Metric-Driven Attributions for Vision Transformers
Authors: Chase Walker
Sumit Kumar Jha
Rickard Ewetz
Venue: ICLR 2025 Poster (2025)
Keywords: Interpretable and Explainable AI
Computer Vision
Vision Transformer
Primary area: interpretability and explainable AI

Abstract: Attribution algorithms explain computer vision models by attributing the model response to pixels within the input. Existing attribution methods generate explanations by combining transformations of internal model representations such as class activation maps, gradients, attention, or relevance scores. The effectiveness of an attribution map is measured using attribution quality metrics. This leads us to pose the following question: if attribution methods are assessed using attribution quality metrics, why are the metrics not used to generate the attributions? In response to this question, we propose a Metric-Driven Attribution for explaining Vision Transformers (ViT) called MDA. Guided by attribution quality metrics, the method creates attribution maps by performing patch order and patch magnitude optimization across all patch tokens. The first step orders the patches in terms of importance and the second step assigns the magnitude to each patch while preserving the patch order. Moreover, MDA can provide a smooth trade-off between sparse and dense attributions by modifying the optimization objective. Experimental evaluation demonstrates the proposed MDA method outperforms $7$ existing ViT attribution methods by an average of $12\%$ across $12$ attribution metrics on the ImageNet dataset for the ViT-base $16 \times 16$, ViT-tiny $16 \times 16$, and ViT-base $32 \times 32$ models. Code is publicly available at https://github.com/chasewalker26/MDA-Metric-Driven-Attributions-for-ViT.

Published as a conference paper at ICLR 2025
METRIC-DRIVEN ATTRIBUTIONS FOR VISION TRANS- FORMERS
Chase Walker', Sumit Kumar Jha', Rickard Ewetz!
1 University of Florida
2 Florida International University
ABSTRACT
Attribution algorithms explain computer vision models by attributing the model response to pixels within the input. Existing attribution methods generate explana- tions by combining transformations of internal model representations such class activation maps, gradients, attention, or relevance scores. The effectiveness an attribution map is measured using attribution quality metries. This leads to pose the following question: if attribution methods are assessed using attribution quality metrics, why the metrics not used generate the attributions? In response to this question, we propose Metric-Driver Attribution for explaining Vision Transformers (ViT) called MDA. Guided by attribution quality metrics, the method creates attribution maps by performing patch order and patch magnitude optimiza- tion across all patch tokens. The first step orders the patches terms of importance and the second step assigns the magnitude to each patch while preserving the patch order. Moreover, MDA can provide a smooth trade-off between sparse and dense attributions by modifying the optimization objective. Experimental evaluation demonstrates the proposed MDA method outperforms existing ViT attribution methods by average of 12% across 12 attribution metrics on the ImageNet dataset for the ViT-base 16 x 16, ViT-tiny 16 x 16, and ViT-base 32 x 32 mod- els. Code is publicly available at ht.tps:: httptppp//gg..bb....m///aaaeeeee
MDA Metrric-Driie De for ViT
INTRODUCTION
Computer vision models have been broadly adopted with applications in domains such as self-driving cars (Ando et al. (023), surveillance (Ho et al.) (219)), and disease detection (Esteva al., (021). However, due to the black-box nature of these models, proper explanations must be available to incite trust in their safety-critical system deployments. Effective explanation methods have been thoroughly explored for Convolutional Neural Networks (CNNs), but are still in their infancy for the more prominent Vision Transformers (ViTs). The most popular attribution methods create huuman-readale explanations using model's 's internal information such class activation maps (Selvaraju al. 2017), gradients (Simonyan et al.) 2014), attention (Vaswani et al.) 2017). or relevance scores (Binder al. 2016). A less abstract method of creating explanations is through feature perturbation. Here, model internals are ignored and input features are masked to discover their effect on the model's decision. However, this class of methods is prohibitively slow for creating the per-pixel explanations required for CNNs (Fisher et al. 2019 Zeiler & Fergus 2014). Thus, only recently have they seen a resurgence for ViTs (Xie et al., 2023 Englebert al.) 2023) whose reasoning over grassegraiied
patches allows the runtime complexity to be controlled. The broad diversity of attribution algorithms necessitates quantitative comparison using metrics for accurate quality assessment.
The most common attribution quality metrics are perturbation based tests (Petsiuk et al.) 2018 Kapishnikov et al. 2019 Walker et al., 2024) which do not need ground-truth labels. The most commonly used perturbation-basee
tests are insertion and deletion (Petsiuk et al. 2018). These metrics ablate the model input in order of highest value attribution features to determine if the features are important for the model's decision indicated. These tests were extended into magnitude aligned scoring (MAS) which also assess the magnitude of the attribution assigned to each feature (Walker et al. 2024). A feature's 's magnitude is evaluated by measuring the alignment with the

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Published as a conference paper at ICLR 2025
feature's 's model importance. This raises the question: can avoid abstract explanation approaches and use these perturbation metrics directly to create better explanations?
In this paper, propose method for creating Metric-Driver Attributions for the VIT called (MDA). The approach creates high-quality explanations for ViTs using a perturbation-basee approach that mimics the methodology of the attribution quality metrics used to assess the specified attributions. The four main contributions of MDA can be summarized, as follows:
1. We provide the first attribution algorithm that is directly driven by the metries used to assess the attributions produced by the algorithm. This is a stark departure from existing approaches that mainly leverage internal model representations and methods.
2. The MDA method creates attributions using patch ordering optimization and patch magnitude optimization. The first step orders the patches in terms of importance while the second step assigns an attribution magnitude to each patch while preserving the patch order.
3. Existing metrics encourage sparse explanations that focus on a few important features within image. We demonstrate that MDA is capable of creating dense attributions that indicate all features of importance by slightly modifying the optimization objective.
4. MDA achieves improved quantitative and qualitative performance compared state-of- the-art VIT attribution methods. On ImageNet, MDA outperforms the SOTA not only for the perturbation metrics it was optimized for, but also six additional attribution metrics across three VIT models with an average 12% improvement across all metrics.
The remainder of the paper organized as follows: the related work in Section 2 the methodology is in Section 3 the experiments are in Section 4 and the conclusion is in Section
2
RELATED WORK
In this section, we first present a detailed explanation of the scoring objectives of the perturbation quality metries of interest. We then discuss the existing approaches to ViT explanation.
2.1
PERTURBATION-BASE ATTRIBUTION QUALITY METRICS
Attribution metrics fit into two groups: comparison against ground-truth masks (Borji et al., 2013)
or perturbation of the model (Adebayo al., 2018 Hooker al. 2019) or the input (Petsiuk et al.)
2018 Walker et al. 2024) without ground-truth. Model perturbation randomizes or retrains the entire model evaluate at scale, which is slow process. Input perturbation therefore the most popular because it can evaluate single images without ground-truth or model changes. The insertion and deletion perturbation metrics expect the modification of an important feature in the model input to cause a change in the output (Petsiuk et al., 2018). They measure how well an attribution indicates important features by performing a linear perturbation process between baseline and an input. We explain insertion with the following text and Figure | Given an attribution A. the input X of size D belonging to class c, and the model F., the test evaluates A over N steps. Let Pa denote the perturbed image step k. For insertion, Po denotes the blurred input baseline and Pv is the original input. In each step, the set of D² (a). These features correspond to the ith most important pixels X; & Pk, and we update P3 as Pk+1 Ps X,, removing the blurring as seen in Figure (b). The model response is defined as:
N i-th highest magnitude features A, & Ps are selected, seen Figure
M R softmax (F (FP)))
Over the N steps of this insertion (ins) perturbation test, the monotonically non-decreasing M Rins curve will be formed on the range [0, 1] as seen in Figure (c). The score of an attribution is then calculated as the area under the M R curve (AUC):
N
1
SCorE N+ km
MR
A higher M Rins AUC indicates better attribution. The AUC in Figure (c) is 0.896. For deletion (del), Po denotes the original image baseline and Py is a black image. The M Rdel curve formed from the test is monotonically non-increasing and has range [1, 0). A lower M Rdel AUC is better.
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Attribution
Step
Stop 2
Step
Step
Insertion Test
Insertion
0.8
0.8
Resgonnee
0.0
0.4
Ins Start
Stop
Stop 2
Step 3
Step 4
0.0
25
50
100
25
50
75
100
Perturbation Parcentage
Perturiatton Percentage
(4)
(b)
Figure I: An illustration of the insertion metric where attribution is evaluated over 4 steps. In each
step, the highest attribution values are chosen (a) and those pixels are unblurred (b). The graph (c)
illustrates the M R generated by this process as described in Eq I and the AUC score from Eq 2
The graph in (d) shows the M R. DR, and APa as described in Eq and the MAS AUC: MR
The MAS insertion and deletion tests calculate the M in the same manner (Wakker al. 2024). These tests additionally introduce the density response (DR) curve which measures the magnitude of each feature. The DR and M R are compared to determine if high and low value attributions are assigned to important and unimportant features, respectively. In insertion, DR tracks what percentage of the total attribution of A has been inserted at step k. and is defined as:
[A:
DR
=
(3)
Li=o |Ai
where J-| denotes absolute value. DRiss is monotonically increasing and on the range [0. 1], seen as the dashed line in Figure I (d). The difference MR DR) is called the alignment penalty (AP), seen in Figure (d). The MAS score is then (M Rin AP) AUC, seen as 0.896 - 0.223 in Figure (d). The AP indicates important (unimportant) features were given too low (high) of magnitude in the attribution. deletion, pixels are removed each step, so DR = DD) the D Ddde curve is monotonically decreasing and (M AP) AUC is the score.
2.2 VISION TRANSFORMER EXPLANATIONS
The ViT model (Dosovitskiy et 2020) embeds the input image as a linear array of patch tokens prepended with classification token (C.S). These are passed through a decoder-only transformer (Vaswani et al. 2017) which extracts important relationships between all tokens via self-attention, and final linear layer classifies the output embedding of the (CLS) token. A VIT explanation assigns one value to each of the 2 patches. For ViT 16 x 16, the 224 x 224px input is broken into 142 patches which are each 16 16px. The resulting 142 grid of attribution values is upscaled to 224 x 224px.
ViT explanations can be derived from the self-attention values of the last layer's 's [CLS] token Vaswani et al. 2017). or the matrix multiplication of the self-atte self-attention through all layers (Rollout) (Abnar & Zuidema 2020). However, attention does not contain class information and is poor explanation alone (Bastings & Filippova, 2020). GradCAM (GC) multiplies the last layer self-attention by its gradients (Selvaraju et al. 20.7). Integrated Gradients (IG) generates an explanation from the mean attention gradients of interpolated inputs between baseline and input (Sundaaaaaaan
al. (201))
Current SOTA methods mix these techniques. Transformer Attribution (T-Attr) (Chefer et al. 2021a
gathers the attention of all layers with layer-wise relevance propagation (Binder et al. 2016) and multiplies by the gradients. Transition Attention (T-Attn) (Yuan et al.) 2021) multiplies Rollout by IG. Bidirectional Attention (Bi-Attn) (Chen al. 2023) introduces head importance to Rollout and multiplies by IG. Attributions generated by internal model representations
valuable, but most methods sacrifice their theoretical foundations by applying ad-hoc poot-procsssing in this manner.
Due to the ViT patch structure, two perturbation methods show promise without using internal model representations. ViT-CX (Xie et al. 2023) creates a set of masked inputs from the model's output embeddings. These are scored by the model's softmax output and the weighted sum of all masks the explanation. Transformer Input Sampling (TIS) (Englebert et al. 2023) performs the same process, but masking occurs inside the model at the token embedding level instead of the input level.
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Published as a conference paper at ICLR 2025
Patch Order Optimization
Patch Magnitude Optimization
Patc order
Remaining Parchus
Input Patches
Patch
Insort
Stop When
Output Aitr bution
Largest
1:
0.1
Mit (1.
10
801
(o)
al partcres set DR MR
Find Hemaiinn Patches with Daletton
Plezh
0:801
Swoe
Smallest Palch
Conntimus
FonAll
25:10
1 2 1312
6
(4)
2120151116
2418172219
Perraining
Search Space Reduction
Create Dense Attributions
An overview of the MDA method. First, the insertion process finds the patch (X,) which induces the highest M Ri Pk+1) at each step & (a) until the M reaches T = 0.9 (b). This produces the minimum ordering needed for good insertion performance. The remaining patches are found through deletion, where the patch which induces the lowest MR is selected each step (c). This yields single, optimized ordering of the patches (d). Next, the produced M R informs the magnitude
Figure 2:
of each patch to be set such that M = DR (e) (see Figure 3 for details). This yields a sparse, high-scoring attribution. The final attribution is upscaled the image size.
None of these existing approaches use the attribution quality metrics to generate attributions. By leveraging the metrics' ability to measure attribution quality, we propose to generate attributions that optimize the metric scores, creating high-quality attributions from the source of their evaluation.
METHODOLOGY
We propose MDA, the first attribution method which generates explanations by directly maximizing attribution quality metric scores. The framework consists of four components: two core optimization steps which generate an attribution and two add-on steps for calibrating and speeding up the process. First, we order the patches to maximize insertion and deletion scores. Second, we set the magnitude of each patch to maximize the MAS insertion and deletion scores. The initial two steps produce sparse attributions with high qualitative scores. Third, we introduce a sliding parameter to allow the creation of dense attributions at the expense of lower score. Fourth, we present techniques to control the runtime complexity. An overview of the framework is illustrated in Figure 2
3.1 PATCH ORDER OPTIMIZATION
In this section, we describe our patch order optimization technique that orders the M patches of the ViT in terms of model importance, which illustrated in (a) through (d) Figure [ The objective of the optimization is to determine the patch order Z which maximizes the insertion and deletion scores. Recall from Eq that the insertion and deletion scores are only function of the patch order. A potential challenge is that the ideal patch order for insertion may be conflicting with the ideal patch order for deletion. Therefore, our approach attempts to determine a patch order which maximizes the joint insertion and deletion scores. We observe insertion is only sensitive to the order of the first few patches whereas deletion is sensitive to the order of all patches. We utilize this by first determining the patches needed for strong insertion score, and then find the remaining patches using deletion. We now describe the method for optimizing the insertion and deletion patch orders.
Insertion-Based Based Patch Ordering: Starting with the blurred input image Po. the MDA framework finds the patch X; that produces the strongest model response and inserts it into the patch order I, which is illustrated in Figure The process of iteratively inserting patch mimics the method for computing the insertion score metric and is therefore expected to score well in terms of insertion. Formally, the patch X; is found directly from the model response follows:
arg max M (PPk + X.) SEZ
where is the index of any patch X, not already inserted in Pç. Next, PA+1 is set to PA + X,. This process of inserting patches X, and updating Ps is repeated until C patches have been inserted, where
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Inpu!
Mean
1.0
Mean MR and AD Zoom
MDA
30
Perturbation Faromtage
50
350
Pesporse
0.8
0.6
Patch
Deletion
16:30 29
48
11
21
19:47
46
2.0
Mean Mil and Al
Mean MR AD
59
22
0.2
25
24.43
Mean
Percentage
MAS Del = 0.037
Perturbaticn Percentage Percrtaatt
Perurtation Porcentago
Measure MR Ins and Del
Find the Mean MR and solve for AD
Set DR AD (c)
(a)
(b)
Figure 3: Given the original image and the patch order, we find M R and M Rddel (a). M Rddel is transformed and averaged with M R'ne to find M Rmean and a quadratic solver finds the new curve AD from M Rmean (b). Note in the zoom, it be observed that AD is monotonically increasing and has a strictly monotonically decreasing derivative. The AD curve is used to assign patch magnitudes, producing high MAS score, attribution (c).
MR(Pc) 2 T MMR(PN) with N = 2 In practice, we set the parameter T to 0.90. The patches determined by the insertion-basee ordering process are shown in Figure Next, the remaining M C' patches are determined using the deletion-based patch ordering process.
Deletion-Based Patch Ordering: Now, we address the deletion test which transitions from the original image with a high model response to a black image with a low model response. Ideally, each deletion generates decrease in the model response and patches which contain the most important class information will evoke the smallest model responses (a large decrease in model response). Intuitively, may seem obvious to find the patch which creates the largest decrease in the model response at every step. However, in deletion, all important features must be removed to have significant decrease in the model response. One ablated patch on an important feature may not remove enough information to change the model response. We therefore reverse the deletion problem to be a modified insertion problem and aim to minimize the insertion score.
We begin with black, low model response image and move towards the original, high model response image. every perturbation step, we find the patch that has the lowest model response:
arg min M R(Px + X2).
(5)
This produces patch order sorted from least to most important, which when reversed, yields the ideal deletion order. As seen in Figure 2 the C' patches found from insertion are an input to deletion and locked as the C' most important patches. Figure 2 (c) shows the least important patches are modified first, and the final patch order (best deletion order), is found in Figure (d).
3.2 PATCH MAGNITUDE OPTIMIZATION
The patch order I from the previous optimization step maximizes the insertion and deletion scores. Therefore, the objective of the patch magnitude optimization is minimize the MAS alignment penalty while preserving the patch order I. thus maximizing the MAS score. Let Ij and A, denote the ordering index and attribution magnitude of patch i, respectively. We wish assign a magnitude to each patch such that the order I is respected as follows:
A > Aj if I I,, J
(6)
The patch order I inherently defines the curves Rins and M Rdel seen in Figure (a). To minimize the alignment penalty AP, the density response DR should be set to be equal to both the model response M gins and M Rdel which is impossible if M Rins and M Rdel are not identical. Therefore.
3
we first combine M pins and M Rdel into M Rinean as:
(MRis + +1 M Rdel))
M.
(7)
2
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where (1 - -MR transforms M R to increase like MR seen in Figure 3 (b). Now, can perform DR M RmRen by setting the attribution value of each patch A, as follows:
A M
MR Ri MR M
(8)
where A M Ri M Ripenn and M Ry = However, the assignment of the attributions using Eq (8) does not ensure that the initial patch order would be preserved, i.e., the constraint on the relative ordering of the patches in Eq (6) may be violated, which would in turn change the model response and insertion and deletion scores. For example, if the patch ordering I (1.2.3) generated (8) yields A = 3, A O, and A3 = 1. These assigned attributions result in revised patch order I (1,3,2) 2} which inconsistent with the initial ordering of the patches. We explain this behavior in the following paragraph.
the model response M Rmman 30.3, 3, 4), then Eq
To determine the attributions using Eq we specify new attribution definition (AD) curve which is similar to M Rmmeen and minimizes the alignment penalty. However, we require the curve to satisfy two additional properties which ensure the patch order preserved, i.e., Eq (6) is satisfied.
1. Property 1:
The curve AD must be monotonically increasing.
2. Property 2: The derivatives of the curve AD must be strictly monotonically decreasing.
The properties from two observations. 1) All attributions A, are positive, so AD by definition, monotonically increasing. 2) From Eq (8). it can be understood that AD; A₂ therefore, to preserve the order for all A,, is implied that AD' must be strictly monotonically decreasing.
We formulate the problem of specifying the curve AD, as follows:
N
Minimize
Σ (AD:
M R.meaay
N
1=0
[AD (+1 S ADD vie [0 AD; E [0, Vi N]
(9)
subject
ADd = and ADN =1
The objective to minimize the quadratic distance between AD and Rmean under the linear derivative constraint. This is clearly a quadratic programming problem and quadratic solver is used find the solution. Two additional constraints are placed on the range of the function and the endpoints to ensure the final result does not escape the original model response definition.
One final problem remains after finding AD. Due the I limitation of the quadratic programming problem, AD has monotonically non-increasing derivative, so Eq (6) is not satisfied. For example, AD = 00, 2, 4] gives A 2 and A 2, implying I, = I2 which is impossible. We introduce a patch order term to Eq 8 to induce the monotonically decreasing derivative property:
N N
A AAD; (AAD,
(10)
where AAD; = AD; AD;-AD;-1 The additional term ensures A, > A411 where AD" 0. For large N. this second term does not increase the AP significantly. We visualize the magnitude optimization in Figure (a) to (c). The final x M attribution is upscaled to the input image size.
3.3 MAGNITUDE OPTIMIZATION FOR DENSE ATTRIBUTIONS
The MAS metric for evaluating attributions encourages the creation of sparse attributions. We call set of attributions sparse if they indicate the minimum amount of information needed for accurate model prediction. On the other side of the spectrum, dense attributions indicate all features of an object which are relevant to accurate prediction. We provide an optional modification to MDA which allows user to specify if the generated attributions are sparse, dense, or a mixture of the two.
Given A sperse as defined from Eq (10,, we find the dense attribution A dense by assigning all important patches magnitude which represents their order:
N sparse
A Aparse 2 K if A.
A dense
(11)
sparse < K

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Insut
NDA
MDA
VDK
Input
MDA
NDA
MDA
MAS Inc 751 1453 = 0.420 Density Response
MA5 - 2.60 MAS Del 0.411
MAS Ins 0.676 MAB Dal 0.421
M45 Ins 3.843 MAS Del 0.088
MAS Ins - 345
MA5 Ins 641 MAS Del 0,07
MA8 Dal 0.074
Pensity Response
Pensity Responge
Density Response
Density Resporce
pensity Responce
1.3
Respero
Nooggne
0.0
Partarbationn
300
100
300
Parturtation
Petturbation
300
Perturtation
y=
==1
y=
y=
Figure 4: We illustrate MDA for the transition - For the elephant, the attribution grows as the magnitude is more evenly spread among features (seen by the more linear DR), indicating only the tusks are needed for classification. For the spider, the DR and attribution do not greatly change, indicating all features of the spider are important for classification.
The parameter controls the model importance cutoff since A, R AMR, In practice, we employ k 0.005 to only strongly attribute patches with more than 0.5% model importance.
We now introduce user-controlled parameter y blend between A Aeporse and dense where y and = 1 yield sparse and dense attributions, respectively:
A = (1 7) aparee dedesse
(12)
In Figure 4 we illustrate this for large and small subject. We see for the large subject, the attribution expands to cover all features, resulting in a more linear density response. For the small subject, the attribution does expand, indicating all important features were already used for classification. A user can tune r to their choosing, but, quantitatively, the best explanation is created with = 0.
3.4 SEARCH SPACE REDUCTION
In this section provide solutions improving the runtime of MDA. A naive implementation of the optimization search over the M coarse- caass--rained ViT patches results in O(M*) runtime. This optimization problem resembles the knapsack problem. but we camnot reduce the search space through common techniques such memoization or tabulation. In this problem, unlike knapsack, the next optimal value M R( Pk++1) 1) is unknown and cannot be assumed be additive, i.e. M R Pi + X.) * MR(P)) + MR(Po X,) where each X, was previously enumerated in the search for PI.
As typical techniques will not work, we take heuristic approaches to reduce the search space, approaching the absolute minimum ((M²) runtime. First, the insertion optimization phase is improved. As we terminate the insertion optimization when we find the C patches needed to produce an MR 0.9 reduce the search space O(CM?). Across 100 images, only 48 48/196 and 6.5/49 patches were needed to reach this model response for the ViT-base 16 x 16 and ViT-base 32 32 models, respectively, resulting in ((M3) insertion search space. For deletion, the order of all patches is needed, so an early stopping technique cannot be employed, yielding a runtime of (MM)). However, we can prune the search space both insertion and deletion.
We can take advantage of the existing VIT attribution method space, and use a SOTA explanation to provide initial ordering of the patches in the image. We choose Bi-Attn (Chen al. 2023) due its low computational cost and strong performance among other ViT methods. For insertion, the input attribution provides an ordering of all patches from high to low magnitude. We use this ordering to inform a smaller search space, i.c. instead of searching through all M k patches not inserted in each step k. we search through the first 2M patches in the ordering which we can assume are valuable to the model. For deletion, the input attribution provides an ordering from lowest to highest value and we search through the first 2M patches in the ordering which we can assume are not valuable to the model. These two steps combined reduce the runtime from ((M*) to O(M²) O(M*) (M)3) and finally, we can approach (MM²) with batched execution. The runtime could be reduced to the minimum ((?)) by selecting M patches at every insertion step instead of 1. but this requires better attributions than what exists to avoid a significant quality penalty. We now evaluate the proposed MDA method with and Bi-Attn (Chen et al. 2023) input.
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4 EXPERIMENTAL EVALUATION
In this section we present qualitative and quantitative evaluations of the proposed MDA VIT attribution method. We perform all experiments using PyTorch (Paszke et al. 2019) and use the ImageNet 2012 validation dataset (Russakovsky et al. 2015) and the ImageNet Segmentation dataset (Guillaumin al. 2014). We employ three ViT models: ViT-base 16 16, ViT-tiny 16 x 16, and ViT-base 32 32 as denied in the ViT paper (Dosovitskiy et al.] (2020). These models are trained on ImageNet and are from the PyTorch Image Models repository (Wightman) 2019). The experiments were run on one server with four NVIDIA A40 GPUs. We compare our method against GC (Selvaraju et al. 2017). IG (Sundararajan al. 2017). T-Attn (Yuan et al., (02T), T-Attr (Chefer et 2021a). VIT-CX (iie et al. 2023). TIS (Englebert et al. 2023), and Bi-Attn (Chen et al. 2023).
4.1
QUANTITATIVE EVALUATION
In this section, we provide quantitative evaluation of our MDA method's performance, and evaluate the parameters used in MDA. We will first evaluate how MDA performs in the perturbation tests that we have have optimized the framework for (Petsiuk et al. 2018 Walker et al. 2024). Next, we evaluate how these optimized attributions perform for three other metrics: pointing game (Chefer et al. 202 positive and negative perturbation (Chefer et al.] 202 l De Young et al. (020). and monotonicity (Arya et al. 2019p. D.. Following these, we evaluate how MDA is affected by the selection of hyperparameters: 7, and K. Lastly, we evaluate runtime. Due to space constraints and their lower importance, we defer evaluations of monotonicity, T, y, and x: to the Appendix.
Optimized Perturbation Metric Evaluation: We have thoroughly described insertion, deletion, and the MAS variants in previous sections. For these tests, all input images are 224 x 224px and we use step size of 224px, for total of 224 perturbation steps in the original implementations. Additionally, for insertion, we use a blurring kernel which results in a softmax score of less than 1%, to improve test accuracy. We use the code provided by the repositories for insertion/deletion and MAS (Petsiuk et al.) 2018 Walker et al. 2024). The results in Table [ all 8 attribution methods over 5000 Image Net images with images per class for the perturbation metrics. We significant improvements by MDA in all tests, except for deletion, where it faces a loss. We see minimum improvement of 9% in insertion deletion, and a maximum improvement of 51% in MAS insertion deletion. The deletion performance of MDA is easily explained by the definition of our patch order optimization. As we optimize the first few patches for a high insertion score, deletion can be penalized as a result (we explore this in A.6). However, as shown by insertion deletion scores, joint optimization nets a positive improvement over all attribution methods. We show the results of this test on ViT-base 32 x 32 and ViT-tiny 16 x 16 models in Tables 4 and S in the Appendix.
Pointing Game Evaluation: In the pointing game, we measure the intersection-over-union (loU), mean average precision (MAP), and Fl scores of each method's 's pointing accuracy when compared to ground-truth segmentation maps of ImageNet Segmentation data. This test uses the default code available in the original author's 's repository (Chefer et al. 2021bb. For each attribution method, threshold is applied, binarizing the attribution to make pointing game accuracy measurements. The metric authors use an attribution's 's mean the threshold. However, since this threshold equivalent to in MDA we select the best for MDA given the three output scores. The results are shown in Table 2 for the ViT-base 32 x 32 model. First, see that choosing the ideal y for MDA to perform
Table 1: Evaluation of MDA the optimized metrics for the ViT-base 16 16 model.
Metric From
Petsiuk al.
2018
Metric From Walker et al.
2024
Test Type
Ins (t)
Del (L)
Ins Del (t)
Ins (1)
Del (L)
Ins Del (t)
GC Seevaraju et al. 2017
0.737
0.241
0.496
0.622
0.312
0.311
IG (Sundararajan et al. 2017
0.741
0.222
0,518
0.623
0.349
0.274
VTI-CX (Xee al. 2023
0.722
0.236
0,486
0.582
0.408
0.174
T-Attn Yuan al. 2021
0.748
0.228
0.520
0.631
0.347
0.284
T-Attr Cheter et al.
2021a
0.741
0.232
0.508
0.638
0.331
0.307
Bi-Attn (Chen et al.
2023
0.760
0.218
0,542
0.649
0.320
0.329
TIS (Fagllbert
2023
0.761
0.196
0.565
0.615
0.385
0.230
MDA (ours)
0.856
0.232
0.624
0.775
0.279
0.497
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Table ImageNet segmentation results for the ViT-base 32 32 model.
Metric
MAP
IoU
F1
GC (Selvaraju ct 2017
0,715
0.570
0.366
IG (Sundararajan et al. 2017
0,687
0.573
0.462
VIT-CX (X1e et al.
2023
0.678
0.535
0.428
T-Attn Yuan al. 2021
0.705
0.594
0.465
T-Attr CCeter et al.
2021a)
0.758
0.648
0.459
Bi-Attn (Chen et
2023)
0.753
0.653
0.491
TIS (Englebert et al.
2023
0.705
0.586
0.460
MDA (ours)
0.796
0.702
0.487
MDA Focused (ours)
0.760
0.661
0.504
well on all three tests leads to a win for MAP and loU, but a minor loss for F1. However, we choose achieve an F1 win while retaining win in MAP and IoU. These results show that optimizing MDA for insertion and deletion extends to high performance in other metrics, making MDA more valuable.
y such that F1 score is prioritized,
Positive and Negative Perturbation Evaluation: The positive and negative perturbation tests functional similarly the optimized metrics, but measure prediction accuracy instead of softmax score. They measure an attribution's ability to explain the model with two-stage process. First, for given set of validation images, an attribution is made for all images. Following this, the pixels of the images are gradually masked, and the resulting accuracy is recorded at each step, forming curve. In positive perturbation, pixels are masked in largest attribution order, and in negative perturbation they masked in lowest attribution order, thus lower and higher AUC scores are better, respectively, We perform these tests with the default code available in the original author's 's repository (Chefer et al. 2021b) using the ImageNet validation set (Kussakovsky al. 2015) the ViT-base 32 32 model and we show the results T In this table we clearly see MDA outperforms the SOTA methods in both tests. These indicate not only that MDA best orders the most important features but also best orders the least important features. Since this test measures via model accuracy and not softmax score, we can confirm MDA was not optimized for this test, yet still outperforms all methods.
Table 3: Positive and negative perturbation tests for the ViT-base 32 32 model.
Metric
Positive (L)
Negative (1)
GC (Selvaraju al. 2017
0.199
0.637
IG (Sundararajan an et at. 2017
0.128
0.698
ViT-CX (Xie et al. 20233
0.143
0.708
T-Attn Yuan et al.
2021
0.140
0.714
T-Attr (Cheter a..
202
0.140
0.708
Bi-Attn (Chen et al.
2023
0.124
0.733
TIS (Englebert et
2023
0.126
0.741
MDA (ours)
0.122
0.789
Runtime Evaluation: We measure the mean runtime of MDA be 13.34s, 3.64s, and 1.13s, for the ViT-base 16 x 16, ViT-tiny 16 x 16, and ViT-base 32 x 32 models, respectively, We provide comparison of these times with SOTA attributions in the Appendix and provide further discussion about the value of online and offline attribution methods.
4.2 QUALITATIVE EVALUATION
In this section we perform qualitative MDA selection and compare MDA against the SOTA methods. In the Appendix, extended these evaluations and explore seed attribution selection.
Evaluation of 7: We compare MDA with y = and y = on the ViT-base 32 x 32 model against Bi-Attn in Figure 5 and make three distinctions. First, existing SOTA methods suffer from attribution on unimportant features, hurting quantitative and qualitative value. Second, at a low 7 MDA provides minimal information attributions, indicating only the most important features. Third,

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Bi-Attn MAS Ins 0.601
MDA (sparse) MAS Ins = 0.764 Del 0.431
MDA 1 (dense) MAS Ins 0.732
Input
MAS Del 0.484
0.433
Attribution on unimportant features
Minimum important attributions
Minimal background attributions
All important attributions
Figure 5: MDA has major visual improvements over the state-of-the-an methods. Unlike BitAttn (Chen et a 2023), MDA does provide attributions for any features unrelated the class subject. In addition, it can provide a sparse or dense attribution while scoring more favorably.
MDA y
MDA
MDA
Input
GC
VIT-CX
T-Attn
Bi-Altn
T-Attr
TIS
2 0.5 2
cruma bird
bulbul
bighom
black swan
Figure 6: In the selected ImageNet examples we compare MDA with 7 = 7 0.5, and 7 1 against GC (Selvaraju et al., 2017), IG (Sundararajan et al. 2017 T-Attn Yuan et al. (021). T-Attr (Chefer et al. [2021a). ViT-CX (Xie et al. (203)). TIS (Englebert al. 2023). and Bi-Attn (Chen et al.. 2023). We see in all examples, MDA y = O provides the best sparse attribution with no background attributions. As y increases, MDA provides dense attributions which lack unimportant attributions.
MDA at a high y provides dense attributions, highlighting all important features, while avoiding unimportant features. We see this behavior continues in additional examples in the Appendix.
SOTA Comparison:
We present four qualitative comparison examples from the ImageNet dataset in Figure 6 for the ViT-base 32 x 32 model. We show MDA with y 0. 0.5, and y across mix of images with a large and small subject. For all examples, = provides a sparse, minimal information attribution which highlights the most important features. As y moves 1, attributions cover more of the image subject and stay retained to the image subject. In all examples, MDA provides reduced attributions on unimportant features when compared to the existing state-of-the-art ViT attribution methods. We show 255 more examples in Appendix A.10 equally divided among the three models. We see the behavior shown in this figure continues across the images presented, indicating that MDA provides more valuable attributions than state-of-the-ar methods.
CONCLUSION
We propose the first-of-its-kind Metric-Driven Attribution for the vision transformer. Through two core optimization objectives, MDA generates attributions which perform highly in the insertion, deletion, and MAS attribution quality metrics. The first objective finds an ideal patch order which jointly maximizes insertion and deletion scores. The second objective finds the ideal magnitude of each patch to jointly maximize the MAS insertion and deletion scores. The result a high-scoring, sparse explanation for only the most important features in image. Through modification of the objective, MDA can additionally create dense attributions, allowing a user to choose the sparse-denss balance. Across three ViT models, MDA shows significant performance gains over SOTA methods, further motivating optimization for attribution metrics. Due to its design, MDA can be applied to any input perturbation metric. The problem of defining the ideal metric is still open, and MDA can evolve with new metrics to create stronger attributions.
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ACKNOWLEDGMENTS
This material is based on research sponsored by DARPA Agreement FA87500-----0-000000 DOE Awards: DE-SC0023494, DE-SC0024428, and DE-SC0024576, and startup funds from the University of Florida. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of DARPA, DOE, or the U.S. Government.
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A APPENDIX
In this section, we present extended quantitative and qualitative results. First, we present the additional tables referenced in the experimental evaluation to present results across all three models. Then, present detailed and extensive qualitative results across all three models.
A.1 LIMITATIONS
In this work, we compare MDA against seven SOTA VIT attribution methods. We recognize that portion of the quantitative tests are performed with perturbation-base attribution quality metrics. While MDA only explicitly optimizes for the RISE and MAS tests, it can be considered an advantage compare against other XAI methods on any perturbation-baser metric. All XAI methods compare with are implemented via their recommended parameters, but it is conceivable that their performance could be "optimized" via careful tuning of their input parameters. However, we note that MDA does not require any parameter tuning and will always produce an optimized result, avoiding undue burden on user. Furthermore, MDA shows superior performance over all compared SOTA methods on the ground-truth ImageNet segmentation test which MDA does not optimize for, thus showing it can maintain its position as the new SOTA in an unbiased test.
A.2 EXTENDED OPTIMIZATION METRIC EVALUATION
We include Tables and which provide the results of the main experimental comparison for the ViT-base 32 x 32 and Vii-tiny 16 x 16 models. The results seen in these tables are consistent with the Table T The only difference in Table 3 where the winner of deletion is ViT-CX. However, referencing Figure 7 deletion, and MDA would clearly win over ViT-CX in deletion if optimized solely for deletion. In Table 4 note maximum improvement of 73% in MAS insertion deletion.
still conclude this is due to joint optimization of insertion and
Table 4: Evaluation of MDA on the optimized metrics for the ViT-base 32 x 32 model.
Metric From Petsiuk 2018
Metric From Walker et al. 2024
Test Type
Ins (1)
Del (1)
Ins Del (t)
Ins (t)
Del (L)
Ins Del (t)
GC (Selvaraju ct al. 2017
0.783
0.262
0.520
0.695
0.339
0.356
(Sundararajan
2017
0.805
0.206
0.598
0.575
0.425
0.151
VTT (Te ei al.
2023
0.813
0.208
0.605
0.615
0.389
0,226
T-Attn Yuan et al.
202T
0.797
0.222
0,576
0.578
0.427
0.151
T-Attr (Cheter et
2021
0.798
0.221
0.576
0.650
0.358
0.292
Bi-Attn (Chen et al.
2023
0.826
0.205
0.621
0.613
0.396
0.216
TIS (Englebert et al.
2023
0.847
0.176
0.671
0.643
0.370
0.273
MDA (ours)
0.908
0.200
0.708
0.851
0.235
0.616
Table 5: Evaluation of MDA on the optimized metrics for the ViT-tiny 16 x 16 model.
Metrie From
Petsiuk al. 2018
Metric From Walker ct al.
2024
Test Type
Ins (1)
Del (L)
Ins Del (t)
Ins (t)
Del ())
Ins
Del (f)
GC (Selvaraju al. 2017
0.729
0.252
0.477
0.623
0.323
0.299
(Sundararajan
2011
0.745
0.233
0.512
0.627
0.355
0.272
VIT-CX (Xie el al.
2023
0.719
0.155
0.563
0.548
0.387
0.161
T-Attn Yuan al.
202T
0.752
0.239
0.513
0.635
0.354
0.281
T-Attr (Chefer et
2021
0.745
0.243
0.502
0.643
0.339
0.304
Bi-Atta (Chen et al.
2023
0.764
0.228
0.536
0.654
0.328
0.326
TIS (Englebert et al.
2023
0.764
0.207
0.557
0.617
0.389
0.228
MDA (ours)
0.858
0.241
0.617
0.777
0.289
0.488
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A.3 MONOTONICITY EVALUATION
The last quantitative attribution metric we include is the monotonicity test (Arya et al. 2019). This test measures if inserting all features in order of largest attribution value will lead to monotonically increasing curve model confidence. Starting from a blurred image, features are inserted and the confidence of the image class prediction is measured. Over all features, this creates the confidence vector c. This vector is then compared to a feature order vector o which denotes the descending token importance. Monotonicity is then measured as MONO p(o, c), where p(.) is the Spearman correlation of the vectors, and a higher score means is more monotonic. We report the results in Table for the ViT-base 32 x 32 model using 100 ImageNet validation dataset images. We see MDA significantly improves over the SOTA methods. This further proves that MDA meets objectives outside of its optimization targets, showing its value as an effective attribution for ViT models.
Table 6: Monotonicity comparison on the ViT-base 32 x 32 model.
Metric
Monotonicity (1)
GC (Selvaraju et al. 2017
0.798
IG
Sundararaaa ct al. 2017
0.791
ViT-CX [Xie ct al.
2023
0.775
T-Attn Yuan et al. 202
0.782
T-Attr (Cheler el al.
202
0.788
Bi-Attn (Chen et al.
2023
0.783
TIS (Englebert el al.
2023
0.770
MDA (ours)
0.820
A.4 QUANTITATIVE EVALUATION
We now explain the deletion loss in Tables and 5 with an ablation study of r in Figure 7 In graph (a). the dots represent the insertion and deletion scores of the attributions and in (b), the dots the MAS scores. Better overall scores are closer to the origin. The 11 dots are generated by varying from 1 to 0 (decreasing by 0.1 left right). As decreases, the deletion score improves and insertion suffers. When T = 1, MDA is optimized solely for insertion (only a blurred baseline is used) and when r = 0, it is optimized for deletion only (only a black baseline used). This is in contrast the implementation of 0.9 which leads to joint insertion and baseline patch ordering, thus both the blurred and black baselines are used, respectively. We circle T = 0.9 in red and draw boundary across the MDA dots. We observe no SOTA methods pass the boundary, signifying there exists configuration of MDA which can win both tests. (c), we show selecting т 0.9, on average, provides peak in the joint scores, indicating it is the correct choice. This analysis was performed on 100 ImageNet images for the ViT-base 32 x 32 model.
Insertion and Deletion for MDA with Varied
MAS Insertion and Deletion for MDA with Varied
Ins Del vs
MDA
MAS Deletion Score
Inseetion-- Deletion
0.7
Derebin Score
GC
VIT-CX
0.4
0.6
T-Attn
T-Attr
0.3
0.5
Ins -el
0.2
Bi-Attn
MAS ins Del
0.875 0.825 0.800
0.5
Insertion
Insertion
(a)
(b)
(c)
Figure 7: We illustrate the impact of r for the insertion, deletion (a) MAS tests (b), and insertion deletion (c). In (a) and (b), a score near the origin is better and we circle 7 = 0.9 in red. We draw boundary across all MDA points and compare the SOTA attributions. We see method breaks this boundary, indicating there is always configuration of MDA which will perform best. We show 0.9 provides the peak score (c), verifying it is the best choice for joint optimization.
We present in Tables 7 and 9 tabular data of this 7 experiment for the ViT-base 16 x 16, ViT-tiny 16 16, and and ViT- base 32 x 32 models when only MDA is considered. As expected, we see for all models that MDA optimized for insertion (r = 1), deletion (r = 0), or with joint optimization (T 0.9) will perform the best on the insertion, deletion, or insertion deletion tests, respectively.
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Table Evaluation of MDA optimization of insertion or deletion on the ViT-base 16 16 model.
Metric From Petsiuk al. (2018)
Metric From Walker et (2024)
Test Type
Ins (t)
Del (L)
Ins Del (t)
Ins (1)
Del (1)
Ins Del (1)
MDA Insertion
0.888
0.501
0.387
0.875
0.649
0.226
MDA Deletion
0.710
0.151
0.559
0.581
0.216
0.364
MDA (ours) 0.864
0.259
0.605
0.781
0.309
0.472
Table 8: Evaluation of MDA optimization of insertion deletion on the ViT-tiny 16 16 model.
Metric From Petsiuk al. (0018)
Metric From Walker et al. (0244)
Test Type
Ins (1)
Del (L)
Ins Del (t)
Ins (1)
Del (4)
Ins Del (1)
MDA Insertion
0.896
0.236
0.660
0.880
0.313
0.567
MDA Deletion
0.706
0.062
0.644
0.640
0.143
0.496
MDA (ours) 0.882
0.140
0.742
0.829
0.163
0.666
Table 9: Evaluation of MDA optimization of insertion or deletion the ViT-base 32 32 model.
Metric From Petsiuk al. (0018)
Metric From Walker et al. (0244)
Test Type
Ins (t)
Del (4)
Ins Del (1)
Ins (1)
Del (4)
Ins Del (f)
MDA Insertion
0.916
0.392
0.523
0.902
0.483
0.418
MDA Deletion
0.827
0.162
0.665
0.772
0.214
0.558
MDA (ours)
0.916
0.206
0.709
0.854
0.243
0.611
Lastly, in Figure we perform a case study to illustrate that patch order is unique to each combination of optimization and baseline. In these images, the dark red represents the most important patch and the first row we compare insertion (a), deletion (b), and
dark blue represents the least important. joint optimization (c) using the black baseline. We see these combinations produce distinct patch orders as supported by the scores. In the second row: (d), (e), and (f), we compare these optimizations with the blurred baseline and see the same behavior. Finally, in (g) present the proposed joint optimization which comes from insertion using the blurred baseline (d) and deletion using the black baseline (b). Of note, we see that (b) and (d) have the highest metric scores with respect to their optimization metric due to the right baseline choice, which produces the best score when using joint optimization (g), supporting design choice of joint optimization.
Insertion Optimized
Deletion Optimized Black Baseline
Joint Optimized
Black Baseling
Black Baseline
Joint Optimized Blurred Insertion
Input
Black Deletion
Ins Score: 0.917
Ins Score: 0.909
Score: 0.882
Score: 0.830 (a)
Del Soore: 0.401
Del Score: 0,423 (c) Blurred Baseline
(b) Blurred Baseline
Blurred Baseline
Score:
Del Score: 0.376 (8)
Ins Score: 0.958
Ins Soore: 0 8.863 Score: (e)
Ins Score: 0.967
Score: (d)
Score: (f)
Figure 8: A visual comparison of the unique patch orders resulting from the various combinations of insertion or deletion optimization with black and blurred baselines and the resulting joint optimization. The darkest red represents the first patch in the order, and the darkest blue represents the last.
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A.5 RUNTIME EVALUATION
We perform a runtime evaluation of all attribution methods under comparison. We report the mean and standard deviation of method's runtime seconds over 100 ImageNet (Russakovsky 2015) images for the ViT-base 16 x 16, ViT-tiny 16 x 16 and 32 x 32 models. These results are shown Table To We see in the results that MDA is clearly slower, but its runtime in the range of 1.1 to 13.3 seconds is still very reasonable for wealwoordd use. Attributions are often discussed as being desirable for real-time use. However, we argue that the use of attributions should not be limited to real-time scenarios only. Specifically in the of MDA, we believe its slower runtime is fair trade off not only for its performance, but also its flexibility which benefits offline utilization, and its lack of need for internal model information. MDA not only achieves improvements of up to 73% over SOTA methods, but it is the sole attribution method which is flexible to user preferences in providing sparse dense attributions. This second attribute is valuable for offline evaluation of neural model, especially as 7 is applied in post without model calls such that only one MDA generation must occur to have access varied set of attributions from y [0, 1]. The flexibility could assist in debugging in ways that current attribution methods cannot.
al.
Table 10: Runtime comparison on the ViT-b 16 x 16, ViT-t 16 x 16, and ViT-b 32 x 32 models.
Mean Runtime per Image (S)
Model
ViT-b 16 16
ViT-t 16 16
ViT-b 32 x 32
GC (Selvaraju et al.
0.014 + 0.006
0.008 + 0.005
0.010 0.006
IG (Sundararajanl an et al. 2017
0.226 + 0.007
0.116 = 0.012
0,144 + 0.007
VII-CX (XIe
2023
0,519 + 0.078
0.189 = 0.020
0.609 + 0.058
T-Attn (Yuan el al.
2021
0.225 + 0.007
0.122 - 0.012
0.143 0.008
T-Attr (Cheler ct al
2021
0.049 + 0.006
0.048 + 0.008
Bi-Attn (Chen
2023
0.226 + 0.007
0.118 0.011
0.141 0.008
TIS (Englebert et al.
2023
1.104 0.015
0.171 0.011
0.359 0.015
MDA (ours)
13.344 + 0.308
3.639 = 0.649
1.130 + 0.249
A.6 QUANTITATIVE 7 EVALUATION
We compare MDA with 0.0, 0.5, and 7= 1.0 on 100 ImageNet images. Table 11 shows the ViT-base x 16 model results. As expected, MDA 7 = achicves the best scores in all tests. However, the score penalty of increasing is not extreme, indicating dense attributions are still of value. We provide results for the ViT-tiny 16 x 16 and ViT-base 32 x 32 models in Tables 12 and 13 below. We find the same results to hold true. We later provide more detailed qualitative examples to compare MDA against SOTA methods and further analyze the effect of y across the models.
Table 11:
Evaluation of MDA with varying levels of on the ViT-base 16 x 16 model.
Metric From Petsiuk et al. (2018)
Metric From Walker et al. (2024)
Test Type
Ins (t)
Del (L)
Ins Del (1)
Ins (t)
Del (L)
Ins Del (t)
MDA 7 -
0.812
0.350
0.462
0.701
0.466
0.235
MDA 0.5
0.849
0.262
0.587
0.781
0.312
0,472
MDA 7 (ours)
0.864
0.259
0.605
0.781
0.309
0.472
Table 12: Evaluation of MDA with varying levels of y on the ViT-tiny 16 x 16 model.
Metric From Petsiuk et al. (2018)
Metric From Walker et al.
2024
Test Type
Ins (1)
Del (L)
Ins Del (f)
Ins (1)
Del (L)
Ins Del (1)
MDA 7
0.861
0.159
0.703
0.792
0.194
0.599
MDA 7 = 0.5
0.882
0.140
0.742
0.827
0.163
0.665
MDA 7 0 (ours)
0.882
0.140
0.742
0.829
0.163
0.666
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Table 13:
Evaluation of MDA with varying levels of y on the ViT-base 32 32 model.
Metric From Petsiuk et al. (2018)
Metric From Walker al. (0224)
Test Type
Ins (t)
Del (4)
Ins Del (1)
Ins (t)
Del ())
Ins Del (1)
MDA 7 =
0.914
0.214
0.699
0.834
0.255
0.578
MDA 7 0.5
0.916
0.206
0.709
0.841
0.243
0.599
MDA 7 = 0 (ours)
0.916
0.206
0.709
0.854
0.243
0.611
A.7 QUANTITATIVE EVALUATION
In this section, we motivate our choice of 0.005 = 0.5% with an ablation study. In these tests we set 7 1 to activate the application of Eq [T]. From Eq (II), K determines the minimum importance a patch must have to be assigned a significant attribution value. Thus, by increasing & an attribution's 's density decreases. In the paper, we choose the small value of 0.5% importance such that all patches with any model importance are attributed. When x = 0% every patch receives a value relative to its order. When x is greater than equal to the importance of the most important patch, A densse == A sporse, In this test, we only report MAS scores (Walker et al., 2024). as changes in k do not affect insertion and deletion scores (Petsiuk al., 2018).
We use K [0, 0.1...1... 0.25, 0.5, 0.75, 1, 2, 3, 5, 10, 15, 20, 25] as percentages and we evaluate over 100 ImageNet images. Figure 9 a) plots MAS insertion deletion as function x. We see when k = 5% the attribution has approached A *ppass as the score stagnates, and when it is 0%, the attribution scores poorly. We choose a such that the attribution scores well and attributes more patches than A Asparse In (b), we plot the model importance of the highest to lowest value patches across all 100 images. This provides insight into what portion of patches are being selected with different values of k. Since the largest value here is 0.04 or 4%, we confirm >>> 5% yields Asparse on average over these images. Furthermore, we see K = 0.5% results in Eq 11 applying to nearly 60/ 60/196 patches. 0.5% provides the right balance between only attributing valuable patches (the score is high) and attributing a significant number of patches (the attribution is dense). Finally, we visually confirm this behavior with Figure 10 where we attributions, increasing ii leads to Asparse and x = 0.5% provides the best balance for A Adense
0% results in poor attributions with too many background
Insertion Deletion
Average MDA Sparse
MDA with Varied
Patch Value
Invertion Deletoon
0.03
= 0.5%
0.02
0.5%
9.3
MDA
0.01
0.00
10
25
100
150
200
Value (a)
Patch Number (b)
Figure 9: Quantitative comparison of MDA with varied k. We k 5% provides the best balance of (a) insertion deletion score and (b) number of patches strongly attributed.
MDA
MDA
MDA
MDA 0.5%
MDA
MDA
MDA
MDA
MDA 25%
Irput
0.1%%
0.2.2%%
swiin
bm
Figure 10: Qualitative comparison of MDA with varied k. We see x= = 5% provides the best choice as it consistently results in attributing all important features without attributing the background.
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A.8 EVALUATION OF MDA VS SHAP
The Shapely value sampling attribution SHAP Lundberg & Lee. 2017) ) is popular perturbation- based method that can be considered in our patch order optimization problem. To make a comparison of our MDA method to SHAP, we would first define our approach as existing between the occlusion perturbation (Zeiler Fergus 2014) and SHAP (Lundberg & Lee 2017) approaches. The occlusion method generates attributions by measuring the impact of masking only one input patch at time. However, this results in issues where relationships between input features cannot be determined, but O(M²) runtime is achieved, where M is the total number of patches. On the other hand, SHAP, if discussed in our context, would generate every possible ordering of the patches in the input image without regard to the metries and then an evaluation of each of the resulting M attributions would be made and the best scoring one would be chosen. This leads to SHAP having a runtime of (22 As benefit of our problem definition and methodical approach, we are able to greedily select the best patch at every search step, preventing an iteration over all orderings. and yielding a (M²) runtime. SHAP has runtime of 2.4s compared to the 1.1s of MDAon the ViT-base 32 x 32 model.
In addition to this, SHAP has significantly worse performance both quantitatively and qualitatively. When performing the segmentation test from Table 2 we see SHAP performs significantly worse than MDA in we see that MDA consistently provides attributions which are both focused on the interesting features of the image subject and do not focus on the unimportant background features, while SHAP struggles with localization and has significant background attributions.
losing in every test by a large margin. In addition, in Figure beloww
Table 14: SHAP vs MDA on segmentation test for the ViT-base 32 32 model
Metric
MAP
IoU
F1
SHAP (Lundberg & Lee 2017)
0.648
0.512
0.405
MDA (ours)
0.796
0.702
0.487
Elephant
Dowilcher
Moped
Warplane
Beseball
Bridge
Input
π1
SHAP
11
MDA
71
Figure 11: A visual comparison of MDA with SHAP. We see clear improvements by MDA over SHAP in all examples. MDA shows reduced background attributions and better subject localization.
A.9 EXTENDED QUALITATIVE EVALUATION
First, we provide detailed qualitative evaluation of the visual effects as MDA attributions move from sparse to dense with varying 7 across all three models. We perform this analysis in Figure 12 for the ViT-base 16 x 16 model in (a). the ViT-base 32 x 32 model in (b), and the ViT-tiny 16 x 16 model in (c). We show the results for 4 images per model as 7 transitions from 0 to by steps of 0.1. For each model, we present a mixture of images with small and large subjects. In Figure 12 (a), we see the two images with small subjects of class "rifle" and "flute" have consistent attributions for all y. This behavior indicates, for these images, the model requires all of the subject's 's features for classification and no less. For the other three images, we see the attributions across the subjects grow in intensity and density with increasing 7, indicating only subset of the subject's features provide a decision. In
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(b) identical behavior to (a), however, could be explained by the larger patches used by the 32 x 32 model which contain more information. Lastly, in (c) observe the change in attribution density with increase in is much less pronounced for the ViT-tiny model. This could be attributed to the fewer layers in the model which results in learning less specific features, thus
larger change between low and high y. This
features of any subject needed for decision be made.
This study shows the effectiveness of MDA for creating both sparse and dense attributions. Addition- ally, see studying MDA attributions with varying 7 can show behaviors otherwise unseen through analysis of current attributions which lack sparsity control. MDA can provide an understanding of the minimum required information a model needs make a decision and how this varies with model parameters, which can be valuable for choosing the best model for given application.
Input
MDA #
MDA 3.1
MDAy 0.2 MDAy 0.3 M 004
MDAy 0.5 yD
y 0.7. MDA 0.8 MDA 0.9 MDA 1.0
water ouza1
SoUp bowe
rho
tue
(a) ViT-Base 16 16
Input
MDA-=06
MDA
monaron
colle
baneball
aitinr
(b) ViT-Base 32 x 32
Input
MDA
MDA y
M -
MDA 0.3
MDA y
M 0.4 -
10A MDAY 0.7 MDA
MDA - 0.9
MDA 1.0
Egyplan CI
abelik
basoball
boogle
(c) ViT-Tiny 16 x
Figure 12: We analyze how changes in y effect the sparsity to density transition of an MDA attribution.
We for the first two ViT-base models (a) and (b) that the sparsity density transition is smooth and significant, meaning the models find many features important, but only need a few. However, the minimal transition for ViT-tiny (c), indicates the model requires more features for a decision.
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A.10 QUALITATIVE EVALUATION OF MDA SEED ATTRIBUTION
MDA as presented and evaluated in this work uses high-quality input attribution to reduce its search space. We present small selection of examples to indicate the impact this "seed" attribution has on the final MDA result. In Figure 13 we present three examples which include the following:
input 2017), 7, IG (Sundararajan et 2017), T-Attn (Yuan et al. (021). T-Attr (Chefer et al. a02 VIT- CX (Xie et al. 2023). TIS (Englebert al. 2023), and Bi-Attn (Chen et 2023) attributions, the output of MDA with each of these attributions as an input, labeled as "MDA seed", and MDA without seed. All examples are for the ViT-base 32 x 32 model and the images are from ImageNet. In the first example (a) we see a wide variety in the input attributions. large portion
image, GC (Selvaraju
GradCAM provides no attribution the bird subject, IG provides attributions of the image, and the remaining methods provide attributions on the bird with varying degrees of background attribution. However,
each MDA attribution seeded by these inputs remains both fairly consistent, and loyal to MDA without a seed. This is desirable, as the input attribution shown to destroy the performance of MDA. In (b) see the same behavior as before. The input attributions vary widely in appearance and quality, yet the MDA outputs maintain a level of consistency, although reduced from the consistency of (a). We see this pattern continue in example (c). Overall. MDA with seed provides the benefit of greatly reduced runtime without a marginal loss in quality. MDA is best used with high-quality attribution, and future nigher-quality attributions could provide better seed for better results.
GC
IG
VIT-CX
T-Attn
Bi-Attn
T-Attr
TIS
Input
MDA
vulture
MDA
MDA
(a)
GC
IG
ViT-CX
T-Attn
Bi-Attn
T-Attr
TIS
Input
MDA
ailiner
MDA GC
MDA
MDA VIT-CX
MDA T-Attn
Bi-Attn
MDA T-Attr
TIS
(b)
GC
IG
VIT-CX
T-Attn
Bi Bi-Atth
T-Attr
TIS
MDA
Pall track
MDA GC
MDA IG
MDA VIT-CX
MDA T-Altn
MDA Bi-Attn
MDA T-Attr
MDA TIS
(c)
Figure 13: We qualitatively compare the performance of MDA with various "seed" attributions used input against MDA without a seed. Regardless of seed quality, MDA provides output consistent with the unseeded version, indicating the input attribution does not have large impact on final result.
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A.11 EXTENDED QUALITATIVE VISUAL PERFORMANCE EVALUATION
We now present a large selection of attribution comparisons generated from the ImageNet validation
dataset which extend the comparisons in Figure 6 We contrast MDA with 7 0.5, and y
against IG (Sundararajan et al. 2017). GC VSelvaraju et al. 2017). T-Attn Yuan et al. 2021), T-Attr
(Chefer 202 Bi-Attn (Chen et al. (023). TIS (Englebert et al. 2023). and ViT-CX (Xie
et al. 2023). The examples are broken in to three sections, in groups of five pages. From page 23 to 27, we display attributions for the ViT-base 16 x 16 model. Pages
contain attributions for the VīT-base 32 x 32 model. Lastly, pages 33 37 contain attributions for the ViT-tiny 16 x 16 model. Across 15 pages we present 255 unique images. MDA presents the most consistent, high-quality attributions across the images and models. The transition from to 1 consistently results in a move towards a dense attribution when the model does not require all features for classification.
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Input
kG
T-Attin
TAttr
BlAAti
TI5
VIT.CX
MDA y 0.0
MDA y 0.5
MUX y 100
bee cator
awtrott
ctrincm
Pee Faard
Hommun TImE
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Inpur
GC
T:Aito
T.ArT
BiAtto
715
VTTEX
MOM y 0.0 MUA y 0.5
MDA
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Inpui
GC
T:Alto
T.Affr
Ri Artn
715
VTTEX
MiDA
MUJ y 0.3
MBA
protoo
mnn
0
OC
Semore
P-
A
miito Boor
HEAR
The
Buaa hound
25

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Input
KG
T-Attin
T-ltr
BlAAti
T15
VIT.CX
MDA 0.0
MDA y 0.5
MUX y 10
mud
hemm cop
8
tam
Englis nd
cou
26

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Inout
OC
T-Aito
T.Aif
B-Artn
T15
VTTCXX
MDA y 0.0 MDA y
MDA y= 1.
da
cowneee
scowerr TV
Jewn
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Inout
13
GCC
T-Aito
TAtttr
3iArtn
TI5
VT-CX
MDA y 0.0 MDA y 0.5
MDA y
00
mm
Samere
28

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Inout
OC
T-ltto
T.Aitr
B-Altn
VT.CX
MDA y 0.0
MDA y 0.5
MDA y 1.
Shink
remode Contral
woster
vpsigg
barenvtei
freesnt
8
8
8
29

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Inout
OC
T-itoo
B-Artn
VTTCC
MDAY= y
MDA y
MDA 1.
Tama
cooltel shakos
conwe
hodon
Chow
Pamingg
Settom
30

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Inpul
GC
T-ttto
T-Aitr
B-Altn
TI5
VT.CX
MDA y 0.0
MDA y D
MEA y
1.
recsherk
red
Seaton
polgie
diper
balence beam
31

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Irout
T-Aito
B-Altn
VITCC
MDA y 0.0
MDA y 0.5
MEA
10
burta
32

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Input
KG
T.Attin
T-Atrr
BLAArn
TI5
VIT.CX
MDA 0.0
MDA y 0.5
MUX y 10
comoreda
Norttk bxrre
Bxndeee pocdl
Scotton dec TOUL
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Input
KG
T.Atton
BLAAri
TI5
VIT.CX
MDA 0.0
MDA D
MUX y 10
Poggesi
rubber CESOO
RUAL
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Input
KG
T.Attin
Tattr
BLAAtt
TI5
VIT.CX
MDA
0.0
MDA y D
MLX, y
1,0
Spurie
airunder
backk
boatoon
35

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Inpus
6
GC
T-Aito
T-Aitr
B.Atth
T15
VIT-CX
MDA y
MBA y 0.5
MDA
Craaate SaiSs
schipinco
chan 100
CENT
white
th Cempacao
Azchim
36

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Input
KG
T-Aftin
T-Alfr
BLAAtii
TI5
VIT.CX
MDA y.0.00
MDA y D.D
MUX. y
1O
SpEcH STutt
golittun
bunio
9
Paloon
37


Reviews:
[{"review_id": "5aHUqo5lWL", "reviewer": "Reviewer_zur2", "summary": "This paper studies the attribution-based ViT explanation methods. The authors propose using attribution\nquality metrics to generate the attributions as explanation results. The designed method, Metric-Driven\nAttribution (MDA), consists of 2 steps: The first step orders the patches in terms of importance and the\nsecond step assigns the magnitude to each patch while preserving the patch order, which can generate\nsmooth results. Experiments on ImageNet indicate the superiority of MDA.", "questions": "As shown in Tables 1 and 2, the proposed MDA method exhibits performance degradation on Del (\"Metric\nFrom Petsiuk et al. (2018)\"). Is there any analysis of this phenomenon? Is this related to how the patch\norder is determined in step 1?", "limitations": "", "rating": 3, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The research question \"why are the metrics not used to generate the attributions?\" is interesting.\n2. The two-step method can reduce the runtime from O(M^4) to O(M^3).", "weaknesses": "1. Motivation.\n\n$\\Delta$-DiT: Accelerating Diffusion Transformers without training via Denoising Property Alignment | OpenReview\nThe reviewer's main concern is the motivation of this work. The proposed method MDA is exclusive to\nperturbation-based evaluation metrics, such as Ins, Del, Ins-Del, etc. However, perturbation-based\nevaluation only represents a specific aspect of desirable properties of explanation results, especially\nconsidering that there are no ground truths for explanation (otherwise, we can adopt ground truths as a\nmethod to generate explanation results). Therefore, the contribution of this work seems insignificant and\neven questionable, as the proposed MDA ignores other evaluation metrics, such as localization ability [1],\nfaithfulness [2, 3], visual quality [1], sanity check [4], etc.\n\n[1] transformer interpretability beyond attention visualization. CVPR 2021.\n\n[2] Rethinking Attention-Model Explainability through Faithfulness Violation Test. ICML 2022.\n\n[3] on the faithfulness of vision transformer explanations. CVPR 2024.\n\n[4] Sanity checks for saliency maps. NIPS 2018.\n\n2. Computational complexity.\n\nAlthough MDA reduces the search space from O(M^4) to O(M^3), it may still be slower than other\nexplanation methods, especially those not based on attributions. A detailed discussion about the\ncomputational/time complexity compared to more methods would strengthen the paper.\n\n3. Comparison to methods based on Shapley Value.\n\nThe idea is similar to Shapley Value [5, 6]. Could the author discuss the advantages and unique\ncontributions of MDA in terms of eﬀectiveness and complexity?\n\n[5] Shap-CAM: Visual Explanations for Convolutional Neural Networks based on Shapley Value. ECCV 2022.\n\n[6] A Unified Approach to Interpreting Model Predictions. NIPS 2017.", "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": "", "extra_scores": {}}, {"review_id": "FyNCCoxr28", "reviewer": "Reviewer_Q9o9", "summary": "This paper argues that attribution quality metrics should be used to also generate the attributions and proposes Metric-Driven Attribution (MDA) for explaining Vision Transformers. Based on the metric, it creates attribution maps by performing patch order-magnitude optimization across the tokens. Patches are ordered according to their importance and then assigned magnitudes. MDA is claimed to provide a smooth trade-off between sparse and dense attributions by modifying the optimization objective.\n\n\nPost discussion final comments:\nThe authors have addressed my concern regarding optimizing and evaluating the same metric. The additional experiments are convincing. While I still believe that some applications can benefit from more reliable attributions even if they are slow, I also support arguments of reviewer DmfJ and reviewer 7fM8 that this method will not easily scale to very large architectures.\n\nIn my opinion, this paper would be of interest to the research community but the rating still stands at 6. Hence, I am maintaing my score.", "questions": "Please see the Weaknesses section and write your response to the queries I have raised.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "The paper gives a sound motivation for its contribution and the proposed approach makes intuitive sense.  \n\nThe paper is well written and easy to follow. \n\nThe proposed method can control the density of attributions. \n\nBetter quantitative results are achieved and the qualitative results also look impressive.", "weaknesses": "I think not optimizing the attribution maps w.r.t. the metric (that measures the attribution quality) is intentional rather than a neglect in the current literature because there is an inherent risk of biasing the results if we use the metric itself for computing the attribution maps. Provided the metric is perfect, this is a reasonable idea. However, metrics for evaluating attribution methods are still an active research topic. I would have to wait and hear the opinion of the other reviewers on this matter. \n \nThe proposed method is computationally very expensive as the insertion and deletion processes are both iterative leading to O(M^4) complexity. The proposed method reduces the search space from O(M^4) to O(M^2) but that is still significant given 14x14 patches = 196. Moreover, the search space reduction relies on using another existing attribution method, making the solution less than elegant. \n\nReal time performance is an important criterion for attribution methods as one may require this information for every decision made by the model. Using insertion-deletion game for evaluating attribution methods, on the other hand, is an offline process so it makes more sense to use it for that purpose. \n\nDuring insertion (page 4), due you use the strongest response with respect to the ground truth? Maybe give a precise definition of model response to avoid confusion. \n\nTypos : \n“may violated” -> may be violated \n“memoization”  -> memorization", "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": "", "extra_scores": {}}, {"review_id": "1MEEEHjEae", "reviewer": "Reviewer_7fM8", "summary": "The paper is interested in a new attribution method, specifically designed for Vision Transformers to maximize the insertion and deletion metrics used for evaluating attribution methods in the literature. The method, called Metric-Driven Attribution (MDA), is separated in two stages. The first stage finds the best order of importance among all the patches, by gradually inserting patches and evaluating each time the model response. The second stage then assigns an attribution magnitude to all patch that will preserve the order found in the first stage. An additional hyperparameter is finally introduced in the attribution magnitudes, to govern the sparsity of the magnitudes. The model is then compared against different attribution methods applied to ViT models, measured using the same insertion and deletion metrics.", "questions": "- Could you provide a running time comparison with the other methods ? I noticed the mean running time per image was reported for MDA, but I would be interested in a comparison.  \n- Could this approach be applied to other types of models (CNNs for instance) by patching the inputs similarly to ViTs ? The only part specific to ViT seems to be the separation into patches of the input images.  \n- I'm not sure to understand why the ordering of the patches is found using two separate processes, since the \"deletion-based patch ordering\" is actually found by insertion of patches. From what I understood, the only differences between the two are: i) the starting image is first a blurred and then a black image, and ii) the ordering is first found from most to least important, and then from least to most important. I doubt the overall ordering found by the two processes are different between them. Could you expand more on why these two processes ? Furthermore, why start from a blurred image for insertion and from a black image for deletion ?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- **Originality**: The underlying idea of the paper of proposing method that measures attribution score with insertion and deletion is sounded and novel. \n- **Clarity**: The organization of the paper and description of the method are clear. The paper also includes multiple well-made figure that helps understand the overall method.\n- **Significance**: The method provides both qualitatively and quantitatively good attribution maps. Attribution maps are usually the type of explanation methods that aligns the most with human preference in terms of explanation. The modular design of the method is also flexible to be further improved.", "weaknesses": "- **Significance**: The major downside of the method is the runtime, as discussed in section 3.4. The runtime depends on both the granularity of the patch decomposition and the complexity of the model to analyze, in a multiplicative way since the method requires multiple forward pass to the model, from $\\mathcal{O}(M^3)$ to $\\mathcal{O}(M^4)$ depending on if the search space is pruned, where $M^2$ is the total number of patch. This can make the computation of the explanation for even a single image very expensive, but it is not compared with the other methods in the experiments. Furthermore, the method is currently limited to ViT models.\n- **Quality**: The metrics considered for quantitative evaluation are only the ones optimized for (insertion/deletion AUC scores). It would be also informative to include a comparison with other types of metrics based on having ground-truths, such as evaluating for the segmentation task using ImageNet-Segmentation, as done in the evaluation of other methods (in Bi-Attn or T-Attr methods for instance).\n- **Clarity**: The description of the metrics in section 2.1 is not really clear, and it is an important part to understand the method and the paper. Equation 2 does not correspond to the area under the MR curve, directly summing all $MR_k$ would not give the AUC. Furthermore, line 97 it is said \"MR curve is formed on the range $[0,1]$\", but it is not clear what variable is ranging in $[0,1]$ here.", "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": "", "extra_scores": {}}, {"review_id": "3UghJ7nvOa", "reviewer": "Reviewer_DmfJ", "summary": "The authors are dealing with Explainable AI subject dedicated to vision transformers. Their idea is to optimize the order of patches based on the insertion-deletion tests. This is done firstly by convert a blurry image into a sharp one and at each time-step to find the most prominent patch (until a given limit). Then, the order of the rest of patches is found by imitating the deletion process. Lastly, a process to set a magnitude per each is described.", "questions": "1) As I understand it, you are selecting an equal number of elements at each time-step ($\\frac{D^2}{N}$). Could you provide an intuition why?\n\n2) How would you suggest tuning the $γ$ parameter for an unknown image?\n\n3) Explainability could be beneficial in debugging misclassified images. It would be nice if you provide examples of misclassified cases and demonstrate how MDA addresses them.\n\nOverall, I find similarities between your approach and general spectral analysis. When moving from a blurry to a sharp image, selecting the subset of pixels that most impact classification at each time-step is somewhat corelated with examining the image’s spectrum. I believe this is good direction for further research that has potential.\n\nI still decided to give this paper a minor negative review due to two main concerns: (1) The method should be evaluated with metrics other than ins-del to ensure a fair comparison, and (2) a comparison of time efficiency is necessary, especially given its detailed discussion in the paper.\n\nThat being said, I think the idea presented in the paper is strong, and I would be willing to upgrade my rating if my concerns will addressed.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 2, "contribution": 3, "strengths": "1) The idea of optimizing based on the examining metric is interesting, and sounds novel to me.\n2) The non-technical parts are fluent and well written.\n3) considering time complexity is important when applying XAI in online real-time applications. I think it is important to pay attention to this when developing a method (even for explainability which consider mostly as offline)", "weaknesses": "1) I find it problematic that the approach uses the same metric for derivation and experimental evaluation. To show agnosticity for the evaluation metric, it is much needed to evaluate in a clean setting when the metric is not involved in the derivation process (or actually optimized by it). Two additional fair potential metrics for evaluation in addition to the one presented in the paper could be: segmentation test and perturbation test. (elaborated on the T-Attr paper by Chefer et al.)\n2) The technical parts are hard to follow, and sometimes indigestible. 1) in line 123 the notations $MR^{ins}$, $MR^{del}$ were used before definition. I would recommend define them first before using them. Moreover, in equation (3) you defined \"$\\|\\cdot\\|$ is the sum of all selected values\" (line 129) - where it appears twice in the equation and in general overlaps with the norm symbol. I would recommend not shortening it and write it explicitly: $\\Sigma_{i=1}^{M}\\|A_i\\|$ where $M$ is total number of attributions.\n3) Some evaluations are missing: a) to better understand its effect on attribution sparsity or metric scores, ablating $\\kappa$ would have been complete the ablation nicely. In a reasonable scale - something like 0 to 20-25 percentage. b) time efficiency comparison is missing and might shed light on the speed-up claims in section 3.4. (did not find also in the Supp.). A complete test comparison should include the timing of several other prominent approaches, however, I am aware that it might be difficult in the rebuttal frame-time. Thus, to have a better sense of timing, it would be nice to measure the time required to obtain explainability using your method for a single image (better to report it with std of several runs).", "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": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)