# ganmex_onevsone_attributions_using_ganbased_model_explainability__f399d404.pdf

GANMEX: One-vs-One Attributions using GAN-based Model Explainability

Sheng-Min Shih * 1 Pin-Ju Tien * Zohar Karnin 1

Abstract Attribution methods have been shown as promising approaches for identifying key features that led to learned model predictions. While most existing attribution methods rely on a baseline input for performing feature perturbations, limited research has been conducted to address the baseline selection issues. Poor choices of baselines limit the ability of one-vs-one explanations for multi-class classifiers, which means the attribution methods were not able to explain why an input belongs to its original class but not the other specified target class. Achieving one-vsone explanation is crucial when certain classes are more similar than others, e.g. two bird types among multiple animals, by focusing on key differentiating features rather than shared features across classes. In this paper, we present GANMEX, a novel approach applying Generative Adversarial Networks (GAN) by incorporating the to-be-explained classifier as part of the adversarial networks. Our approach effectively selects the baseline as the closest realistic sample belonging to the target class, which allows attribution methods to provide true one-vs-one explanations. We showed that GANMEX baselines improved the saliency maps and led to stronger performance on multiple evaluation metrics over the existing baselines. Existing attribution results are known for being insensitive to model randomization, and we demonstrated that GANMEX baselines led to better outcome under the cascading randomization of the model.

1. Introduction

Modern Deep Neural Network (DNN) designs have been advancing the state-of-the-art performance of numerous

*Equal contribution 1Amazon. Correspondence to: Sheng-Min Shih <shengminshih@gmail.com>, Pin-Ju Tien <pinju.tien@gmail.com>, Zohar Karnin <zkarnin@gmail.com>.

Proceedings of the 38 th International Conference on Machine Learning, PMLR 139, 2021. Copyright 2021 by the author(s).

machine learning tasks with the help of increasing model complexities, which at the same time reduces model transparency. The need for explainable decision is crucial for earning trust of decision makers, required for regulatory purposes (Goodman & Flaxman, 2017), and extremely useful for development and maintainability.

Due to this, various attribution methods were developed to explain the DNNs decisions by attributing an importance weight to each input feature. In high level, most attribution methods, such as integrated gradient (IG) (Sundararajan et al., 2017), Deep SHAP (Lundberg & Lee, 2017), Deep Lift (Shrikumar et al., 2017) and Occlusion (Zeiler & Fergus, 2013), alter the features between the original values and the values of some baseline instance, and accordingly highlight the features that impacts the model s decision. While extensive research has been conducted on the attribution algorithms, research regarding the selection of baselines is rather limited, and it is typically treated as an afterthought. Most existing methodologies by default apply a uniformvalue baseline, which can dramatically impact the validity of the feature attributions (Sturmfels et al., 2020), and as a result, existing attribution methods showed rather unperturbed output even after complete randomization of the DNN (Adebayo et al., 2018).

In a multi-class classification setting, existing baseline choices do not allow specifying a target class, and this has limited the ability for providing a class-targeted or one-vsone explanation, meaning explaining why the input belongs to class A and not a specific class B. These explanations are crucial when certain classes are more similar than others, as often happens for example when the classes have a hierarchy among them. For example, in a classification task of apples, oranges and bananas, a model decision for apples vs oranges should be based on their color rather than the shape since both an apple and orange are round. This would intuitively only happen when asking for an explanation of why apple and not orange rather than why apple .

In this paper, we present GAN-based Model EXplainability (GANMEX), a novel methodology for generating onevs-one explanations leveraging GANs. In a nutshell, we use GANs to produce a baseline image which is a realistic instance from a target class that resembles the original instance. A naive use of GANs can be problematic because

GANMEX: One-vs-One Attributions using GAN-based Model Explainability

the explanation generated would not be specific to the to-beexplained DNN. We lay out a well-tuned recipe that avoids these problems by incorporating the classifier as a static part of the adversarial networks and adding a similarity loss function for guiding the generator. We showed in the ablation study that both swapping in the DNN and adding the similarity loss are critical for resulting the correct explanations. To the best of our knowledge, GANMEX is the first to apply GAN for addressing the baseline selection problem, and furthermore the first to provide a realistic baseline image, rather than an ad-hoc null instance.

We showed that GANMEX baselines can be used with a variety of attribution methods, including IG, Deep LIFT, Deep SHAP and Occlusion, to produce one-vs-one attribution superior compared with existing approaches. GANMEX outperformed the existing baseline choices on multiple evaluation metrics and showed more desirable behavior under the sanity checks of randomizing DNNs. We also demonstrated that one-vs-one attribution with the help of GANMEX provides meaningful insights into why samples are mis-classified by the trained model. Other than GANMEX s obvious advantage for one-vs-one explanations, we show that by replacing only the baselines and without changing the attribution algorithms, GANMEX greatly improves the saliency maps for binary classifiers, where one-vs-one and one-vs-all are equivalent.

2. Related Works

2.1. Attribution Methods and Saliency Maps

Attribution methods and their visual form, saliency maps, have been commonly used for explaining DNNs. Given an input x = [x1, ..., x N] RN and model output S(x) = [S1(x), ..., SC(x)] RC, an attribution method for output i assign contribution to each pixel AS,c = [a1, ..., a N]. There are two major attribution method families: Local attribution methods that are based on infinitesimal feature perturbations, such as gradient saliency (Simonyan et al., 2014) and gradient*input (Shrikumar et al., 2016), and global attribution methods that are based on feature perturbation with respect to a baseline input (Ancona et al., 2018). We focus on global attribution methods since they tackle the gradient discontinuity issue in local attribution methods, and they are known to be more effective on explaining the marginal effect of a feature s existence (Ancona et al., 2018). We will also focus on only the visual forms of attributions and will use attributions and saliency maps interchangeably throughout the paper. In this paper, we discussed five popular global attribution methods below:

Integrated Gradient (IG) (Sundararajan et al., 2017) calculates a path integral of the model gradient from a baseline image x to the input image x: IGi = (xi

xi) R 1 α=0 xi S( x + α(x x))dα. The baseline is commonly chosen to be the zero input and the integration path is selected as the straight path between the baseline and the input.

Deep LIFT (Shrikumar et al., 2017) addressed the discontinuity issue by performing backpropagation and assigns a score C xi t to each neuron in the networks based on the input difference to the baseline xi = xi xi and the difference in the activation to that of the baseline t = t(x) t( x), that satisfies the summation-to-delta property P

i C xi t = t.

Occlusion (Zeiler & Fergus, 2013; Ancona et al., 2018) applies full-feature perturbations by removing each feature and calculating the impacts on the DNN output. The feature removal was performed by replacing its value with zero, meaning an all zero input was implicitly used as the baseline.

Deep SHAP (Chen et al., 2019; Lundberg & Lee, 2017; Shrikumar et al., 2017) was built upon the framework of Deep LIFT but connecting the multipliers of attribution rule (rescale rule) to SHAP values, which are computed by erasing features . The operation of erasing one or more features require the notion of a background, which is defined by either a distribution (e.g. uniform distribution over the training set) or single baseline instance. For practical reasons, it is common to choose a single baseline instance to avoid having to store the entire training set in memory.

Expected Gradient (EG) (Erion et al., 2019) is a variant of IG that calculates the expected attribution over a prior distribution of baseline input, usually approximated by the training set XT , meaning EGi = E x XT α U(0,1)(x x)i xi S( x+α(x x)) where U is the uniform distribution. In other words, the baseline of IG is replaced with a uniform distribution over the samples in the training set.

A crucial property of the above methods is their need for a baseline, which is either explicitly or implicitly defined. In what follows we show that these methods are greatly improved by modifying their baseline to that chosen by GANMEX.

2.2. The Baseline Selection Problem

Limited research has been done on the problem of baseline selection so far. A simple most natural input , such as zero values of all numerical features is commonly chosen as the baseline. For image inputs, uniform images with all pixels set to the max/min/medium values are commonly chosen. The static baselines frequently cause the attribution to only focus on or even overly highlight the area where the feature values are different from the baseline values, and hide the feature importance where the input values are close to the baseline values (Sundararajan & Taly, 2018; Adebayo et al., 2018; Kindermans et al., 2017; Sturmfels et al., 2020).

GANMEX: One-vs-One Attributions using GAN-based Model Explainability

Several none-static baselines have been proposed in the past, but each of them suffered from its own downsides (Sturmfels et al., 2020). Fong & Vedaldi (2017) used blurred images as baselines, but the results are biased toward highlighting highfrequency information from the input. Bach et al. (2015) make use of the training samples by finding the training example belonging to the target class closest to the input in Euclidean distance. Even though the concept of minimum distance is highly desirable, but in practice, the nearest neighbor selection in high dimensional space can frequently lead to poor outcome, and most of the nearest neighbors are rather distant from the original input.

Along the same concept, EG simply samples over all training instances instead of identifying the closest instance (Erion et al., 2019). EG benefits from ensembling in a way similar to that of Smooth Grad, which averages over multiple saliency maps produced by imposing Gaussian noise on the original image (Smilkov et al., 2017; Hooker et al., 2019). We claim however that averaging over the training set does not solve the issue; for example, due to the foreground being located in different sections of the images, the average image would often resemble a uniform baseline.

2.3. One-vs-One and One-vs-All Attribution

In multi-class settings, while one-vs-all explanation AS,co(x) was designed to explain why the input x belong to its original class co and not the others, one-vs-one explanations aim to provide an attribution AS,co ct(x) RN

that explains why x belong to co and not the specified target class ct. Most existing attribution methods were primarily designed for one-vs-all explanation, but was proposed to extend to one-vs-one by simply calculating the attribution with respect to the difference of the original class probability to the target class probability Sdiff(x) = Sco(x) Sct(x) (Bach et al., 2015; Shrikumar et al., 2017).

It is easy to think of examples where this somewhat naive formulation will not provide correct one-vs-one explanation. Taking the example of fruit classification, for both apples and oranges the explanation could easily be the round shape, and taking the difference between those will result in an arbitrary attribution. We claim that without a class-targeted baseline, the modified attributions will still omit the vsone aspect of the one-vs-one explanation. Take IG for example, AS,diff(x) = AS,co(x) AS,ct(x). With zero baseline, the target class score Sct(x) and its gradient will likely stay close to zero along the straight path from the input to the zero baseline, meaning that AS,ct(x) 0 because the instance never belongs to the target class. With this in mind the one-vs-one explanation is not very informative with respect to the target class ct.

Few class-targeted baselines were proposed in the past. The minimum distance training sample (MDTS) described in

Section 2.2 is class-targeted as the sample was selected from the designated target class. While the original EG was defined for one-vs-all explanation only, we extended the method to one-vs-one by sampling the baselines only from the target class. However, as mentioned in Section 2.2, MDTS is frequently hindered by the sparsity of the training set in the high dimensional space, and EG suffers from undesired effects caused by uncorrelated training samples. The problem of baseline selection, especially for the onevs-one explainability, has presented a challenging problem, because the ideal baseline choice can simply be absent from the training set.

2.4. GAN and Image-to-Image Translation

Image-to-Image Translation is a family of GAN originally introduced by Isola et al. (2017) for creating mappings between two domains of data. While the corresponding pairs of images are rare in most real-world dataset, Zhu et al. (2017) has made the idea widely applicable by introducing a reconstruction loss to tackle the tasks with unpaired training dataset. Since then, more efficient and better performing approaches have been developed to improve few-shot performance (Liu et al., 2019) and output diversity (Choi et al., 2020). Nevertheless, we found the Star GAN variant proposed by Choi et al. (2017) specifically applicable to the baseline selection problem because of its standalone class discriminator in the adversarial networks as well as the deterministic mapping that preserve the styles of the translated images (Choi et al., 2020). Since we require the closest yet realistic example, the lack of randomness in the output would not impact the performance of our method. GANs have not been applied for explaining DNNs in the best to our best knowledge.

Prior to our work, Chang et al. (2018) proposed the fill-in the dropout region (FIDO) methods and suggested generators including CA-GAN (Yu et al., 2018) for filling in the masked area. However, the CA-GAN generation was designed for calculating the smallest sufficient region and smallest destroying region (Dabkowski & Gal, 2017) that only produced 1-vs-all explanations. FIDO is computationally expensive as an optimization task is required for each attribution map. The fill-in method requires an unmasked area for reference, hence only works for a small subset of attribution methods. More importantly, the FIDO is highly dependent on the generator s capability of recreating the image based on partially masked features. With pre-trained generators like CA-GAN, we argue that the resulting saliency map is more associated with the pre-trained generator instead of the classifier itself.

GANMEX: One-vs-One Attributions using GAN-based Model Explainability

Figure 1. Intuition of using GANs for generating class-targeted baselines in SVHN dataset. Without GANs, a closest target class sample can easily be unrealistic (a), while the GAN helps confine the sample in the realistic sample space (b). The MDTS baseline and other training samples used in EG can be very different from the input (c). (d) shows the zero baseline that is the most commonly used option.

3. GAN-based Model Explainability

It has been previously established that attribution methods are more sensitive to features where the input values are the same as the baseline values and less sensitive to those where the input values and the baseline values are different (Adebayo et al., 2018; Sundararajan & Taly, 2018). Therefore, we expect a well-chosen baseline to differ from the input only on the key features. Good candidates for achieving this would be the sample in the target class but with minimum distance to the input.

Formally, for a one-vs-one attribution problem AS,co ct(x), We define the class-targeted baseline to be the closest point in the input space (not limited to the train set) that belongs to the target class

Bct(x) = arg min x Gct x x (1)

Here, Gct is the set of realistic examples in the target class, and is the Euclidean distance. By using this baseline we have AS,co ct(x, Bct(x)) providing the explanations as to why input x belongs to its original class co and not class ct. Now, since it isn t realistic to optimize within the actual set Gct we work with a softer version of Equation 1: Bct(x) = arg min x RN ( x x log T( x, ct)). where T( x, ct) represent the probability of x belonging to the target class, meaning x Gct. Given a classifier S(x) = [S1(x), ..., SC(x)], we have the estimate Sc( x) to the probability of a realistic image x to be in class c. In order to make use of this we decompose T( x, ct) = R( x)Sct( x) where R( x) indicates the probability of x being a realistic image. We end up with the following objective for the baseline instance.

Bct(x) = arg min x RN( x x log R( x) log Sct( x)) (2)

3.1. Applying Star GAN to the Class-Targeted Baseline

Here we introduce GAN-based Model EXplainability (GANMEX) that uses GAN to generate the class-targeted baselines. Given an input x and a target class ct, GANMEX aims to generate a class-targeted baseline G(x, ct) that achieve the three following objectives:

1. The baseline belongs to the target class (with respect to the classifier).

2. The baseline is a realistic sample.

3. The baseline is close to the input.

To further explain the need for all 3 objectives, we point the reader to Figure 1. The GANMEX baseline represents the closest and realistic target class baseline . Without the assistance of GANs, the selected baseline can easily either fall into the domain of unrealistic image. A naive fix will choose a realistic image from the training set, but that will not be close to the input. Finally, for correct one-vs-one explainability we need the baseline to belong to a specific target class. We have provided more intuitions behind the baseline selection requirements in Appendix F.

We chose Star GAN (Choi et al., 2017) as the method for computing the above T or rather R function. Although many Image-to-Image translation methods could be applied to do so, Star GAN inherently works with multi-class problems, and allows for a natural way of using the already trained classifier S as a discriminator, rather than having us train a different discriminator.

Star GAN provides a scalable image-to-image translation approach by introducing (1) a single generator G(x, c) accepting an instance x and a class c, and producing a realistic example x in the target class c, (2) two separate discriminators: Dsrc(x) for distinguishing between real and fake

GANMEX: One-vs-One Attributions using GAN-based Model Explainability

images, and Dcls(x, c) for distinguishing whether x belongs to class c. It introduced following loss functions

Ladv = Ex[log(Dsrc(x))]

+Ex,c[log(1 Dsrc(G(x, c)))] (3)

Lr cls = Ec ,x c [ log(Dcls(c |x))] (4)

Lf cls = Ex,c[ log(Dcls(c|G(x, c)))] (5)

Lrec = Ec,c ,x c [ x G(G(x, c), c ) 1] (6)

Here, E [] defines the average over the variables in the subscript, where x is an example in the training set, and c, c

are classes. Ladv is the standard adversarial loss function between the generator and the discriminators, Lr cls and Lf cls are domain classification loss functions for real images and fake images, respectively, and Lrec is the reconstruction loss commonly used for unpaired image-to-image translation to make sure two opposite generation action will lead to the original input. The combined loss functions for the generator and the discriminator are

LD = Ladv + λr cls Lr cls (7)

LG = Ladv + λf cls Lf cls + λrec Lrec (8)

The optimization procedure for Star GAN alternates between modifying the discriminators Dsrc(x), Dcls(x, c) to minimize LD, and the generator G to minimize LG.

Equation 8 is almost analogical to Equation 2. The term Ladv corresponds to log R( x) and the term λf cls Lf cls corresponds to the term log Sct( x). There is a mismatch between the term λrec Lrec and x x . One forces the generator to be invertible, while the other forces the generated image to be close to the original. We found that the Lrec term is useful to encourage the convergence of the GAN. However, a similarity term x G(x, c) is also needed in order for the baseline image to be close to the origin - this allows for better explainability. We show in what follows (Figure 5.B, Section 5) that without this similarty term, the created image can indeed be farther away from the origin. Other than the added similarity term, for GANMEX we replace the discriminator Dcls(c| x) with the classifier Sc( x), since as mentioned above, this way the generator provides a baseline adapted to our classifier. Concluding, we optimize the following term for the generator

Lf G = λf src log(1 Dsrc( x)) λf cls log(Sc( x))

+λrec x G( x, c ) 1 + λsim x x 1 (9)

where x is short for G(x, c). Notice that we used L1 distance rather than L2 for the similarity loss, because L2 distance leads to blurring outputs for image-to-image translation algorithms (Isola et al., 2017)). Other image-to-image translation approaches can potentially select baselines satisfying the criteria (2) and (3) above, but they lack the replaceable

class discriminator component, that is crucial for explaining the already trained classifier. We provide several ablation studies in Section 5 where we show that without incorporating the to-be-explained classifier to the adversarial networks, the GAN generated baselines will fail the randomization sanity checks. We provide more implementation details including hyper-parameters in Appendix A.2.

4. Experiments

In what follows we experiment with the datasets MNIST (Le Cun & Cortes, 2010), Street-View House Numbers (SVHN) (Netzer et al., 2011), CIFAR10 (Krizhevsky, 2009), apple2orange (Zhu et al., 2017), and BAM (Yang & Kim, 2019). Further details about the datasets and classifiers are given in Appendix A.1.

Our techniques are designed to improve any global attribution method by providing an improved baseline. In our experiments we consider four attribution methods - IG, Deep LIFT, Occlusion, and Deep SHAP. The baselines we consider include the zero baseline (the default baseline in all four methods), minimum distance training sample (MDTS), and the GANMEX baseline. We also compared our results with a modified version of EG aimed to provide 1-vs-1 explanations, which runs IG over a randomly chosen target class image from the training set, as opposed to any random image from the whole training set.

4.1. One-vs-one attribution for Multi-class Classifiers

We tested the one-vs-one attribution on three multi-class datasets - MNIST, SVHN, and CIFAR10. As shown in Figure 2.A, the GANMEX baseline successfully identified the closest transformed image in the target class as the baseline. Take explaining why 0 and not 6 for example, the ideal baseline would keep the C -shape part unchanged, and only erase the top-right corner and complete the lower circle, which was achieved by GANMEX. Limited by the training space, MDTS baselines were generally more different from the input image. Therefore, the explanation made with respect to GANMEX baselines were more focused on the key features compared to that of the MDTS baseline and EG. We observed the same trends across more numbers, where GANMEX helps IG, Deep LIFT, Occlusion and Deep SHAP disregard the common strokes between the original and targeted digits, and focusing only on the key differences. The out-performance of GANMEX was even more apparent on the SVHN datasets, where the numbers can have any font, color, and background, which presents more complexity and diversity. Notice that both MDTS baseline and EG cause the explanation to have more focus on the background, and in contrast, the GANMEX example focuses only on the key features that would cause the digit to change.

GANMEX: One-vs-One Attributions using GAN-based Model Explainability

Figure 2. (A) Saliency maps for multi-class datasets (MNIST, SVHN, CIFAR10) generated with various baselines, including zero baseline (Zero), MDTS and GANMEX, with the original and target classes co ct indicated for each example. (B) Mis-classification analysis showing with the (mis-classified class, correct class) pairs. The baseline columns show the expected images generated by GANMEX for the correct classes, and the saliency maps show the explanation of why not the correct class produce by IG, Deep LIFT (DL) and occlusion (Occ).

GANMEX: One-vs-One Attributions using GAN-based Model Explainability

Table 1. Inverse localization metrics for IG on the BAM dataset using the zero baseline (Zero), MDTS, and GANMEX (GAN), compared with expected gradient (EG).

Integrated Gradient EG

Zero MDTS GAN

Different object 0.711 0.850 0.459 0.610 Different scene 2.440 1.254 1.027 1.074 Overall 1.591 0.852 0.747 0.846

One-vs-one attributions for CIFAR-10 were challenging as it required identifying the common features shared across the original class and the target class, which was often nontrivial to achieve. Comparing MDTS with GANMEX, the baseline images selected by MDTS were rather uncorrelated to the original input image, causing random attributions to be present in the saliency maps. In comparison, GANMEX was much more successful in keeping the common features unchanged in the baselines, and this has helped the saliency maps focus on the differentiating features.

Zero baselines, on the other hand, were generally unsuccessful in making one-vs-one explanations. The attributions on MNIST look similar to the original input and ignores everything in the background, and the attributions on SVHN and CIFAR10 were rather noisy. As shown in Supplemental Figure 9, attributions based on zero baselines only varied marginally with different target classes. This shows that zero baseline attributions were not sensitive to the target classes and that purposely designed class-targeted baselines are required for meaningful one-vs-one explanation.

Mis-classification Analysis We next demonstrated how one-vs-one saliency maps can be used applied for troubleshooting mis-classification cases. For an input x that belongs to class co but was mis-classified as class cm. AS,cm co(x) = AS,cm co(x, Bco(x)) provides explanation to why x belongs to cm and not co according to the trained classifier, and this can help human understand how the classifier has led to the incorrect decisions. We provided examples in Figure 2.B where the samples were mis-classified. For MNIST and SVHN samples, the misclassification mostly happened when the digits were presented in a non-typical way. The GANMEX baseline Bco(x) show how a more typical digit should have been written according to the trained classifier, and the attribution AS,cm co(x) highlights the area that led to the misclassification.

CIFAR10 presented more complex classification challenges, and the classifier can easily confuse a ship with an airplane because of the pointy front and the lack of sea horizon, or a dog with a cat because of the shape of the ears and the nose, and those areas were successfully highlighted in the

Figure 3. Sanity checks showing the original saliency maps (Orig) and saliency maps under cascading randomization over the four layers: output layer (Output), fully connected layer (FC), and two CNN layers (CNN1, CNN2).

one-vs-one saliency maps generated with GANMEX.

Quantitative Evaluation To evaluate the saliency methods for one-vs-one attribution, we leverage the Benchmarking Attribution Methods (BAM) dataset (Yang & Kim, 2019) that was constructed by pasting foreground objects onto background scene images, which allows using the groundtruth information of foreground/background areas to benchmark attribution methods. Instead of training classifiers for distinguishing either the objects or the scene as proposed in the original paper, we treated every object-scene pair as a separate class. For any original class and target class sharing the same background scene but different foreground objects, we would expect the one-vs-one attribution located in the object area, whereas for any original class and target class sharing the same object but different scenes, the one-vs-one attribution located in the background scene area.

For any original class/target class pairs sharing common features set Sc, we defined L(A(x)) = ( 1 card(Sc) P

i Sc |Ai(x)|)/( 1 card(Sd) P

i Sd |Ai(x)|), the inverse localization metric, for measuring how the attributions are constrained within the differentiating feature area. Here Sd = Sc is the distinguishing feature set, card(.) measures the cardinality of feature sets, and x and A(x) are the sample and the corresponding saliency map. A lower L(A(x)) would mean that the saliency map A(x) is more localized in the focus area. Lower L(A(x)) scores would indicate better saliency maps, and the inverse relationship ensures that the incorrect attributions are penalized.

In Table 1 we compared IG saliency of different baseline choices as well as EG saliency. The results showed that the attribution methods overly focused on the object even when the background scene was the differentiating features (the different scene row). Out of all the methods that were compared, IG+GANMEX achieve the best L(A(x)) scores, while the one-vs-all baseline (zero baseline) were

GANMEX: One-vs-One Attributions using GAN-based Model Explainability

Figure 4. Saliency maps for the classifier on the apple2orange dataset with six baseline choices: zero baselines (Zero), maximum value baseline (Max), blurred baselines (Blur), MDTS, Expected Gradient, and GANMEX baselines. The zero and maximum value baselines frequently lead to incorrect attributions in the background. Attributions with the blurred baselines tend to highlight the edges only. The MDTS saliency maps sometimes mistakenly introduced new features (highlighted by the red rectangles) from the MDTS baseline images, and lastly, results with EG were rather noisy and mistakenly highlighted backgrounds.

the worst performer. Such results confirmed that GANMEX provides desirable attributions while used with IG, while the non-class-targeted zero baseline is generally not suitable for one-vs-one attributions.

Cascading Randomization (Sanity Checks) We performed the sanity checks proposed by (Adebayo et al., 2018) that randomize layers of the DNN from top to bottom and observe the changes in the saliency maps. Specifically, layer by layer we replace the model weights with Gaussians random variables scaled to have the same norm. For meaningful model explanations, we would expect the attributions to be gradually randomized during the cascading randomization process. In contrast, unperturbed saliency maps during the model randomization would suggest that the attributions were based on general features of the input and not specifically based on the trained model.

Figure 3 shows the experiment on MNIST data with the network layers named (input to output) CNN1, CNN2, FC, Output. It shows that even though the saliency maps generated by the original IG, Deep LIFT and Occlusion were rather unperturbed (still showing the shape of the digit) after the model randomization, with the help of GANMEX, both the baselines and the saliency maps were perturbed over the cascading randomization. EG, while showing more randomization compared to the zero baseline saliency maps, still roughly shows the shape of the digit throughout the sanity check. Therefore, out of all the attribution methods we have tested, those using GANMEX baselines were the only ones passed the sanity checks.

4.2. Attribution for Binary Classifiers

In addition to the one-vs-one aspect, GANMEX generally improves the quality of the saliency maps compared with the existing baselines, and this can be tested on binary datasets where the one-vs-one explanations and the one-vs-all explanations are equivalent. For apple2orange dataset, conceptually apples and oranges both have round shapes but have different colors, so we would expect the saliency maps on a reasonably performing classifier to highlight the fruit colors, but not the shapes, and definitely not the background.

In Figure 4 and Supplemental Figure 10 we compared the saliency map generated by Deep LIFT and IG with the zero input, maximum-value input, blurred image, with those generated with the GANMEX baselines. With any non GANMEX baselines (Zero, Max, Blur) we commonly observe one of two errors in the saliency map - (1) highlighting the background, and (2) highlighting the edges of the fruits providing the false indication that the model is basing its decisions on the shape of the object rather than its color. It was quite clear that neither of these errors occur when using the GANMEX baselines as it always highlighted the full shape of the apple(s)/orange(s) as supposed to the edges, and the attributions were minimal in the backgrounds.

5. Ablation Studies

Here we analyzed the possibilities of using other GAN models. Different from Star GAN, most other image-to-image translation algorithms do not have a stand-alone class discriminator that can be swapped with a trained classifier. To simulate such restrictions, we trained a similar GAN model but with the class discriminator trained jointly with the generator from scratch. Figure 5.A shows that while the

GANMEX: One-vs-One Attributions using GAN-based Model Explainability

Figure 5. (A) Cascading randomization on baselines generated by a stand-alone GAN lead to little randomization on the saliency maps. (B) Colored-MNIST dataset. GAN baselines generated with both similarity loss and reconstruction loss (S+R), similarity loss only (S), reconstruction loss only (R), and none of those (NA). Only S+R and S successfully constrained the baselines in the same modes (colors) with the inputs.

stand-alone GAN yields similar baseline with GANMEX, both the baselines and saliency maps of the stand-alone GAN remains unperturbed under cascading randomization of the model. This indicates that the class-wise explanations provided by stand-alone GAN were not specific to the to-be-explained classifier.

The importance of the similarity loss in Equation 9 can be demonstrated on a colored-MNIST dataset, where we randomly assigned the digits with one of the three colors {red, green, blue}, with labels of the instances remain unchanged from the original MNIST labels of {0, ..., 9}. The classifier was trained with the same model architecture and training process as for MNIST.

The dataset demonstrated different modes (colors in this case) that are irrelevant to the labels, and we would expect the class-targeted baseline for x to be another instance with the same font color as x. Figure 5.B shows that the similarity loss is the crucial component for ensuring that the baseline has the same color with the input. Without the similarity loss, the generated baseline instance can easily have a different color with the original image. The reconstruction loss itself does not provide the same-mode constraint because a mapping of G(red) green and G(green) red is not penalized by the reconstruction loss. While the reconstruction loss was not required for GANMEX to satisfy

the same-mode constraint, we observed that some degrees of reconstruction loss help GANs converge faster. Further analysis regarding tuning the relative weights between the loss terms were provided in Appendix D.

6. Conclusion and future work

We have proposed GANMEX, a novel approach for generating one-vs-one explanation baselines without being constrained by the training set. We used the GANMEX baselines in conjunction with IG, Deep LIFT, SHAP, and Occlusion, and to our surprise, the baseline replacement was all it takes to address the common downside of the existing attribution methods (blind to certain input values and fail to randomize with the model randomization) and significantly improve the one-vs-one explainability. The out-performance was demonstrated through evaluation using purposely designed dataset, perturbation-based evaluation, sparseness measures, and cascading randomization sanity checks. The one-vs-one explanation achieved by GANMEX opens up possibilities for obtaining more insights about how DNNs differentiate similar classes.

The main issue we tackled in this paper, is that of deleting a feature. Doing so is a crucial part in feature importance or saliency map generation. For images, this is a particularly challenging task, since its unclear what it means to delete a pixel. The solution provided by GANMEX to this issue can be, in high level, translated to other regimes where it is not entirely clear what it means to delete a feature. Indeed there is no consensus for this issue in tabular data, nor in NLP.

The limitations we observed were associated with a combination of number of classes, number of images per class (the more the better), image dimensions, and the complexities of the task. That being said, our experiment did show that even in scenarios where the GAN did not always product high quality baselines, they still outperformed the naive baselines commonly used to date. We emphasize the usefulness of having a GAN trained based on the model as a discriminator, as opposed to pre-trained GANs, or methods oblivious to the model. This is crucial for identifying problematic models, and is empirically shown in the cascading randomization sanity checks.

Overall GANMEX provides an opportunity to redirect the problem to the use of GAN, which will be benefited from the advancement in future GAN research. In addition to one-vs-one explanations and binary classification one-vs-all explanations, open questions remain on how to apply GANMEX to one-vs-all explainability for multi-class classifiers, and how to best optimize the GAN component to effective generate baselines for classification tasks with large number of classes.

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