word as a node and connecting adjacent nodes by undirected and unweighted edges using a sliding window of size 2.
TADF Singlet-Triplet Energy Splittings. Approx. 500000 molecular graphs of the TADF dataset (0016). We use the singlet-triplet energy splittings ÆST the 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 novel, low-cost OLED materials (Endo et al. 2011 Zhang et al. 2012).
Gómez-Bombarelli
4.2 METRICS
We measure similarity to the ground truth explanations using AUROC, as done by McCloskey et al. (2019). We measure sparsity on binarized explanations, which are generated by thresholding model's continuous attributions. We also measure explanation fidelity as described in Yuan al.) (022) and additionally provide the fidelity of random explanations for comparison. More details can be found in Appendix B.2
For the multi-explanation models, we define the Fidelity" metric: Considering regression an example, we argue that the positive explanation channel is faithful to the predicted output, exactly the model output becomes significantly more negative when the positive channel is withheld from the model, as is then missing all supposedly positive information about the graph. The same applies to the negative channel, which when withheld, should produce this sense, we calculate a deviation Ay for each channel by supplying corresponding binary importance mask R (see Figure which completely blocks channel k. channel's deviation then contributes positively to the overall value if that deviation is along the expected direction as defined before:
positive output. In
1 K
+ A
if direction of deviation expected for channel k if direction of deviation not as expected for channel &
Fidelity* *
(11)
Consequently, positive values of Fidelity* show good alignment of explanations with their respective channel's intended interpretation, while low and negative values indicate misalignment.

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Table I: Results for computational experiments with synthetic graph regression dataset. We report the mean value for 50 independent experiment repetitions in black, as well as standard deviation in gray. We the best result for each column in bold face and underline the second best result. The first section of the table shows results for the single-explanatonn experiments and the second section shows the results for the dual-explanation experiments.
(9) Model trained explanatiot-superviee with ground truth explanations.
Mulii--xplanation case measures Fidelity" metric introduced in Section
Model
MSEL
F
Node AUC 1
Edge AUC t
Sparsity /
Fidelity t
Fidelity rand
Grad x Input
1.08
0.66
0.75 0.00
0.73
0.17=0.12
1.14
0.66:20.65
GradCAM
1.08
0.66
0.66
0.50 1.50=0.00
0.14=0.11
0.50
0.36
GnnExplainer
1.08
0.66
0.73
0. 76.608
0.18
1.34 20.94
0.82 0..22
GNESS original
0.91=0.04
0.01:0.01
0.59
0.58
0.12=0.07
1.11
0.51::0455
GNES lised
0.92
0.71 +0.01
0.85
0.78 8..02
0.19
1.22 20.76
0.69
MEGANO.0
0.47 #0.18
80.00
0.74 +0.12
0.70=
0.14 0.08
3.11 +3.08
1.96
MEGAN
1..0s
0.86:1.02
0.97 00000
0.98 0.000
0.17=0.11
1.44=1.06
1.19::1.09
MEGAN?.
0.27 20.04
0.91 20.01
0.94 0.00
0.90 0.06
0.10=o.06
2.00
MEGAN
0 10.03
00.01
0.99 0.001
0.99 00001
0.09 0.06
1.91 11.15
4.3 SYNTHETIC DATASET SINGLE EXPLANATIONS
We demonstrate the capabilities of our model first for the basic single-channel explanation (K 1) case. The experiment is conducted on the synthetic RbMotifs dataset. We primarily compare re- gression performance (MSE, r²) and similarity to know ground truth explanations (Node AUC, Edge AUC). We compare with established post-hoc baselines Grad, GradCAM (Pope et al. 2019) and GNNExplainer (Ying et al. 2219). Additionally, we compare with the explanation supervision method GNES (Gao et al.) [2021] I, which we had to modify to facilitate proper applicability
gression problems (for details refer to Appendix C) We report our results in Table ] and illustrate examples in Figure
Our results show that the explanation-supervisee single-channel version MEGAN of our network outperforms the runner-up modified GNES model by significant margin, achieving almost perfect node and edge explanation accuracy. Additionally, our model also significantly outperforms the GCN models used as the basis for the other methods in terms of target value prediction.
4.4 SYNTHETIC DATASET- MULTI EXPLANATIONS
In the second experiment, we demonstrate our model's capability when moving to multi-channe explanations (K = 2). In this case, the existing ground truth explanations were also split into two channels, where the first channel contains all those explanatory motifs that contribute negatively to graph's label and the second channel contains all those motifs that contribute positively. Our results firstly show that the regression performance of our model further increased when employ- ing an additional chamnel. Additionally, the explanation supervised version MEGAN2.5) is able to correctly learn explanations, even they are split into different channels, as indicated by the near perfect explanation accuracy. More importantly, MEGAN? 1.00 which is not explanation-supervised but uses the explanation co-procedure achieves similarly good results.
We illustrate the added value of multi-channel explanations in the example in Figure 5 that the multi-channel explanations add a highly valuable dimension to the interpretability of expla- nations: While some of the single-chan channec are able identify the explanatory motifs accurately, the singular explanations fail to capture that in reality both of the motifs represent semantically oppos- ing evidence. The multi-channel MEGAN model however is able to correctly decipher this property
We argue

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(a) Caemical Knowledge
(b) Reproduces Friederich et al (2021)
(c) New Hypotheses
Negative Channe
Positive Chaamed
Triphoglamine
Conjungated Bridge
Carbonyl Group
Silame Groupe
Phosphino Oxides
Figure Selected examples for the prediction of singlet-triplet splitting energy for molecular graphs. Darker highlights for nodes and edges indicate higher predicted importance values. (a) Explanations consistent with chemical knowledge. (b) Explanations in support of hypotheses pub- lished by FFiiederich et al. (202I). (c) New hypotheses generated by MEGAN.
of the motifs, even without external intervention in the form of explanation supervision. Moreover, during our experiments, we notice that single-channel methods often fail identify two motifs of opposing evidence in the same graph and assume that this fact is major reason for the bad performance of the baseline methods for datasets of this type.
4.5 REAL- DATASETS
Besides the synthetic dataset, we also apply our model on several real-world datasets. We report hyperparameters for these experiments and the detailed results in Appendix
The MovieReviews dataset requires the binary classification of movie review sentiment into the two classes "negative" and "positive". terms of classification, our model performs comparably base- line GNN approaches from literature, yet significantly worse than state-of-the-e NL.P approaches (Table 6). However, we find that our model still produces explanations consistent with human intu- ition, it appropriately declares negative adjectives like "bad"" "unfunny" and "disappointing" as explanations for the negative class and likewise positive adjectives like "good", "remarkable" and "clever" explanations for the positive class. We illustrate one example movie review along with our model's 's explanations in Table 2 and more in Appendix E.3
Table 2: Example for movie review sentiment classification dataset. Punctuation and capitalization were removed pre-processing. Higher node importance values are indicated by more intense color highlights.
Negative
Positive
overall avengers endgame was a remarkable movie and worthy culmination of the meu to this point there
overall avengers endgame was a remarkable movie and worthy culmination of the meu to this point there
some genuinely heartreeking moments and breathtaking action sequences but be honest movies had to through to get here were not
some genuinely heartbreainng moments and breathtaking action sequences but be honest movies had to through get here were not worth some of the early meu movies und veries leading to this finale found rather bland unfunny and sometimes just downright bud this movie while
worth some of the early meu movies und series leading to this finale found rather bland unfunny and sometimes just downright bad this movie hest movies have
hest movies
while
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The Solubility dataset requires the prediction of the logS value for water solubility of various chem- ical compounds. For this task, our model is able to achieve ofate-of-the- art regression performance (r² = 0.91, see Table 5 similar to results from the literature. We find that explanations of our model accurately reproduce chemical intuition about this task. Large non-polar carbon structures are pro- vided as explanations for negative influence, while polar oxygen and nitrogen functional groups highlighted as evidence indicative of positive influence on the target value prediction.
We also apply our model to the prediction of the singlet-triplet energy gap from the TADF dataset. Our model achieves a high predictivity of , = 0.9 on the regression task. Additionally, the explana- tions of our model are able to reproduce non- non-trivial structure- knowledge. As shown in Figure a) for example, triphenylamine bridges are known to be associated with low energy gaps, as they cause the necessary twist angles between the fragments, decoupling electron donating and electron accepting parts of a molecule to reduce the exchange interaction be- tween the frontier orbitals which would otherwise lower the triplet state compared to the singlet state, thus preventing undesired singlet-triplet splittings. We are also able to support hypotheses published in previous work by Friederich et al. (202T), who use an interpretable decision tree method to gener- ate explanatory hypotheses for the same task. Our model for example also finds conjugated bridges as positive evidence and carbonyl groups as negative evidence as shown in Figure (b). Furthermore, are able to propose novel hypotheses for explanatory motifs: As shown in Figure 4c), we for example observe silane groups and phosphine oxides to be consistently highlighted as evidence for high target values. In total, we propose 5 new motifs as shown in Appendix E.2
relationships from chemical
LIMITATIONS
Despite the encouraging experimental results, there are limitations the proposed MEGAN archi- tecture: Firstly, there is no hard guarantee that each channel's 's explanations align correctly according to their predetermined interpretations. This alignment mainly promoted through the explanation co-training, whose influence on the network is dependent on the hyperparameter y. We observed "explanation leakage" and "explanation flipping" on rare occasions even with reasonable values of y. In those rare 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. The second limitation is in the de- sign of the explanation co- co-training itself, which essentially amounts to reducing the problem to a subgraph detection/counting task. While there many important real-world applications that can be approximated as such, it still presents an important limit to the expressiveness of our model's explanations.
CONCLUSION
In this paper, we present MEGAN, the multi-explanation graph attention network architecture. Our model uses attention mechanisms to produce node and edge attributional explanations along multiple channels for graph classification and regression tasks. Our fully differentiable and self-explaining model is specifically designed to facilitate explanation supervision. On synthetic graph regres- sion dataset, we demonstrate that our explanation-supee suspeiiioo--- model significantly outperforms ex- isting baseline approaches in terms of prediction performance and explanation accuracy, achieving a near-perfect similarity to ground truth explanations. Furthermore, we emphasize the importance of moving away from single-channel and towards multi-channel explanations for regression tasks. We argue that single-channel explanations for regression tasks fail to capture the reality of oppos- ing evidence. An additional channel however allows to separate explanations that provide evidence for high target values and the opposing evidence for low target values. Using a special explana- tion co- co-training routine promote the explanation channels of our model to behave according to these pre-determined interpretations. We show that this co-training is effective in producing accu- rate explanations, which are faithful to the model prediction and outperform the single-channel case across all metrics. At last, we apply our model to several real-world datasets and demonstrate that the produced explanations are consistent with human intuition in sentiment analysis and chemical property prediction. We can furthermore show that our model's explanations reproduce non-trivial structure-pree prrpperryy relationships from chemical knowledge, supports previously published explana- tion hypotheses, and propose novel hypotheses for explanatory motifs.

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7 REPRODUCIBILITY STATEMENT
Our model is implemented using KGCNN framework (Reiser al. 2021 which implements graph neural networks in TensorFlow and Keras. The full source code is publicly available and can be found at https: / githtb....... com/ www55kst120df........ htapd///gaaapa/eeeeeeeeeg at attention. student In the source repository, we have aimed to provide some simple example scripts that illustrate a basic case of our model. Additionally, modules that contain the full information about the model hyperparameters and processing steps of the results. We also provide list of the essential hyperparameters Appendix B
have packaged each of our experiments separate code
We provide additional information on the used datasets in Appendix A For the Solubility and MovieReviews datasets, we provide references where they are publicly available. Our own syn- thetic datasets and the TADF dataset are packaged publicly available at httttss:: / com/ awa 120df/ / vvvvvaal sual__raahhh dat aset s Furthermore, we desecribe the most important pre-processing steps for the dataset, while the exact details can be found in our source code.
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A
DATASET DETAILS
A.1 RBMOTIFS
RbMotifs (red & blue motifs) is synthetic graph regression dataset. It consists 5000 randomly generated graphs with node counts between 10 and 40. Each node is associated with three node feature values in the range [0, 1], which represent RGB color values. Node colors are randomly sampled from predefined set of 7 colors. Edges
undirected and unweighted. Additionally to the random nodes, graphs may be seeded with one of four subgraph motifs, each associated with a constant value. The target value for each graph is then calculated the sum of all the motif-specific values of all motifs which are contained in the graph and a random component ó ~ (1(0.5 0.5):
y
true
Σ TT
y +
(12)
where y" is the constant value associated with the m-th motif contained the graph. The four subgraph motifs consist of specific combinations of colored nodes, where two motifs form a similar pair, whose nodes are either dominated by red or blue nodes. This means there are two possible red motifs and two blue motifs. The red motifs are associated with positive constant value, while the blue motifs are associated with negative values. Figure S illustrrte this and shows some examples of graphs from the dataset. Figure shows the distribution of color values as well as the distribution of how many motifs are contained within the graphs.
Subgraph: Motifs
[6)
Positore
Nepative
+0.03
+2.00
-2.4
Figure 5: (a) The subgraph motifs used in the RbMotifs dataset and their associated values. (b) Example graphs from the dataset annotated with their target value
2548
Number Graphs
Target Value
Number of Motafs in Graph
Figure 6: (a) Distribution of target values for the RbMotifs dataset. The limits 3 and +3 were imposed as hard limits during the generation process. (b) The distribution of the number of motifs contained within graphs. For motifs, any combination exists.
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A.2 AQSOLDB SOLUBILITY
We use the A dataset introduced by /Sorkun et al. (2019), which consists of 9982 chemi- cal compounds, annotated with measurements of water solubility (logS) at room temperature. The dataset was created by merging multiple existing datasets. We follow the instructions in (Sorkun et al. (021) and and use all of the 1290 compounds originally contained within the so-called Hu- uskonen dataser (Huuskonen) 2000) as the test set for all experiments. For the remaining elements apply the same pre-processing steps:
Remove all compounds which do not contain a carbon atom
Remove adjoined mixtures
Remove compounds that contain charged atoms
After the application of these pre-processing steps, that leaves approx. 7000 molecules in the training dataset. We process all of the SMILES strings into molecular graphs using RDKit (Landrum 2010).
A.3 MOVIEREVIEWS
MovicReviews is a real-world text classification dataset consisting of 2000 movie reviews from IMDB. Each movie review is to be classified into one of the two sentiment classes "positive" and "negative"" Within the dataset, both classes are represented equally. We take this dataset from the ERASER benchmark (De et al., 2020) and process it in similar way as it was done in Rathee al. 2022) as well.
First, the strings are converted into token lists, where tokens are individual words and other sen- tence elements such as punctuation, In this step, we remove punctuation and capitalization. The string tokens are then converted into 50-dimensional numeric feature vector by using pre-trained GLOVE (Pennington et al.] 2014) model. We convert the token lists into graphs by interpreting every token graph node and connecting each node with its neighboring nodes (according to the order of the token list/sentence order) using a sliding window of size 2. This means that every word is connected to the 2 neighboring words in both directions. Edges undirected and unweighted. For all experiments, we use the canonical train-test split as defined by Young et al. (2020).
A.4 TADF- SINGLET TRIPLET ENERGY GAP
The dataset consists of approx. 500000 molecular graphs. Annotations were created during high-throughput virtual screening experiment conducted by Gomee-Bombarelli et al. (2016) with objective to discover novel materials for an application OLED technology. Specifically, the authors aimed to discover materials that show specific characteristic of thermally activated delayed fluorescence (TADF). This class of materials a promising approach to avoid the high cost of typically used phosphorescent OLED materials (Endo al. 2011 Zhang al. 2012)-
In their work, the authors use a virtual screening approach to identify particularly promising candidates. From an initial library of almost million compounds, they use neural network to predict an estimate for the delayed fluorescent rate constant (KTAdF). Candidates with especially promising values were subjected to quantum chemical simulations to obtain more accurate values. Through this process approx. 500000 compounds were annotated with the results from quantum chemical simulations. In the end, the top results were presented to human experts which selected molecules that were experimentally assessed.
Along the delayed fluorescent rate constant property kTADE, the dataset also contains annotations for the singlet-triplet gap Ag and the oscillator strength f. which the main properties from which KTADF is calculated.
In our work, we train our network to predict the singlet-triplet energy gap A A because there al- ready exists some chemical knowledge about some structure-propers relationships regarding it. Moreover, previous work by (Friederich et al. (202T) already investigate possible explanatory motifs for this property using interpretable decision tree approach.
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B EXPERIMENT DETAILS
B.1 EXPLANATION PRE-PROCESSING
We pre-process all explanations of MEGAN and GNNExplainer by normalizing the attribution val- [0, 1] value range. This is done all explanation channels, which means that the relative differences between the explanation channels remain the same.
B.2 EVALUATION METRICS
Explanation Accuracy. For cases where definite ground truth explanations are available, we measure the accuracy of the generated explanations by computing the area under the ROC curve (AUROC), it is done in McCloskey al. (2019), for the entire validation set. The AUROC value in the range [0, 1]. where 1.0 indicates a perfect classifier and 0.5 indicates a random classifier.
Sparsity. We calculate the sparsity as the percentage of nodes/edges contained the binary ver- sion of the predicted node/edge importance vector. The binary version of these vectors calculated with threshold of 0.5.
Fidelity. For single-explanation cases, we calculate Fidelity as described in Yuan et al. (2022):
The Fidelity value is the deviation of the predicted output when the given binary explanation removed from the input of particular sample. In this case, removal means setting all the feature values of the corresponding input elements zero. The binary version of the explanation vectors calculated with simple threshold at 0.5.
Since changes in regressed value are harder put into context than for normalized classifica- tion output, which is always in the [0. 1] value range, we also provide Fidelity rnd as reference. This is the Fidelity value that results from a randomly generated explanation mask, which has the same sparsity value the original explanation mask. Consequently, regression explanations can be considered faithful their Fidelity values are significantly higher than the Fidelity rand baseline.
B.3 SYNTHETIC DATASET EXPERIMENTS
The first experiment on the RbMotif's dataset compares GNNExplainer with MEGAN models, which only use a single explanation channel (K = 1). In this experiment, the ground truth explanations are considered to consist of the union of all subgraph motifs that appear in the respective graph. The individual model and training parameters are reported Table 3
The GNNExplainer explanations are based network. The GCN network trained on the same train set as the MEGAN models. Afterward, GNNExplainer optimization is performed for each element of the test set to obtain the explanations. We note that we use slightly modified implementation of GNNExplainer contained in the KGCNN library Reiser et al. (221).
standard multi-layer GCN (Kipf & Welling 2017)
The MEGAN models used this first experiment use only one explanation channel. Since the K 1 case is not covered in Section 3.3 these models do not use any additional explanation step at all (- = 0).
The second experiment compares different MEGAN configurations for the dual-explanation K = 2. In this case, ground truth explanations are split into two channels. The first channel contains all blue (negative) motifs that appear in the graph and the second channel contains all red (positive) motifs. The individual model and training parameters are reported in Table 3
The results of 50 independent repetitions of these experiments can be found in Table
B.4 REAL-WORLD DATASET EXPERIMENTS
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 clas- sification of movie reviews. For both experiments, we only report one configuration of the MEGAN architecture. The model and training parameters can be found in Table 4 For each experiment,
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Table 3: Model and Training parameters used for the experiments with the synthetic dataset Rb- Motifs. The columns from left to right are: The model name, the learning rate, the batch size, the number of training epochs, the number of convolutional layers used for the network, the hidden units used for each of the convolutional layers, the hidden units used for the MLP layers, the sparsity coefficient and the total number of parameters of the model.
Model
LR
BS
Epochs
Depth
Conv. Units
MLP Units
Param.
GCN Baselines
0.001
64
100
3
(5, 5)
(1)
86
GCN GNES
0.001
64
100
3
(5,5,5)
(1)
MEGAN'
0.001
64
100
3
(5,5,5)
(1)
1.0 267
MEGAN2
0.01
64
100
3
(5, (5,5,5)
(1) 1.0
853
Table 4: Model and Training parameters used for the experiments with the real-world datasets. The columns from left right are: The model name, the learning rate, the batch size, the number of training epochs, the number of convolutional layers used for the network, the hidden units used for each of the convolutional layers, the hidden units used for the MLP layers, the sparsity coefficient and the total number of parameters of the model. The specified dropout percentages indicate the dropout which is applied after each layer.
Dataset
LR
BS
Epochs
Depth
Conv. Units
MLP Units
B
# Param.
Solubility
0.001
512
250
5
(50, 50, 50, 50, 50) 30% Dropout
(50, 20, 1)
1.0
150593
0% Dropout
MovieR.
0.001
50
5
(50, 50, 50, 50) 30% Dropout
(50, 20, 2)
1.0
117914
0% Dropout
TADF
0.001
1024
25
5
(50, 50, 50, 50, 50) 0% Dropout
(50, 20, 1)
1.0
150593
0% Dropout
briefly optimize the hyperparameters manually. Most importantly, find that dropout regular- ization proves increasingly useful for increasing numbers of node features and layers. The given dropout percentages applied after each layer.
The results of 50 independent repetitions of the solubility experiment can be found in Table 5 We also report the results Sorkun al. (2021) for the same test set.
Overall repetitions, our model performs consistently well in terms of predictivity (12² = 0.91), slightly worse than those achieved by the consensus model employed by Sorkun et al. (2021). However, we especially point out the high Fidelity" value for our model. On the one hand, this indicates that the explanation co-training effectively promotes the learned explanations to remain truthful to the intended interpretations of the respective channels. 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 on the concept of solubility in general.
although the results
Table 5: Results for computational experiments with solubility dataset. For our own experiments, we report the mean value for 50 independent experiment repetitions in black, as well as the standard deviation of the distribution in gray.
Source
Model
RMSE
R
Node Sparsity
Edge Sparsity
Fidelity*
Sorkun al. 2021
Consensus
0.54
0.93
ours
MEGAN
0.60
0.91
0.29
0.29 20.13
1.20
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The results of 50 independent repetitions of the MovieReviews experiment can be found in Table 6 We also report the results of De Young et al. (2020), who use BERT encoder and LSTM network, and Rathee et al. (2022). who use the same pre-processing steps to provide baseline for simple
GCN network.
Overall, De Young al. (2020) clearly show the best classification performance. 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. To our surprise, however, our results are marginally worse than those of GCN baseline model reported by Rathee et al. (2022. We hypothesize that this due to our usage of a 50-dimensional GLOVE model instead of the full 300-dimensional version
used by Rathee et al. (2022). In the future, we want to investigate different language encoder models in junction with our model.
Table 6: Results for computational experiments with solubility dataset. We report the median value for 50 independent experiment repetitions in black, as well as the 75th percentile (upper) and 25th percentile (lower) of the distribution in gray.
Source
Model
Node Sparsity
Edge Sparsity
Fidelity"
De Young al. 2020
BERT+LSTM
0.97
Rathee 2022)
GLOVE++CN
0.85
ours
MEGAN
0.84
0.02
0.02
0.76
The results of 3 independent repetitions of TADF experiment can found Table For this experiment, we conducted only 3 independent repetitions due to the drastically increased computa- tion time for the larger dataset. We are not able to provide a direct comparison from the literature because the original authors Köómez-Bombaree diction of the kTADF property. Using a neural network they achieve R² = 0.92 for the prediction of ITADE
et al. (2016) only publish their results for the pre-
In regards to our own results, we can summarize that we are able to achieve overall good predic- tivity for the main prediction task well. The network generates explanations that are sparse and faithful to the respective channel's 's intended interpretation, as it can be seen by the positive value of Fidelity". One thing of note that the Fidelity" value much lower when compared to the solu- bility experiment (see Table 5). 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 [-16, 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 have smaller absolute values.
Table 7: Results for computational experiments with TADF dataset. We report the mean value for independent experiment repetitions black, as well as standard deviation of the distribution in gray.
Source
Model
RMSE
R²
Node Sparsity
Edge Sparsity
Fidelity*
ours
MEGAN .o 0.13
0.90
0.09
2.09
0.68+0.a8
C GNES IMPLEMENTATION
In Table we compare the results of our own model with various baseline methods from the lit- erature, including the GNES framework as was proposed by Gao et al. (2021). In the GNES framework, the authors propose to use existing differentiable post-hoc explanation methods to fa- cilitate explanation supervision. For that purpose the authors propose a generalized formulation of the explanation supervision loss, which consists of term for node-level loss and one term for
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edge-level loss:
Can where M and E are the node and edge-level explanations generated by the model and M' and E' are the corresponding ground truth explanations.
M') + disis(EE,
(13)
The authors additionally introduce generalized formulations for node and edge-level explanations which can be derived from model. They define the attributional explanation for node n at layer / w.r.t. to the predicted output for class c as
Oye aF. (
_ ReLUU
((F())) ||
(14)
where F.l denotes the node's ' activation at layer 1. 9(-) and It(-) are generie functions that can be defined for specific implementations of explanation methods. Similarly, the attributional explanation for an edge between nodes n and m at layer is defined as:
dye
OF()) aAm,m
( m,
ReL.U(g(
A(F F(!))) II
(15)
OFU
where the term OFU7 functions that can be defined for specific implementations of explanation methods.
3y
aA.. represents the gradient of the edge. 9(-) and h(-) are again generic
ap
The authors show that by choosing the functions g(.) and h(-) appropriately, this formulation can be used to replicate several existing post-hoc explanation methods such simple gradient-based saliency maps (GRAD), GradCAM and Excitation Backpropagation (EB).
For our experiments, YuyangGao/ / GNES as their implementation exclusively supports binary classification problems and is limited to batch size of 1. Consequently, we re-implement GNES based on the KGCNN (Reiser et al. 2021) library to support graph regression tasks and arbitrary batch sizes. Table | we list two variations of GNES, which adapted the original formulation as previously described. We have found that this variant performs very poorly in terms of similarity to the explanation ground truth, even below the other baseline methods. For GNESiixed we modify the basic formulation by replacing the ReI.U(.) operation with the absolute value operation || and find that this variant performs significantly better, outperform- ing the other baseline approaches.
were not able to the code provided https: / com/
have call GNES and GNES For GNESn
Our experiments with Grad and GradCAM explanations on regression datasets show that in the pres- ence of opposing evidence within the graphs, the gradients of the network w.r.t. to the regression output also tend to be positive and negative. We believe that this is the main reason for the bad per- formance of the GNESaniginal variant. The ReLU operation essentially discards half of all evidence, thus leading to a particularly bad performance on the RbMotifs dataset, which was specifically en- gineered contain opposing explanatory motifs.
D GNN BENCHMARK
As already pointed out in Section the results in Table I indicate that our proposed MEGAN architecture significantly outperforms baseline methods in terms of similarity explanation ground truth as well as prediction accuracy. All baseline explanation methods used in our experiments are based on a simple 3-layer GCN (Kipf Welling 2017) architecture (see Table 3). On the RbMotifs dataset, this simple architecture achieves mean predictivity of up to r = 0.71. In contrast to that, a 3-layer dual-channel MEGAN model achieves a mean predictivity of up to r 0.90 on the same dataset.
Based on these results we compare our MEGAN architecture with several state-of-the-ar GNN ar- chitectures and find that our model is able to achieve state-of-the, theee-rrt performance many graph regression and classification tasks. For comparison, we use the standard implementation of several recently proposed model architectures from the KGCNN library (Reiser et al.) 2021). Continu- ously updated benchmarking results and hyperparameter configurations can be found at https: hargg/esultsss
//qithub. com/ simat wawplaab/oae /cnn/ keras / htt.://attttrrrreeee
We report some benchmarking results in Table 8 and Table In both cases, our model ranks second best when compared to some of the current state-of-the-art GNNs.
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Table Benchmarking results for the ESOL dataset (Delaney 2004), which consists of 1 1128 chem- ical compounds and their corresponding water solubility. We report mean absolute error (MAE) and root mean squared error (RMSE). Each cell shows the mean value of random 5-fold cross-validation in black and the standard deviation in gray. Results are sorted by performance. Additionally, we highlight the best results in bold and underline the second-boc results.
Model
Epochs
MAE
RMSE 4
GCN
800
0.59
0.81=000
Megnet
800
0.54
0.77=0.01
HamNet
400
0.55#0.02
0.76=0.02
GraphSAGE
500
0.50#0.01
0.72=0.08
MAT
400
10.03
0.72
NMPN
800
0.50 10.02
GAT
500
0.49
0.70=0.00 04
GIN
300
0..02
0.70=
CMPNN
600
0.48 +0.03
0.68=0.02
INorp
500
0.49 #0.01
0.68=0.03
GATv2
500
0.47#0.08
0.67=0.03
Schnet
800
0.46
0.65
DimeNetPP
872
0.46 10.04
0.65
DMPNN
300
0.45=0.02
0.63=0.02
AttentiveFP
200
0.46=10.01
0.63=0.03
MEGAN
400
0.44 10.03
0.60=0.05
PAiNN
250
0.43 00.02
0.60:10.02
Table 9: Benchmarking results for the Lipop dataset (Wu et al. 2018), consists of 4200 chemical compounds compounds. Graph labels for regression octanol/ water distribution coefficient (logP at pH 7.4). We report mean absolute error (MAE) and root mean squared error (RMSE). Each cell shows the mean value of random 5-fold cross validation in black and the standard deviation in gray. Results are sorted by performance. Additionally, we highlight the best results in bold and underline the second-best results.
Model
Epochs
MAE 4
RMSE 1
GAT
500
0.50=0.02
0.70
INorp
500
0.46=0.01
0.65=0.01
Schnet
800
0.48 20.00
0.65:10.00
GIN
300
0.43=20.1
0.64
HamNet
400
0.45
0.63
AttentiveFP
200
0.45
0.62.10.01
GATv2
500
0.41.1..0
0.59.0.01
PAiNN
250
0.40=0.01
0.58
CMPNN
600
0.41=0.01
0.58
MEGAN
400
0.40
0.56
DMPNN
300
0..0
0.55
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E ADDITIONAL EXAMPLES
E.1 SOLUBILITY
Training
Thining
Prodiction
6.02
Prodictinn. 2.17
Prodetion. 2.17
Prodiction:
0.91
Negative
Cheanel
Positive
Chantel
Figure 7: Examples that show that the model learns to associate carbon groups with a negative influence the solubility value and oxygen functional groups (especially OH groups) with positive influences on the solubility value.
cleeerc1D(ct toe
clee((Decct0
Traming 30
Training 30 Ground Troth: -4.88
Training 30 Ground Trath: -5 22
Trazning 30
Ground Truth 1515 Prediction:
Ground Trith: -3.11
Prediction:
Negative Channe
Positive
Channel
Figure 8: Examples which show that in the absence of any large carbon structures, the positive channel is usually not activated at all, further supporting the assumption that the model learns to associate carbon structures with low solubility. We point out that although the model provides heuristical explanation consistent with chemistry knowledge here, this still shows limitation of simple attributional explanations: Despite being explained a similar fashion, the samples shown here still vary considerably in their actual solubility value. We argue that in such cases simple attributional explanations as used here are not sufficient to accurately communicate the underlying reason for those differences in value.
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CooSone--tD 1300
Trainig 30
Training 30
Training 90
Traninng 30
Ground Thusk: -4.24
Ground Trotie -3.26
Ground Truth: -0.95
Groend Truth:
-0.06
Prediction:
-3.2
Prediction: -3.58
Prediction:
Prediction:
Negative Channel
Positive Channel
Figure 9: Examples which show that the model learns to associate nitrogen functional groups with positive influences on the solubility value as well.
(rch9:s20t--0 05VG30t--ee09 Geleee(C1))et
Training
Trinmnn
Trnining 10 Truth
Tratung
Tresh:
Prediction:
-3002
Prediction:
-187
Prediction:
Prediction:
-0.15
Negarive Channel
Positive
Channel
Figure 10: Examples that show that the quality of the explanations can be inconsistent within as well between independent repetitions model training. The first sample is taken from the 30th repetition of the solubility experiment, from which all the good examples of the previous figures have been drawn as well. incorrectly shows strong activation of the negative channel and a weak activation of the positive channel, even though there are many characteristic oxygen and nitrogen functional groups present. In this case, faulty explanation is actually reflected in the relatively large eиrоr in the model's prediction well. The other three samples were drawn from the 10th repetition, which shows worse explanations overall. Despite the relatively accurate predictions, all three samples show very indiscriminate explanations, that feature lot of similar activations in both channels.
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E.2
SINGLET TRIPLET ENERGY SPLITTING
Triming
Training Prediction:
Explanation Hypetheess
Prodiction:
0.88
Protiction
0.89
0.85
Negadoee Toffomme
Nogative Channel
Positive: Channel
Teiphenylamiiee
Figure 11: Selected examples, which illustrate the pructure-propenne explanations generated by our model. We find that triarylamine bridges are consistently highlighted in the negative explanation channel as evidence for lower target values. We find these explanations consistent with chemical knowledge: "Low singlet-triplet splittings TADF molecules are typically achieved by decoupling electron donating and accepting parts of molecule to reduce the exchange interaction between the frontier orbitals which would otherwise lower the triplet state compared to the singlet state and open undesired singlet-triplet splitting. The decoupling of the fragments be achieved by introducing twist angles close to 90 between the fragments. One way to accomplish this are trialyamine bridges between the fragments" quote Friederich et (2021
Grouad Troth: 0.38
Training
Ground Truth: Prediction:
Training
0.58 Ground Troth: Prediction:
Teiining
Explonation Hypotlisst Negatres
Nogative Chamel
Poeitive Channel
Carbouyl Geoup
Figure 12: Selected examples, which illustrate the structure- proourrrrppprtyyy explanations generated by our model. We find that carbonyl groups are consistently highlighted in the negative explanation channel as evidence for lower target values. These explanations of our model directly support the hypothesis previously published by Friederich et al. (202T), who used an interpretable decision tree approach generate their hypotheses.
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Tramznng Ground Truth:
Traming Ground Truth: 0.89 Prodiction
Training Ground Truth:
1.44
1.52
Explansiaa Hypschosts
Prodiction: 1.3
100
Prediction:
102
Posilies Infoncuce
Negative Channel
Postivve Channal
roooll
Conjungated Bridgga
Figure 13: Selected examples, which illustrate the pnuuctuur--rrppery explanations generated by our model. We find that conjugated bridges are consistently highlighted the positive explanation channel as evidence for higher target values. These explanations of our model directly support the hypothesis previously published by Friederich et al. (202I), who used an interpretable decision tree approach to generate their hypotheses.
Toxmingg
Training Ground Truth: 1.00
Trwining Ground Thuthh
Ground Truth:
0.58
0.57
Explanation Hypethusis
Productio:: 0.8
Prediction: 077
Prediction: 0.48
Posities Infrennce
Negative Channe]
Positive Channel
Thiophene Rings
Figure 14: Selected examples, which illustrate the structure- proopery-property explanations generated by our model. We find that thiophene and thiazole rings are consistently highlighted in the positive explanation channel as evidence for higher target values. These explanations of our model directly support the hypothesis previously published by Friederich et al. (2021), who used an interpretable decision tree approach to generate their hypotheses.
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Training Prodiction.
Explonaiioe Hypelhsni Pevilins Infrocnce
Prodictions
0.1
Prediction:
0.97
0.58
Negative Channel
Positive: Channel
Silano Gooupe
Figure 15: Selected examples, which illustrate the structure-property explanations generated by our model. We find that silane groups are consistently highlighted in the positive explanation channel as evidence for higher target values. We propose this as a new hypothesis for a possible structure- property relationship.
Explanation Hypethusia
Production: 0.9
Prediction:
1.04
Prodiction:
1.29
Positiee Infracnce
Negative Channel
Position: Channel
Phosphine Orldes
Figure 16: Selected examples, which illustrate the strueture structure-propers proveettrortttyyyyy explanations generated by model. We find that phosphine oxides are consistently highlighted in the positive explanation channel as evidence for higher target values. We propose this as new hypothesis for a possible structure-property relationship.
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Explansiion Hypothess
Prodiction.
0.94
Prodiction
0.63
Prodiction.
0.17
Weyndine Iullumee
Negative Channel
N
Positive: Channel
Figure 17: Selected examples, which illustrate the proopetr-propprty explanations generated by our model. We find that eyano groups consistently highlighted in the negative explanation channel as evidence for lower target values. We propose this as new hypothesis for a possible structure- property relationship.
Tesining
Explanation Hypethusta
Production: 0.94
Prediction:
0.83
Prodiction:
1.01
Positiee Infrocuce
Negative Channel
Boods
Positivn: Channel
Dennotsiaboll
Figure 18: Selected examples, which illustrate the structure- structure-property explanations generated by our model. We find that benzotriazole derivatives consistently highlighted in the positive explanation channel as evidence for higher target values. We propose this as new hypothesis for a possible structure-property relationship.
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Explanation Hypeshista Pevélins Infracnce
Prodiction: 0.97
Prediction: 0.47
Prodiction:
0.88
Negative Channel
Positive: Channel
Tilaaole Bridges
Figure 19: Selected examples, which illustrate the structure structure-property explanations generated by our model. We find that triazole bridges consistently highlighted in the positive explanation channel as evidence for higher target values. We propose this as a new hypothesis for a possible structure- property relationship.
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E.3 MOVIE REVIEWS
Example for movie review which contains positive and negative sentences, which are conrectly sorted into the respective channels. However, this example also shows some sort of bias by including the first sentence as a negative explanation. Objectively the first sentence does not contain any sentiment. The false explanation of the model is supposedly caused by the word "criminals" which is presumably often used in junction with negative adjectives.
Table 10:
Negative
Positive
couple of criminals mario van peebles loretta conning them out of their jewels however someone else steuls the jewels before they able get them writer mario van peehles delivers clever script with several unexpected plot twists but director mario van peebles undermines his own high points with haphazurd camera work editing and pacing it felt as though the
couple of criminals mario van peebles loretta devine move into rich fumily house in hopes of
devine move into rich family house in hopes of conning them out of their jewels however someone else steals the jewels before they able get them peebles delivers clever script with several unexpected plot twists but director mario van peebles undermines his own high points with haphazurd camera work editing and pacing felt as though the film should have been wrapping up the hour mark alas there was still more minutes to go daniel baldwin ca n't believe "m about to type this gives the best performance in the film outshining the other talented members of the cast
writer
film should have been wrapping up the hour mark
alas was still more minutes to go daniel baldwin ca n't believe "m about to type this gives the best performance in the film outshining the other talented members of the cast
Table 11: Example for an exclusively positive review. Due to the overall lack of negative adjectives, the negative channel isn't 't activated all.
Negative
Positive
this three hour movie opens up with view of singer guitur player musician composer frank zappa rehearsing with his compilation of footage mostly from the concert at the palladium in new york city halloween 1979 other footage shows backstage foolishness and amazing clay
this three hour movie opens up with view of singer guitar player musician composer frunk zappa rehearsing with
members
rest displays
rest displays compilation of footuge 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 titties
members
animation by bruce biekford the performance titties and beer played in this movie is very entertaining with beer played in this movie is very entertaining with
drummer terry bozzio supplying the voice of the devil frank guitar solos outdo any vun halen or hendrix "ve ever heard bruce bickford outlandish clay animation is that beyond belief with zooms morphings etc
drummer terry bozzio supplying the voice of the devil frank guitar solos outdo any balen or hendrix 've heard bruce bickford outlandish clay animation is that beyond belief' with zooms morphings etc actually does n't even look like clay looks like meat
actually does n't even look like clay it looks like
meat
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Table 12: Example which shows that the model currently doesn't It understand negations and sarcasm. We point out that the partial sentence "never a bad thing" in the middle of the review sorted into the negative channel. Another example is the first sentence: The praise it features is meant sarcastically, but it is still sorted into the positive channel.
Negative
Positive
burnt money is perfect festival film 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 eusily of the year worst billed us 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 send his boys out to get the gay guys one whom may not actually be gay hiding out in prostitute upartment the two men must fight off' police and gang memhers in very long showdown for the movie conclusion if caught they risk losing the money 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 it was little hard to pick up not much could have really huppened though the main events 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 reason but there no purpose to anything this film most of the sex and violence scenes come off as silly while the heavy drug use comes off ridiculous and depressing appears pi eyro who from novel by ricando 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 bumnt money pointless the performances are bad tries to thrill and shock but only causes boxedom god forbid it will ever get a distributor another disappointing film from this year so called emerging masters series on by
burnt money is the perfect festival film 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 easily of the year worst billed as gay bonnie
and clyde this grity film from director marcelo pi eyro has its only highlight in a well designed title sequence two lovers get involved in a bank robbery that makes gang leader whose plan they screwed angry this causes gang leader send his boys out to get
the gay guys one whom may not actually be gay hiding out in prostitute upartment the two men must fight off' police and gang members in very long showdown for the movie conclusion if caught they risk losing all the money 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 movic striving virtue so it was little hard to pick up not much could have really huppened though the main events 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 ridiculous and depressing appears pi eyro who wrote with marcelo figuerus from novel by ricardo piglia purposefully adds more blood and lovemaking for his own amusement he makes
with murcelo figueras
the actors as sweaty and ditty as possible makes them
snort cocaine gives them guns and condoms and lets them go burnt money pointless the performances bad 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
29


Reviews:
[{"review_id": "y9wPPradZxJ", "reviewer": "Reviewer_Bi9b", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "\nThis paper introduces  a multi-explanation graph attention network architecture by useing attention mechanisms to produce node and edge attribution explanations along multiple channels for graph classification and regression tasks. Experiments demonstrate the effectiveness of the proposed model. \n", "summary_of_the_review": "Strength:\n1. The research problem is very important and this paper provides different aspects to provide explanations in GNNs. \n2. This paper is easy to follow and clearly written.  \n\n\nWeaknesses\n\nThere are some concerns regarding this paper.\n\n\n1. The novelty of this paper is limited. The proposed framework of multi-explanation graph attention network is straightforward by using attention mechanisms to produce node and edge attribution explanations along multiple channels for graph classification and regression tasks. \nIt would be better if they detail more their novelty. Also, it's unclear the contributions of this work.\n\n2. This work misses some advanced related works and baselines in their experiments. This work mainly compared with GNNExplainers, and this work can be more solid if they can compare some advanced GNN explanations methods.\n\n\n3. Evaluation in GNNs explanations are not convincing enough.  Maybe more real-world datasets and evaluation metrics can enhance the effectiveness of the proposed method. \n", "strength_and_weaknesses": "Strength:\n1. The research problem is very important and this paper provides different aspects to provide explanations in GNNs. \n2. This paper is easy to follow and clearly written.  \n\n\nWeaknesses\n\nThere are some concerns regarding this paper.\n\n\n1. The novelty of this paper is limited. The proposed framework of multi-explanation graph attention network is straightforward by using attention mechanisms to produce node and edge attribution explanations along multiple channels for graph classification and regression tasks. \nIt would be better if they detail more their novelty. Also, it's unclear the contributions of this work.\n\n2. This work misses some advanced related works and baselines in their experiments. This work mainly compared with GNNExplainers, and this work can be more solid if they can compare some advanced GNN explanations methods.\n\n\n3. Evaluation in GNNs explanations are not convincing enough.  Maybe more real-world datasets and evaluation metrics can enhance the effectiveness of the proposed method. \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "kn6vXeQNYAa", "reviewer": "Reviewer_8m6Y", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes the multi-explanation graph attention network (MEGAN), which is an attention-based self-explaining model for graph regression and classification. MEGAN features multiple explanation channels independent of the task specifications. The edge explanations are given as the edge importance tensor, which is calculated from the concatenation of attention logit tensors. The node importance tensor, which represents node explanations, is then given as the product of node importance embeddings and the pooled edge importance tensor. The paper first evaluates MEGAN on a synthetic graph regression dataset, and further demonstrates the advantages of multi-channel explanations on two real-world datasets: the prediction of water solubility of molecular graphs and sentiment classification of movie reviews. The authors claim that MEGAN produces explanations consistent with human intuition.", "summary_of_the_review": "The framework of MEGAN is well illustrated in this paper, but in the experiments the baseline is too weak and not appropriate.  It is not fair to compare a post-hoc method (GNNExplainer) with a self-explaining method (MEGAN). ", "strength_and_weaknesses": "- Strength\n    - The paper proposes an attention-based self-explaining model for graph regression and classification, which features multiple explanation channels independent of the task specifications. \n    - The paper is well organized in illustrating the overall framework and the process of how to generate multi-channel explanations. It is easy to follow the technical details.\n- Weaknesses\n    - The only baseline in the experiments is GNNExplainer, which was published 3 years ago, and there are quite a few new models offering better performance on explaining graph-based prediction tasks. More importantly, GNNExplainer is a post-hoc method for explaining blackbox GNN models, but MEGAN is a self-explaining models including both prediction and explanation modules. The baseline is too weak, and it is not fair to compare a post-hoc method with a self-explaining method. The paper should compare MEGAN with some more appropriate baselines, which are also self-explaining methods, such as (Gao, et al., 2021), (Zhang, et al., 2022) and (Magister et al., 2022).\n        - (Gao, et al., 2021) GNES: Learning to Explain Graph Neural Networks\n        - (Zhang, et al., 2022) ProtGNN: Towards Self-Explaining Graph Neural Networks\n        - (Magister et al., 2022) Encoding Concepts in Graph Neural Networks\n    - For evaluating the interpretability of MEGAN, quantitative analysis is only conducted on the synthetic data set. More experiments should be done on real-world datasets as well. \n    - BAShapes and TreeCycles are synthetic datasets most widely used as benchmark of GNN explanation tasks. However, this paper only uses the RbMotifs dataset created by the authors themselves in the experiments. For fairness of experiments, the authors need to give an explanation for this issue as well.\n- Question\n    - For the explanation co-training, the reference value y_c seems to be unspecified. How do we define this value in training as it seems to affect the model's effectiveness.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "ONtfH-G77bh", "reviewer": "Reviewer_EFXj", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper introduces a new explainable graph attention network model. The highlight of this model is its multi-channel explanability. Along with outputing node predictions, the model also generates extra edges and nodes importance scores across preset channels. To along these importance scores with multi-explanation channels, the authors introduce a new way of training the model, named explanation co-training. It adds an explanation step, where the model will be penalized when the importance scores are not aligned with the ground truth label. The authors evaludated their model in one synthetic dataset and two real-world datasets and showed the proposed model gets great empirical results as well as reasonable explanations.", "summary_of_the_review": "I think this paper is well organized and the idea will be beneficial to other researchers in this field.\n\n\n\n---- update after seeing other reviewers' comments and authors' response\nOverall I still think this is a good paper. Other reviewers called out that comparisons with many other GNN explanable models are missing and the experimental sections could've been more thorough. I think their points made sense, so I'm lowering my score to marginal accept for now.", "strength_and_weaknesses": "Strength:\n1. The paper is well written and well organized. The motivation of multi-explanation is explained clearly. It's not hard to follow how the authors designes the model to have multiple explanability channel in the methodology part. \n2. The idea of multi-explanation is novel and fits the graph idea well. The authors did a great job on analyzing potential issues of multi-channel  explanations and proposing a novel solution (co-training) to address some of the issues. In section 5, the authors thoroughly discussed the limitations of the proposed model.\n3. The expermental results look promising. The authors showed that the explanations generated by the propose model were reasonable and aligned with the ground truth. It also outperforms the baseline model on many aspects.\n4. The authors released their codes anonymously and included detailed comments and docs about codes itself and how to re-run the experiments.\n\nQuestions:\n1. If you train the model twice with same datasets but different random seeds, do the same explanation channels (by index) in each run align with each other? I think this is an important aspect to discuss when you have multiple explanation channels. If it's stable, the same channel (by index) should refer to the same underlying latent space. If it's not stable, is there a way we can make it stable, or we can somehow find a mapping between new channels and old channels? For example, someone uses this model and spends quite a lot of resources to figure out what each explanation channel roughly means, then they get some new graphs data and need to re-train the model, how can they make use of the understandings of old explanation channels? Would like to see some discussions on this.\n2. In the movie review datasets, the authors mentioned \"our model’s accuracy is consistent with that achieved by other GNNS\nas reported by ...\". It would be nice to include the metrics somewhere. Maybe I missed it, but I couldn't find them in the main body or the appendix.\n3. Would it be possible to run MEGAN over non graph datasets? Namely just graphs with zero edges. Just curious how MEGAN would perform comparing with those non-graph based explanability models.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "GUA7wr1pjwu", "reviewer": "Reviewer_NxCN", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This work proposes MEGAN, a multi-explanation graph attention network model that leverages attention mechanism to produce node and edge attribute explanations along multiple channels for graph classification and prediction tasks. The proposed approach is explanation co-training: along with the prediction task, and explanation task is trained where, based on node importances, an importance value is generated per channel. Channels are defined based on the task: for regression, the explanation task is whether the the importance value is greater than y_channel, or less than y_channel, whereas for classification, the number of channels is the number of possible output classes C. \n\nThe models are compared with GNNExplainer model over datasets RbMotifs, Solubility and MovieReviews datasets. The metric used is Area under ROC curve (AUROC), which measures similarity to ground truth explanations. Another metric used is fidelity metric, which looks at faithfulness to predicted output. Experiments are also run on synthetic datasets. MEGAN reports better R^2, node and EDGE AUC and Fidelity metrics and lower MSE.", "summary_of_the_review": "While the problem is well motivated and the paper is well written, with experiments on several real and synthetic datasets, the notion of channels for explanations seems rather limited and needs to be better described. The performance improvements over metrics for explanations needs statistical significance to be reported. ", "strength_and_weaknesses": "Strengths:\nThe paper is well written and the problem is well motivated. \nThe proposed architecture is outlined is good detail. \nExperiments are run on real world and synthetic datasets.\n\nWeaknesses:\nThe notions of channels for explanations and how explanations are defined needs to be described in greater detail.\nExperiments report performance at various percentiles of metrics, but statistical significance is missing.\nProposed approach is compared only with a single baseline approach, need more approaches to be covered in prior work and compared with. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject