What You See is What You Classify: Black Box Attributions
Authors: Steven Stalder
Nathanaël Perraudin
Radhakrishna Achanta
Fernando Perez-Cruz
Michele Volpi
Venue: NeurIPS 2022 Accept (2022)
Keywords: Computer Vision
Explainable Machine Learning
Saliency Maps
Attribution

Abstract: An important step towards explaining deep image classifiers lies in the identification of image regions that contribute to individual class scores in the model's output. However, doing this accurately is a difficult task due to the black-box nature of such networks. Most existing approaches find such attributions either using activations and gradients or by repeatedly perturbing the input. We instead address this challenge by training a second deep network, the Explainer, to predict attributions for a pre-trained black-box classifier, the Explanandum. These attributions are provided in the form of masks that only show the classifier-relevant parts of an image, masking out the rest. Our approach produces sharper and more boundary-precise masks when compared to the saliency maps generated by other methods. Moreover, unlike most existing approaches, ours is capable of directly generating very distinct class-specific masks in a single forward pass. This makes the proposed method very efficient during inference. We show that our attributions are superior to established methods both visually and quantitatively with respect to the PASCAL VOC-2007 and Microsoft COCO-2014 datasets.

What You See is What You Classify: Black Box Attributions
Steven Stalder Swiss Data Science Center ETH Zurich, Switzerland
Nathanaël Perraudin Swiss Data Science Center ETH Zurich, Switzerland
Radhakrishna Achanta
Swiss Data Science Center EPFL, Switzerland
Fernando Perez-Cruz Swiss Data Science Center ETH Zurich, Switzerland
Michele Volpi
Swiss Data Science Center ETH Zurich, Switzerland
Abstract
An important step towards explaining deep image classifiers lies in the identification of image regions that contribute to individual class scores in the model's output. However, doing this accurately a difficult task due to the black-box nature of such networks, Most existing approaches find such attributions either using activations and gradients or by repeatedly perturbing the input. We instead address this challenge by training second deep network, the Explainer, to predict attributions for pre-trained black- box classifier, the Explanandum. These attributions are provided in the form of masks that only show the classifier-relevant parts of an image, masking out the rest. Our approach produces sharper and more boundary- precise masks when compared to the saliency maps generated by other methods. Moreover, unlike most existing approaches, ours capable directly generating very distinct class-specific masks single forward pass. This makes the proposed method very efficient during inference. We show that our attributions are superior established methods both visually and quantitatively with respect the PASCAL VOC-2007 and Microsoft COCO-2014 datasets.
Introduction
Image recognition and classification systems based on deep learning considered black boxes. It often hard, not impossible, to directly locate the portions of the input image responsible for a given classification output. Being able systematically perform such attributions is crucial step towards explainable deep learning, which can contribute to its widespread adoption. Attribution allows understanding the potential errors and biases [13] 17 21 It also enables the of deep networks as decision support tools, e.g. in medicine [15], and facilitating meeting legal regulations [8]. Note that we refer attribution as the goal of associating input image regions model decisions, which differs from the notion of interpretability that relates to models that can be directly used to infer causal general structural relationships that link inputs and outputs 23
The problem of performing attribution for deep image classifiers has been addressed by several recent works. These belong two broad categories. The first relies visualising the derived model's activations and backpropagated signals [31 24 3. Although these methods provide a direct way to visualize salient areas, they heavily depend the quality of the trained models' architectures and weights. Furthermore, some of these methods turn out to be independent of the labels the model has been trained on, as well through randomization tests [.] This suggests that many of these methods are strongly influenced by low-level, class-agnostic features and are therefore inadequate. The second category relies on
some extent the parameters of the models, as shown
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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Bicycle
Matorbike
Person
Cat
Dog
Bicycle
Matorbike
Person
Cat
Dog
C'Cam
BP
Ours
Figure 1: Visual comparison of per-class attributions provided for VOC-2007 by our Explainer, alongside Grad-CAM (GCam) (24] and Extremal Perturbations (EP) 12] for the VGG-16 architecture [25 Our attributions have sharper boundaries and at the same time are more class-accural accurate than Grad-CAM or EP. Attributions for only five out of the twenty VOC-2007 classes are shown for convenience. Colormap ranges from low (blue) to high (red) saliency.
local perturbations of the input images and is often model- aggnsss.. These models rely on masking strategies infer local feature importance, which often results in loss of visual detail, ambiguity and high computational cost. Nonetheless, results suggest that local perturbations, like masking, are an effective way to analyze and explain the response a model 20 22
This last line of reasoning posits that attribution can be formulated as additional task complement- ing the classification from the Explanandum (i.e. the model be explained). Therefore, it natural to consider learning an Explainer (i.e. the model that explains) that specifically addresses the task of attribution. We approach attribution supervised meta-learning problem through the use of complementary convolutional neural network, which learns to produce dense class-specific attribution masks, balancing preservation and deletion of information from the input image as dictated by the Explanandum.
The resulting Explainer efficiently masks and precisely locates regions of the input image that responsible for the classification result of pre-trained and frozen Explanandum (see Fig. and Sup. PASCAL Visual Object Classes (VOC-2007) 9
Mat. Sec. C.. We evaluate methodology and Microsoft Common Objects in Context (COCO-2014) [18]. To sum we present an efficient attribution method, which has the following advantages:
Our Explainer directly provides precise mask for each class label in Fig.
Our Explainer provides attributions for test images with single very efficient forward pass, orders of magnitude more efficient as compared to other perturbation-base approaches.
Our Explainer works with any architecture of the Explanandum.
2
Related Work
Activation and gradient-based methods. The methods in this category attempt explain trained model by leveraging its weights and its activations for given image to be explained. Zhou al. BI initiated this line of research with Class Activation Mapping (CAM), where the authors built particular architectures around notion of global average pooling and illustrated the intrinsic localization performed by a classification network. Grad-CAM (4 removed the dependency CAM on specific architectures by reconstructing the input heatmap through weighted average of gradients, rather than directly projecting back activations. Further extensions to this are Grad-CAM++ [3], which is CAM weighted by averaged second order gradients, Score-CAM 229 which is CAM weighted by faier-wise class activations, or Ablation- CAM 77. which is CAM weighted by neuron ablation.
Some methods directly engineer the backpropagation and network architectures in order retrieve pixel-level saliency maps. One such example is the deconvolution approach of Zeiler and Fergus 30), where the authors propose to revert forward propagation (mapping activations to pixels instead of mapping pixels to activations) to visualize features and functions of intermediate layers. From this, Springenberg et (66 derived guided backpropagation. Although the focus of their work was on developing efficient fully convolutional neural network, they show how by combining

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traditional backpropagation and deconvolutions, one can retrieve salient regions of the input for specific class. In another line of work. Wagner al. [28 frame the problem as defense against adversarial perturbations and tackle it by constraining and selectively pruning activations.
Local perturbations and local models. The idea behind these methods is that by perturbing the input to the trained network, one can retrieve an explanation signal by summarizing changes in the classification scores. RISE introduced way of retrieving a saliency heatmap based on random perturbations of the input image [20] and recently, [27] extended similar reasoning for object detection systems. The input image is randomly masked several times, changes in the model scores tracked, and aggregated by a weighted average. LIME proposes a similar setup, but instead uses
random switches on unsupervised segmentation [22].
Fong and Vedaldi [] extend these ideas by reformulating the attribution problem as a meta-learning task, where the optimal mask can be found by optimizing a score. Fong et al. [12] extend their previous work [[T] through the definition of extremal perturbations, which are the family of transformations that maximally affect a classification score. They propose to use Gaussian blur to assess perturbations over fixed set of mask areas. Dabkowski and Gal [5] rely on a similar intuition, and the Explainer is directly optimized based on meta-learning around the Explanandum. In these settings, the Explainer optimizes a loss which balances preservation of the classification score on the active parts of the image, while minimizing the score for areas that are not active. These works also make use of regularization to constrain the mask area and its smoothness. In similar fashion, Chang et al. 2 learn a
dropout as a Bernoulli distribution, which used to retrieve a mask and evaluate extremal perturbations. Unlike Fong et al. [12.. Chang et al. [2) return the parameters of the learned per-pixel Bernoulli distribution as the saliency mask. Recently, Khorram al. [T6] proposed iGOS++ which frames attribution as optimizing over a mask which optimally balances preservation of useful information and removal of unnecessary information, regularized by bilateral total variation.
In this paper, we propose method which learns a dense perturbation, the attribution mask, over input images. Unlike existing approaches, we optimize to balance low multi-label binary cross entropy for the unmasked portion of the input image, and high entropy for areas of the image masked out by the Explainer. Compared to most perturbation-baal based methods, our Explainer can predict attribution masks for all classes (and not only the predicted class) in single forward pass, thereby being orders of magnitude faster. addition, we beat state-of-the-ar on standard benchmarks.
3 Training the Explainer
In this section, we present our Explainer architecture, which is trained to detect image regions that a given pre-trained classifier, the Explanandum, relies on to infer semantic object classes. Training of our model does not require any pixel-wise annotations. relies on the Explanandum's ss training data (including labels) and model. This makes our technique generalizable to any Explanandum architecture through which we can back- pook-propagate the classification loss. In this paper though, we only consider Explanandum models which are trained for image classification and not for object detection or semantic segmentation.
As illustrated in Fig. 2 the Explainer sees an image and outputs a set of masks S of the same resolution, containing one segmentation mask s. for each class c C. The values of the class masks S, are bounded in the range [0, 1] through a sigmoid function o()) e² (1 + e²), where / represents the predicted pixel-wise logits. Values of or 0 in the mask result in the full preservation or deletion of the corresponding pixel value, respectively. Note that the sum of the class masks does not need to be equal to one.
Using the target label(s) for the input image, we split the class segmentation masks into two sets: one that consists of masks that correspond to any ground truth class appearing in the training image, while the other contains the remaining ones. We merge each set into single mask by taking the pixel-wise maximum value for each pixel position. The target mask m (obtained from the first set) serves to locate the regions corresponding to (any of) the label(s) contained in a given training image, while the non-target mask n (obtained from the second set) allows us to gather false positive activations. Finally, the inverted mask m 1 m is used to ensure that once the object of interest is removed, the Explanandum cannot address the task anymore. Note that during inference, the mask aggregation step is not needed and our Explainer provides one explanation mask for each class.
3

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CLASS
NACRED IES
CLASS
EPLANABEN
LEGTT
NEW SUREET
MIDK
Figure 2: Overview of our method. Given pre-trained Explanandum F, whose weights frozen, the Explainer network & learns to produce masks S, for each class. The masks corresponding to the label(s) associated with the input image (shown in green) maximum over masks (shown as 1's), to obtain a target mask m and its complement m (i.e. inverted mask). All the other masks (shown in red), which do not correspond to the labels of the input image but might still score positively for the given image, are merged separately to obtain the non- non-targer mask n, which is also used in the loss term. The images obtained by multiplying the target mask and its complement with the input image (shown by x's) are fed to the given pre-trained Explanandum separately, generating two outputs which compute losses. The set of per-class masks S and the aggregated larget mask m serve as the attributions provided by our Explainer.
merged by taking the pixel-wise
Note that for the selection of true classes, we chose to utilize the same ground truth labels that the Explanandum was given during training on unobstructed images. We believe that using ground truth label helps in handling attributions for false negative predictions of the Explanandum as we optimize the attributions also for classes which are not predicted with high probability on the unmasked images. Alternatively, one could directly take the predictions of the Explanandum for the selection of true classes. This requires a thresholding operation, which an additional complication. However, relying on the Explanandum' 's predictions might be more suited if expect the Explanandum to still make a significant amount of false positive predictions on the training set (which was not the case for the architectures and datasets we decided to explain). We assume that the Explainer requires an Explanandum that performs very well on the training set, to minimize the effect of misleading training signals. Given the results in Sup. Mat. Sec. C are able to show that under these assumptions, this design choice does not hinder the ability the Explainer to generate attributions that are faithful to the Explanandun's predictions.
3.1 Training loss
We formulate the loss combination of four terms:
(1) where (x,,)), ), m) is the binary cross-entropy loss over the masked image, (x m) is entropy term over the image masked with the complement of m, La (m, n, S) is a regularization term accounting for the of the true and false positive masks, and (to,m, n) regularization term favouring smooth masks. Xeş X and Ato are hyperparameters balancing the loss terms.
Cr(x, m, n) (x(x,,, V/, m) AxC. m) AmC n, S. + AeoLeo( n).
Classification loss: Lx(x, V. m). A model should be able to make correct decisions exclusively using the relevant portions of the image, ignoring all the rest. Under this assumption, we define the classification loss
binary cross-entropy terms, one for each class contained in the image.
Representing the Explainer as E and the frozen Explanandum as F, we define p F(x m) as the probability vector returned by the model F applied on the masked image, using the aggregated (element-wiss maximum) mask m provided by E. For all classes C in the training data and the set of target classes y in the image, we compute:
Cx - Eice log (pie)) + [c & y1 log (1 p(c))
where [c E V denotes the Iverson bracket, returning if the condition is true (the image contains class c), otherwise. This allows training mask when multiple classes are present in the training

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image, as in multi-label classification problems, where multiple masks are active at the same time and some pixels are free not to belong any mask (contrarily to using cross-entropy). Therefore, the model is free to learn dependencies and co-occurrences between different classes. This loss pushes the Explainer learn masks approximating F(x C m) R F(x), i.e. masked images are classified as correctly as possible in the eyes of the (pre-)trained Explanandum.
Negative entropy loss: (x) This part of the loss pushes the Explainer to provide masks whose complements do not contain any discriminative visual cuc, i.e. parts of the image that the Explanandum could use to infer the correct class. In other words, the classifier scores the mask complement should provide class probabilities p = F(x o m) as uniform as possible. To this end, aim at minimizing the negative entropy of the predictions over the class memberships, as:
(x m
1 C
Σ log p(c]
(3)
c=1
Note that this loss the negative entropy, as aim for high entropy for the background.
Area loss: La (m, S). With the terms Le and L. alone, our Explainer would have incentive to produce a target mask that conceals image areas. Clearly, a target mask m with everywhere would minimize these terms with respect m. To make sure m conceals background, we add two terms to the loss that correspond to two crucial desiderata: The mask should be as small as possible, but if the objective would favour larger areas, a whole range of areas in between a minimal and maximal percentage should not be penalized further.
The regularization as A(m) = Ž Ei, m(i.j], where Z is the number pixels. We want this area to be small, but non-zero. The same is required of the non-tan non-target mask n as well.
the area is simply formulated the mean of the mask values, computed
The term bounding the mask area from both above and below is formulated starting from the constraint presented by Fong et 112. However, instead of constraining the final image mask to a fixed area, we extend their technique to determine a valid minimum area and a maximum area b for those class segmentation masks that correspond to least one object the image.
Given such class segmentation mask 8e, we flatten it to a one-dimensional vector, and then sort its values in descending order. Let v(s.) be the vectorization operation and r(v(s))) be the sorting of the vectorized class mask sc. We then define two vectors qmin and 9max. each starting with predefined number of I's and padded with 0's to match the length of v(s.), where the amount of corresponds to the minimum 0) < a < b or maximum < b < 1 area, respectively. We also define qmask. which corresponds to S., vectorized, and sorted. Concretely:
Qmask (u (s.)) [0, 1]2, quin [1 Ze] .0 (1--))]] qmax [1| ... (( b)1]. (4)
To constrain the minimum and maximum area covered by the class segmentation mask, we then compute area bounding measure B given by:
z
1 z
B(s) = 7
Σ
max max((min/) 9mask ()),0)
+ 7 max
Σ
qmax [i), 0).
(5)
where the first term penalizes the mask only if the largest |Za| values are smaller than while the second term penalizes the smallest Z [b] values greater than 0. Our goal is for the mask to cover least certain area independently of its maximum size.
The final area regularization is therefore:
Ic E V) Ee [ E
La (m, n. S) = A(m) + A(n) +
(6)
where )' is again the subset of the classes that are present in the given input image according to the given training labels. Note that the last term of (6) used in conjunction with the smoothness loss presented below favors masks with sharp transitions between 0 and 1.
5

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Smoothness Loss: (m, n). As a final requirement, we are interested in generating masks that appear smooth and free of artifacts. For this purpose, we utilize a total variation (TV) loss on the masks as used by Fong and Vedaldi [1] and Dabkowski and Gal [5], albeit we use the anisotropic variant given by:
1 Z
TVXx)=
Σ
x(i + +1 + [x[t,]] - x(i, 1|| x
where x is a two-dimensional array of values. The smoothness term of the loss relates to the target mask and non-target mask
L (m, n) TV(m) + (V)
(8)
This smoothness term encourages our attributions to appear visually coherent.
4 Experiments
We present three results to establish the advantages of our Explainer over existing approaches. Although continuous in nature, our masks show a sharp transition from background foreground, making it effectively binary. Additionally, our masks adhere tightly to region boundaries. Since common objective metries may fail convey this, we provide a brief visual comparison. The next result shows how our masks are class-specific, which provides more interpretive power than combined masks. The third result shows that our combined masks outperform existing methods on standard metrics for semantic segmentation.
Since we expect our Explainer to learn class-specific semanties and generate class-specific masks of the same resolution as the input image, we employ DeepLabV3 [ with a ResNet-50 backbone, an architecture commonly used for semantic segmentation tasks. We train this model from scratch to avoid any bias, iee an information leakage from the semantic segmentation dataset from which DeepLabV3 has been pre- pre-trained on.
For the Explanandum, we use VGG-16 25 and ResNet-50 14] models, both pretrained on Ima- geNet (6) We fine-tune them the multi-label classification tasks for VOC-2007 and COCO-2014 (i.e. on natural unmasked images), and then freeze the models. To this end, we use the full training of VOC-2007 and 90% of the COCO-2014 training set for fine-tuning. To assess generalization, we use the test set of VOC-2007 and the validation set of COCO-2014, respectively, For choosing hyperparameters, we use the VOC-2007 validation and the remaining 10% of the COCO-2014 training set. In this work, we implemented models and experiments using PyTorch 19 and PyTorch Lightning [10
4.1 Visual Comparison
Visually, our Explainer leads to sharp and meaningful masks. F a visual comparison of how our Explainer attributions perform compared the saliency maps obtained from Grad-CAM (GCam) 224 RISE (20), Extremal Perturbations (EP) [12), iGOS++ (iGOS) [16], and Real-Time Image Saliency (RTIS) (5). For the RTIS baseline, we could not retrain their model on VOC-2007 and COCO-2014, as it was not possible to employ their architecture multi-class classifiers. Instead, we use their loss to train our architecture. Accordingly, we fine-tuned some hyperparameters of our RTIS implementation, while leaving the remaining ones at the default values as given in their paper. For all our experiments, we resized input images to 224x224 pixels and normalized them on the mean and standard deviation of ImageNet.
Our approach provides sharp masks, which contrasts with classical saliency methods such as Grad- CAM or RISE. EP and iGOS+ provide masks which are better localized, although not as sharp as the ones produced by RTIS or our Explainer. Our implementation of RTIS provides sharp masks, but the overall attribution tends to be leaking over object borders. Our area constraints, in combination with the entropy term over the mask complement m. enforce tight masks over object classes of different sizes. For instance, Fig, 3 2), Fig. 5)., or Fig. 3(8) show how our masks align much more clearly with the objects. This not only holds for single-class images, but also when we have multiple
'Code is available at: httpp//s//ggttt.booooo//////aaae

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Inpur
OCam
Qurs
Inger
RISE
EP
IGOS
2
5
7
10
13
14
Figure 3: Visual comparison of our attributions for VGG-16 network fine-tuned on images from the VOC-2007 dataset and frozen. Our attributions much more effective retaining object class regions and discarding the rest. Examples 13 and 14 show cases where our Explainer is inaccurate.
Fig. 3 12)). or different classes (Fig. 6), Fig. 3()), instances of the same class (Fig Fgg
Fig. 10s.31100 10)). Attribution of some animals (e.g. Fig. 3 7), Fig. 3 110). Fig. 11)) often tends to be focusing on heads. Most training images containing animals have unobstructed heads, which can explain such behaviour. For some classes, all methods agree the importance of an image region that is not actually part of the actual object. A good example for that is Fig. 33,, where the train tracks are part of the attribution. Since most training images of trains also show train tracks, it seems obvious that the Explanandum learns to see the train tracks as discriminative semantic co-occurrence. With the help of Explainer, such unintended biases can quickly be detected.
Fig. 13)) and Fig. 114 show two examples where our Explainer less precise. For Fig. 11), our attribution leaks over to the bars below the horse. Even though the classifier might indeed have made a connection between these bars and the "horse" class, Grad-CAM, RISE, EP, and iGOS++ appear to agree that the main importance should be attributed to the actual objects in the image. In Fig. 3 14), is difficult to interpret our attribution for the class "boat" as some parts of the attribution lie on the actual object but also significant area of the surrounding water is activated (underlining potential discriminative co-occurrence). However, the other methods also provide varying explanations, with iGOS++ masking mostly the boat, but Grad-CAM attributing all importance to the water. For more results on COCO-2014 and VOC-2007 please refer to Sup. Mat. Sec. D and
4.2 Class-specitic masking
Our Explainer provides class-specific masks. In Fig. [T we have already hinted how our Explainer is able to provide more class-specific masks than the other techniques. In this section we evaluate this numerically. To this end, we have selected five target classes from the VOC-2007 dataset, for which we evaluate how the class masks interact with the classification confidence of the VGG-16 Explanandum. We have selected the classes "cat" and "dog" as they are two animals that often occur in similar settings, the most prevalent class "person" that can often be seen together with a variety of other classes and often inside the fourth class "car", well as the "bottle" class, to include VOC-2007 class that is very difficult to detect for the Explanandum. For each test image containing one of the target classes, we first evaluate the classification performance of the Explanandum on the unmasked image (""onee" column) and then on masked images where the image is masked once with each the class-specific masks. Specifically, for each of these continuous masks we report the mean softmax probabilities for the target class, after we threshold each mask over nine uniform values in ( at 0.1 intervals. Note that here we use the softmax instead of the sigmoid function despite multi-class setting since want to evaluate the activation confidence for single class compared
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Explainer
Mask
Grad-CAM
Mask
none
bottle
car
cat
dog.
parson
Done
bottle
car
dog.
Target Class
battle
20.57
15.29
4,91
4.82
4.82
2.72
Targel Clas
botile
20.57
16.10
5.24
4.85
4.76
3.61
70.52
6.71
022022
6.67
6,66
7,1
car
70.52
6.93
50.19
6.65
6.53
8.92
72.78
6.09
6.18
5.74
dog
58.00
4.67
4.70
5.95
$7.60
4.58
dog
58.00
4.46
4,39
8.25
41 13
4.38
person
69.37
8.90
6.18
porson
69.37
11.81
5.90
8:45
Mask
Mask
RISE
RTIS
bottle
call
dog
person
bottle
dog
person
Turger Cluss
bottle
20.57
18:67
10.94
12.05
10.70
9.73
bottle
20.57
18,92
11.19
13.37
13.44
17.24
70.52
29.75
56.66
30.27
34.43
32.42
70.52
41:25
67.02
40.69
31.87
54.31
car 72.78
37.89
28
49.61
41.89
36.02
Target
cat 72.78
45.84
36.27
72.62
59:21
dog 58.00
19.64
20.34
23.72
45.12
22,83
dog
$8.00
41.37
34.76
57.59
61.22
58, 76
person 69.37
56,06
54.81
person
69.37
43.42
Table 1: Comparison of cless-specific masks generated by our Explainer, Grad-CAM (24) RISE 20. and adapted RTIS [5]. Images containing the target class specified in the row are masked with the thresholded class masks specified in the column and given to VGG-16 for classification. In any given cell we report the mean softmax probabilities over all mask thresholds and for every test image containing the target class. If the mask class equals the target class, want high scores, if it is different, we want low scores. We additionally compute the softmax scores achieved for unmasked images ("none" column) for reference.
to all other (ideally masked-out) classes. This can of course affect the scores for the completely unmasked images where multiple object classes may be present.
In Tab. [ show the evaluations for Explainer, Grad-CAM, RISE and RTIS. For EP and iGOS++ it was not feasible to conduct these experiments since these methods take a very long time to generate masks compared to the other ones (see Sup. Mat. Sec. A). We can clearly see how the masks produced by our method allow the Explanandum to retain very good classification confidence for the target classes when the correct mask is taken but render it completely uncertain when any other mask is put on the image. This is in stark contrast to RISE and RTIS especially, which produce overall larger, less precise masks. Even though the Explanandum has high confidence after masking the images with their corresponding correct masks, the same is still true when any wrong mask is used. Only Grad-CAM achieves comparable performance to our Explainer but results in considerably worse scores for the correct masks for 4 out of 5 classes and still shows some increased confidence when the wrong mask is put on the images of an often co-occurring target class (e.g. "cat" and "dog". or "person" and "car").
4.3 Segmentation accuracy
Our attribution quality approaches object segmentation. While our Explainer architecture pro- vides excellent attributions visually, we also confirm this quantitatively. Our explanations approximate object-level segmentation and can thus be evaluated using standard instance and semantic segmen- tation benchmarks. In Tab. 2 we illustrate the accuracy of the masking strategies, on VOC-2007 and COCO-2014, 4, with VGG-16 16 and ResNet-50 as Explanandum, respectively. To provide fair comparison with our method, we evaluate all methods by aggregating the masks from multiple classes into a single one, as shown in Fig. 3 We also provide four base measures that serve as sanity check basclines in Tab. 2. i.e. the columns "0", "0.5", "1", and "G.T." (ground truth). These measures show how the assessment metrics range under border conditions: with completely null mask (composed of only O's), with a mask composed fully of 0.5's, with a non-mask composed of only I's and finally with mask which is perfectly equal to the ground truth segmentation.
We employ four different metrics, namely Accuracy (Acc), Mean IoU (IoU), Saliency (Sal) and Mean Absolute Error (MAE). All metrics are computed on per-image basis, by using the ground truth segmentation masks and the aggregated mask of the true classes present in each image, then averaged over the test set. The Accuracy is computed pixel-wise over the continuous masks without thresholding. The same holds for the IoU, where we take the pixel-wise minimum of the mask and the ground truth as the intersection and the maximum as the union, respectively. The Saliency score
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16OS+
Metric
GCam
Expl.
0.5
G.T.
RISE
065
1 Acc ToU
66.29
50,00
33.71
100
70.53
56.98
63.91
70.17
59.63
74.60
VGG
23.42
33.71
100
28.78
28.62
34.95
24.05
39.94
38.04
Sal
-0.85
-0.53
-1.32
VOC-
MAE
33.71
50.00
66.29
29.47
43.02
36.09
29.83
40.37
25.40
Ace
66.29
50.00
33.71
100
68.54
57.37
61.43
69.23
50.77
73.56
ResNet
IoU
23.42
33.71
100
30.75
28.42
34.88
24.25
36.46
34.23
Sal
-0.67
-0.68
-0.08
-1.13
-1.29
-1.02
-0.77
-1.92
-0.35
-1.33
MAB
33.71
50.00
66.29
31,46
42.63
38.57
30.77
49.23
26.44
70.39
50.00
29.61
66.31
52.35
57.01
68.70
39.18
69.90
COCO-201 2014
VGG
IoU
20.87
29.61
100
25.63
25.50
29.23
20.35
31.16
31.59
Sal
-0.1
0.03
0.72
-0.38
-0.67
-0.31
-0.13
-1.12
0.65
-0.51
.AR
29.61
70.39
33.20
47.15
42.55
29.83
ResNet
70.39
50.00
29.61
67.25
55.05
69.57
41.40
ToU
20.87
29.61
100
24.84
25.98
29.75
21.63
30.76
27.42
Sal
0.2
-0.25
0.37
-0.88
-0.66
-0.44
-0.24
-1.19
0.17
-0.64
MAE
29.61
49.36
70.39
32.36
44.44
42.68
30.02
58.4
34.35
Table 2: Segmentation scores for the attribution models. We have compared the methods against the pixcl-wise segmentation ground truths of all 210 VOC-2007 test images that include such annotations as well as for randomly selected subset of 1000 COCO-2014 images out of our entire test set of over 41K images (due long compute times of certain methods, Sup. Mat. Sec. Ap. Columns "0", "0.5", "1" and "G.T." (ground truth) represent the sanity check baselines to allow for a relative understanding of the scores. The upward arrows 1 (downward arrows indicate that higher (lower) values are better.
adapted from Dabkowski and Gal (5] and computed as:
Sal(m. p) log (max(A(())00005) -log
Eplel
(9)
where Y is the set of classes present in the image. This metric balances the size of the mask with the Explanandum outputs. Smaller masks minimize the first term but have a tendency to lower the classification confidence, thus increasing the second term. It is therefore possible to get lower score compared to the ground truth mask as a very small mask reduces the first term greatly, while it might still preserve lot of the classification confidence. This is the disadvantage of our method, as we aim to also attribute regions of lower (but still significant) importance instead of only the most distinguishing features. Finally, the MAE corresponds to the mean absolute
over the full dataset,
which is computed for each input image as: MAF(m, g) = ž Eis jm [, g(i, j]l. where g is the aggregated ground truth segmentation map for all object classes the input image. Note that certain metrics might favor very small masks (e.g. Sal), while others favor very large masks (e.g. IoU).
The assessment this sub-section assumes that an ideal method should perform attribution over whole ground truth segmentation, which is not the case in certain situations, as attributions should only cover classifier-relevantt parts of the object class (e.g. face instead of whole body). We argue that although attributions do not directly correspond semantic segmentations, and while different methods target different goals for attribution, the combined evaluation of these metrics can still be used for standardized assessment.
4.4 Limitations
Not all pairs Explainer and Explanandum interact equally well and allow straightforward training.
We observed that, while the explanation of VGG-16 and ResNet-50 on the VOC-2007 dataset performs consistently, the explanation for COCO-2014 is harder on ResNet-50 than on VGG- 16 (see Sup. Mat. Sec. and F),, even though the accuracies are comparable (see Sup. Mat. Sec. B Tab. 4). Sometimes, masks fail precisely cover the discriminative objects parts. Some examples are given in Fig. B 13) and Fig. 14), and further examples given in the Sup. Mat. Sec. D and

---

5 Conclusions
We have presented an approach for visually attributing the classification result of frozen, pre-trained, black-box classifier (the Explanandum) on specific regions of an input image. This involves training an Explainer architecture with the training data that was used train the Explanandum. The resulting model generates attributions in the form of class-wise attribution masks, as well as an aggregated foreground mask with a single forward pass for any test image. As compared to the gradient and
activation- based approaches. which often generate blurry saliency maps, our masks locate object
regions more accurately and the delineation of these regions is sharp (Sec. 4.T). D. As compared to the approaches that use perturbed inputs, the Explainer is not only more precise, as we prove quantitatively (Sec. 4.2 and 4.3). but also computationally more efficient (Sup. Mat. Sec. (A].
We observe that the Explainer can be learned well if the pre-trained classifier exhibits a good level of accuracy, Since learning the attribution fully depends on the signals provided by the Explanandum, this comes as no surprise. If instead of the original image, we use inputs that are masked by our Explainer, the accuracy may slightly decrease (Sup. Mat. Sec.IBp. Since our masks are so parsimonious in retaining the essential parts of the original image, it points to the fact that the drop in accuracy might come from the Explanandum being deprived of the Explainer is trained to generate masks, one could imagine retraining the Explanandumn with the original as well as syplainer-masker data. This can ensure that classification accuracy can be both high and free of influences from non-object regions. Finally, while our work focuses on explaining deep image classifiers, we believe it should be possible to extend such an approach to other black-box classifiers, other data modalities, and other learning tasks such as regression.
biases. Therefore, once
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11


Reviews:
[{"review_id": "lC5gFzWPAJy", "reviewer": "Reviewer_wP4a", "summary": "The authors propose to train a deep network - the explainer to estimate attributions for a pre-trained black-box classifier. The attributions are defined as image masks, in particular two masks - the class-relevant mask and the rest. Local and smoothness constraints assist the explainer in generating crisp, highlight localized attribution masks. The authors evaluate the approach on multiple datasets and compare with standard explanation methods. \n", "questions": "Lines 29 and 30 - The authors portray the dependence of the explainability methods on trained model architectures and weights as undesirable. I however, would argue that this is desirable to enhance the faithfulness of the explanations tied to the trained model. The authors have to either elaborate more on their claim or provide ‌references supporting their claim. The subsequent sentence (line 31) is more appropriate. There is evidence suggesting that the explanations generated through certain methods appear to be independent of model parameters (Adebayo et al., and Sixt et al).\n\nThe third advantage (line 53) is confusing. If explanandum is not required, then how does one ensure the faithfulness of the explanations to the explanandum? Perhaps the authors refer to a model-agnostic explainer?\n\nLine 65- Perhaps the citation is incorrect. Adebayo et al [1] do not handle issues arising from high sensitivity to noise and clipping effects of gradients. \n\nLine 114 - target label(s) for the input image - are these the predicted labels of the explanandum or the ground truth labels? If it is ground truth labels, then the explainer can never be faithful to the explanandum - what is the explainer then explaining? The authors should clarify if their method is post-hoc or explainable by design?\n\nI reiterate the initial concern on faithfulness based on the observations in lines 475-482 (supplementary material). The explainer does not seem to be faithful to the explanandum!\n\nFurthermore, I notice almost no highlights for regions other than the top predicted class (Figures 4, 5 supplementary material). How does the model explain non-zero probabilities assigned to the other classes?\n", "limitations": "not applicable.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n\nThe ability to automatically generate reasonably accurate segmentation masks (albeit in an opaque manner) is a key strength of the approach. \n\nThe authors have experimented with multiple datasets and architectures to validate the method. \n\nThe paper is well-written and structured. It is easy to follow.\n\nWeakness\n\nIt is interesting to note that Grad-CAM results in comparable segmentation masks without the need to train an additional mask generator (Table 1). Grad-CAM extrapolates the low dimensional mask to the original image size that adds some noisy artifacts. Unlike the proposed explainer, it does not enforce any locality/smooth constraints. Despite these artifacts, Grad-CAM a very simple approach in contrast to the proposed explainer, can generate good segmentation masks. Thus, the proposed method’s advantage is unclear.\n\nWhile the authors provide a quantitative comparison of existing approaches through the segmentation dataset, as the aim is to provide a human interpretable explanation, a user study to validate the same will strengthen the contribution.\n\nFinally, the approach reads as a blackbox (mask generator) trying to explain another blackbox (classifier).\n\n", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "h7XO2jPIp0X", "reviewer": "Reviewer_sJ2V", "summary": "The paper proposes a method to identify regions of the images that identify and contribute decisively at identifying image by the decisive  object. The task is approached by using two network entitled Explanandum (i.e. the model to be explained) and Explainer (the model that explains) and training process based on 4 losses. The method is evaluated in conjunction with Pascal VOC 2007 an MS-COCO 2014 datasets", "questions": "1. To me the details of the problem to be solved are not firmly established. The paper says  that it uses the  \"multi-label classification tasks\" version of the two databases. Yet, only single class examples are shown in the evaluation. Than it speaks about \"attribution\" and at last about segmentation. I am missing some phrases (in different parts of the text) that: \n - say simply what the paper tries to solve\n - how can one evaluate the quality of this solution and why. The evaluation section carries the reader between different metrics and (unfortunately) excuses why some tests couldn't have been run in full. \n- how can one use the heat masks found\n\n\n2. The method is not explained well:\n- l.104 \"given pre-trained classifier\" \n- l 108 \"Explainer sees an image and outputs a set of masks S\". \n Then how the Explainer relates to the pre-trained classifier!? It seems to me that the two are independent. The first time \\mathcal{F} appears  is at line 133, again it is not explained well", "limitations": "The paper (approached problem and solution) does not raise any ethical or societal impact. Therefore, there is no (need for) discussion from this point of view.\n\nThe paper discusses technical limitations.", "rating": 7, "confidence": 4, "soundness": 4, "presentation": 2, "contribution": 4, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n - the idea of using another network to infer the internal mechanism of a base one is very appealing\n\nWeaknesses:\n - on the technical side, I view this paper contribution more closely to \"incremental\" than \"outstanding\". The idea to use two networks in a differentiating analysis is known.  None of the loss terms used in optimization are new; the approach is related to image saliency and object segmentation\n- given the limited contribution on the idea side, the evaluation should have been stronger. PASCAL - VOC 2007 is the smallest version, MS COCO is larger, but only parts of it were used. On the visual comparison (fig 3- main paper), the proposed method is the sharpest, but EP, with another threshold on the heat map gives very similar results. \n\nOverall, the paper is not so strong on either side to be viewed as a clear accept.  \n\nOther small issues:\n -  If accepted, the evaluation section should be re-written to enhance the strengths (positive part). Also, the explanation of experiments details (database presentation, .. l196-205)   needs to be separated  from the actual experiments \n - figure 2 - is rather poor: Who is \\mathcal{F} in the figure? \\mathbf{m}? \\mathbf{S}?", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "3IMhr9PBwa7", "reviewer": "Reviewer_Aofh", "summary": "This manuscript focuses on to provide an elegant approach to visually attributing the classification result of a frozen, pre-trained,\nblack-box classifier called as Explanandum on the input image(s). The author provides a solid method for the second deep network (called \"Explainer\") to provide a robust mask and attributions for test images. Together with solid experiments and solid baselines, the author achieves competitive results for attributions on the well-known datasets of PASCAL VOC and MS-COCO. \n\n", "questions": "There is a small concern I faced in this manuscript about training the explainer, but little-to-less information has been provided on the black-box classifier (Explanandum), as we could see the explainer is trained to generate the masks, the retaining of the Explanandum with original + explainer-masked data information is missing in this section. Could I please request the authors to give some views on this as I tried to identify this root cause but found no such information on this? ", "limitations": "My assumption is that the author neglected on the part about tiny objects/having occlusions etc. I believe this methodology works great in general but general scenarios could also have tiny object and objects with occlusions, can the author please provides some views on this. Even though this approach sounds significant and I'm more inclining towards accepting this paper, as I found out this could potentially be a significant contribution to the computer vision community. ", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Clarity: \n++ The paper reads very well and provides a very good description of related work and background, motivating the problem. Even outside of the contribution of this paper, I would recommend this paper to people getting started with deep learning/understanding black-box classifiers as it provides a thorough description of the part of the pipelines it deals with.\n\nNovelty: \n++ The proposed approach formulation is concise, convincing, and novel. A seemingly reasonable approach has been conducted in this manuscript. Compared to the prior work on performing attributions for deep learning image classifiers, the current strategy involves supervised meta-learning to produce dense class-specific attribution masks, which balances the preservation and deletion of information from the input image(s) \n++ The idea of incorporating the Explainer to generate masks and retraining the Explanandum with the original as well as Explainer-masked data can ensure that classification accuracy can be high and free of influences from non-object regions. A pretty decent methodology has been applied to this attribution problem by the authors on this.\n\nExperiments: \n++ There are a number of experiments performed across datasets that are extensive, fair, and provide solid foundations. The fact that the proposed methodology achieves competitive results makes me confident in the result as the implementation and experiments are sufficient and presented clearly. Additionally, the improvements are fairly consistent. Besides, in-depth analyses have been provided on the approach for different tasks and enough information has been provided via a thorough analysis of where the benefits of the approach have been obtained.\n\nReproducibility: \n++ Thanks to the author's efforts in giving enough clarity about the given methodology, this can be replicated with some efforts. I believe this could be a significant contribution this time in NeurIPS. ", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept