F-Fidelity: A Robust Framework for Faithfulness Evaluation of Explainable AI

## Abstract

Abstract Recent research has developed a number of eXplainable AI (XAI) techniques, such as gradient-based approaches, input perturbation-base methods, and black-box explanation methods.
Although extracting meaningful insights from deep learning models, how to properly evaluate these XAI methods remains an open problem.
The most widely used approach is to perturb or even remove what the XAI method considers to be the most important features in an input and observe the changes in the output prediction.
This approach although efficient suffers the Out-of-Distribution (OOD) problem as the perturbed samples may no longer follow the original data distribution.
A recent method RemOve And Retrain (ROAR) solves the OOD issue by retraining the model with perturbed samples guided by explanations.
However, the training may not always converge given the distribution difference.
Furthermore, using the model retrained based on XAI methods to evaluate these explainers may cause information leakage and thus lead to unfair comparisons.
We propose Fine-tuned Fidelity (F-Fidelity), a robust evaluation framework for XAI, which utilizes i) an explanation-agnostic fine-tuning strategy, thus mitigating the information leakage issue and ii) a random masking operation that ensures that the removal step does not generate an OOD input.
We designed controlled experiments with state-of-the-art (SOTA) explainers and their degraded version to verify the correctness of our framework.
We conducted experiments on multiple data structures, such as images, time series, and natural language. The results demonstrate that F-Fidelity significantly improves upon prior evaluation metrics in recovering the ground-truth ranking of the explainers.
Furthermore, we show both theoretically and empirically that, given a faithful explainer, F-Fidelity metric can be used to compute the sparsity of influential input components, i.e., to extract the true explanation size.

## 1 Introduction

EXplainable AI (XAI) methods have been widely used in many domains, such as Computer Vision (CV) (Chattopadhay et al., ; Smilkov et al., ; Jiang et al., ; Zhou et al., ; Selvaraju et al., ), Neural Language Processing (NLP) (Lyu et al., ; Luo et al., ; Zhao et al., ), Graph Neural Networks (GNNs) (Ying et al., ; Luo et al., ; Yuan et al., ; Vu & Thai, ), and Time Series (; Queen et al., ).
There are various types of explanation methods, in which the most predominant one is post-hoc instance-level explanation.
Given a pre-trained classifier and a specific input, these methods aim to identify the most important features of the model’s output.
For instance, such explanations map to a subset of important pixels in image classification (Ribeiro et al., ; Selvaraju et al., ; Lundberg, ).
Existing research has proposed a number of XAI methods to draw post-hoc explanations — such as Integrated Gradients (Sundararajan et al., ), CAM-based approaches (Selvaraju et al., ), and SmoothGrad (Smilkov et al., ).

Despite extracting useful insights about model decisions, how to faithfully evaluate and compare explanation methods remains an open challenge.
There have been some existing efforts to address this issue.
The preliminary works create datasets with “ground-truth” explanations for XAI evaluation, such as the MS-CoCo dataset in CV, (Lin et al., ), the Mutag dataset in graph (Debnath et al., ), and the e-SNLI dataset in NLP (Camburu et al., ).
However, these datasets are still limited to certain tasks and cannot be generalized.
More importantly, these “ground-truth” explanations are created based on humans’ understanding of a data sample, which may not reflect an ML model’s decision-making processes, and thus may still give unfaithful evaluations.
More recent works propose the removal strategy, which does not rely on “ground-truth” explanations (Zhou et al., ; Selvaraju et al., ; Rong et al., ; Hooker et al., ; Madsen et al., ; ; Hase et al., ; Zheng et al., ; Yuan et al., ).
Technically speaking, the removal strategy removes certain parts of an input that are deemed as (non-)important and records the changes in the model prediction.
A larger drop in accuracy when removing the important parts reflects the removed parts are indeed important and thus validates the faithfulness of the corresponding explanation method.
Specific metrics designed based on the removal strategy include
the Most Relevant First (MoRF) and Least Relevant First (LeRF) (Samek et al., ; Yuan et al., ) in CV and Importance Measures (Madsen et al., ; ) in NLP.
However, these removal-based explanations suffer from the Out-Of-Distribution (OOD) issue (Hooker et al., ), as the perturbed samples with removed features may no longer follow the original distribution.
As a result, the model predictions of the perturbed samples are unreliable, regardless of the explanation faithfulness.

To address the OOD problem, RemOve And Retrain (ROAR) (Hooker et al., ), proposed retraining the model for evaluating the explainer, where the model is trained using explanation-guided data augmentations.
However, retraining the model based on the explainer output leads to information leakage and convergence issues (Rong et al., ). An additional issue, which has been overlooked in prior works, is that the removal strategy is highly dependent on explanation size ( or sparsity).
That is, the size of the explanation part (or non-explanation part) that is removed affects the evaluation output.
In the absence of ground-truth explanations, it is not clear what fraction of the input elements should be removed as part of the explanation, which leads to inconsistent evaluations.

To address the aforementioned challenges, we introduce Fine-tuned Fidelity (F-Fidelity), a novel framework to evalute the performance of explainers. F-Fidelity leverages i) an explanation-agnostic fine-tuning strategy to prevent information leakage and ii) a controlled random masking operation to overcome the OOD issues observed in the application of prior evaluation metrics. The fine-tuning process employs stochastic masking operations, such as randomly dropping pixels in images, tokens in language, or time steps in time series data, to generate augmented training samples. This augmented data is then used to fine-tune a surrogate model. Unlike previous approaches such as ROAR (Hooker et al., ), our strategy effectively mitigates the risk of information leakage and label bias by using explanation-agnostic stochastic masks, while also offering improved efficiency as it eliminates the need to retrain the model for each individual explainer. During the evaluation phase, F-Fidelity implements a removal strategy that generates stochastic masks conditioned on the explainer output, designed to be in-distribution with respect to the masks used in the fine-tuning step, which mitigates the OOD issues observed in the application of prior evaluation metrics.

To verify the effectiveness of F-Fidelity, we
provide comprehensive empirical faithfulness evaluations
on a collection of explainers that are systematically degraded from an original explainer through controlled random perturbations. Thus the correct (ground-truth) ranking of the explainers, in terms of faithfulness, is known beforehand.
The experiments on multiple data modalities demonstrate the robustness of F-Fidelity through both macro and micro correlations. Macro correlations measure the Spearman rank correlation between the ground truth and the overall performance across all sparsity levels, while micro correlations capture the average Spearman rank correlation between the ground truth and performance at individual sparsity levels. In both aspects, F-Fidelity consistently outperforms existing methods. Furthermore, we show both theoretically and empirically that, given a faithful explainer, the F-Fidelity metric can be used to compute the size (or sparsity) of ground-truth explanations. To elaborate, we show that the F-Fidelity metric output, when evaluated a function of mask size, produces a piecewise constant function, where the length of the constant pieces depends on the explanation size. The following summarizes our main contributions:

- •
We introduce a novel evaluation framework for measuring explanation faithfulness with strong theoretical principles that is robust to distribution shifts.
- •
We design and implement a rigorous experimental setting to fairly compare metrics. Our comprehensive evaluations across multiple data modalities (images, time series, and natural language) demonstrate the superior performance and broad applicability of F-Fidelity.
- •
We theoretically and empirically analyze the relationship between the explanation size and the F-Fidelity metrics and demonstrate in F-Fidelity, the ground truth explanation sizes can be inferred.

## 2 Preliminaries

This section introduces the notation and key background concepts used throughout the paper.

### 2.1 Notation

Sets are denoted by calligraphic letters such as $\mathcal{X}$.
The set $\{1,2,\cdots,n\}$ is represented by $[n]$.
Multidimensional arrays (tensors) are denoted by bold-face letters such as $\mathbf{x}$.
Upper-case letters such as $X$ represent random variables, and lower-case letters such as $x$ represent their realizations. Similarly, random tensors are denoted by upper-case letters such as $\mathbf{X}$.

### 2.2 Classification Models and Explanation Functions

Let $f:\mathbf{X}\mapsto Y$ be a (pre-trained) classification model — such as a neural network — which takes an input $\mathbf{X}\in\mathbb{R}^{t\times d}$ and outputs a label $Y\in\mathcal{Y}$, where $\mathcal{Y}$ is a finite set of labels. In CV tasks, $t=h\times w$, where $h,w$ are the height and width, and $d$ is the number of channels per input pixel. Analogously, in NLP and time series classification tasks, $t\in\mathbb{N}$ represents the time index, and $d$ is the feature dimension. An explanation function (explainer)
consists of a pair of mappings $\psi=(\phi,\xi)$, where $\phi:\mathbf{X}\mapsto\mathbb{R}_{+}^{t\times d}$ is the score function, mapping each input element to its (non-negative) important score, and a mask function $\xi:\phi(\mathbf{X})\mapsto\mathbf{M}$,
mapping the output of the score function to a binary mask $\mathbf{M}\in\{0,1\}^{t\times d}$ . The masked input $\mathbf{X}\odot\mathbf{M}$ is called the explanation for the input $\mathbf{X}$ and model $f(\cdot)$, where $\odot$ represents elementwise multiplication. We denote the explanation size by $S=\|\mathbf{M}\|_{1}$, where $\|\cdot\|_{1}$ is the $\ell_{1}$ norm. That is, the explanation size $S$ is the number of non-zero elements of $\mathbf{M}$. In general, the size may be deterministically set to a constant value $s$, or alternatively, it may depend on the output of the score function, e.g., input elements receiving a score higher than a given threshold are included in the mask and the rest are removed.
Let us assume that the (ground-truth) data distribution is $P_{\mathbf{X},Y}$. Then, a ‘good’ explainer is one which minimizes the total variation distance $d_{TV}(P_{Y|\mathbf{X}},P_{Y|\mathbf{X}\odot\mathbf{M}})$, while satisfying an explanation size constraint $\mathbb{E}_{\mathbf{X}}(\|\mathbf{M}\|_{1})\leq s$, where $s\in\mathbb{N}$ is the desired average explanation size. The minimization of the total variation essentially enforces that the posterior distribution of the classifier output be mostly determined by the masked input explanation, implying that the subset of input components which are removed by the mask have a low influence on the classifier output.

### 2.3 Quantifying the Performance of Explainers

A key challenge in explainability research is to quantify and compare the performance of various explainers. The performance of an explainer can be formally quantified in terms the total variation distance $d_{TV}(P_{Y|\mathbf{X}},P_{Y|\mathbf{X}\odot\mathbf{M}})$ as a function of the average explanation size $\mathbb{E}_{\mathbf{X}}(\|\mathbf{M}\|_{1})$. However, in most problems of interest, the underlying statistics $P_{\mathbf{X},Y}$ is not available, and hence direct evaluation of the aforementioned total variation distance is not possible. As discussed in the introduction, some datasets are accompanied by ground-truth explanations, which enables the use of measures such as AUC and IoU for evaluating the quality explainers. However, the ground-truth explanations are available only for a limited collection of datasets, and even when ground-truth explanations are available, they may not accurately reflect the model’s internal decision-making processes.
To address the aforementioned issues, a widely used set of metrics have been proposed in the literature which are based on the removal strategy.
In CV, two removal orders have been considered (Samek et al., ; Yuan et al., ), MoRF, where the removal process begins with the most influential pixels, and LeRF, where it starts with the least influential pixels. In the graph domain, an alternative removal strategy is used, where first the size of explanation subgraphs is determined according to a sparsity parameter, and then edges are removed either from the explanation subgraph of the desired size, or the non-explanation subgraph which is its complement. In this paper, we use metrics which are based on the removal strategy used in the graph domain, called the Fidelity (Fid) metric in the literature Pope et al. (); Bajaj et al. (); Yuan et al. (). Formally, given the input and label pair $(\mathbf{x},y)$ and a binary mask $\mathbf{m}$, the $Fidelity$ metrics are defined as follows:

$$ $\displaystyle Fid^{+}(\psi)$ $\displaystyle=\frac{1}{n}\sum_{(\mathbf{x}_{i},y_{i})\in\mathcal{T}}\mathds{1} (y_{i}=f(\mathbf{x}_{i}))-\mathds{1}(y_{i}=f(\mathbf{x}_{i}-\mathbf{x}_{i} \odot\mathbf{m}_{i}))$ (1) $\displaystyle Fid^{-}(\psi)$ $\displaystyle=\frac{1}{n}\sum_{(\mathbf{x}_{i},y_{i})\in\mathcal{T}}\mathds{1} (y_{i}=f(\mathbf{x}_{i}))-\mathds{1}(y_{i}=f(\mathbf{x}_{i}\odot\mathbf{m}_{i} )),$ (2) $$

where $\mathcal{T}$ is the dataset used for evaluating the performance of the explainer, $n$ is the size of the dataset, $\mathds{1}(\cdot)$ denotes the indicator function, and $\mathbf{m}_{i}=\psi(\mathbf{x}_{i})$ is the explanation corresponding to $\mathbf{x}_{i}$ produced by the explainer $\psi(\cdot)$.

In R-Fidelity (Zheng et al., ), which considered the evaluation of GNN explainers, it was argued that the Fidelity metric highly relies on the robustness of the underlying classifier to removal of potentially large sections of the input, e.g.,the removal of a large subgraph explanation for $Fid^{+}$ or its complement for $Fid^{-}$. That is, the classifier should be robust to out-of-distribution (OOD) inputs for Fidelity metric to align with those of the (theoretically justified) total-variation-based metric discussed in the previous sections. To mitigate these OOD issues in the evaluation of the Fidelity metric, the following Robust Fidelity metrics (RFid) was introduced:

$$ $\displaystyle RFid^{+}(\psi,\alpha^{+},s)$ $\displaystyle=\frac{1}{n}\sum_{(\mathbf{x}_{i},y_{i})\in\mathcal{T}}\mathds{1} (y_{i}=f(\mathbf{x}_{i}))-P(y_{i}=f(\chi^{+}(\mathbf{x}_{i},\alpha^{+},s))$ (3) $\displaystyle RFid^{-}(\psi,\alpha^{-},s)$ $\displaystyle=\frac{1}{n}\sum_{(\mathbf{x}_{i},y_{i})\in\mathcal{T}}\mathds{1} (y_{i}=f(\mathbf{x}_{i}))-P(y_{i}=f(\chi^{-}(\mathbf{x}_{i},\alpha^{-},s)),$ (4) $$

where $\chi^{+}(\mathbf{x}_{i},\alpha^{+},s)$ is a sampling function which randomly, uniformly, and independently removes $\lfloor s\alpha^{+}\rfloor$ elements from the $s$ highest scoring elements of $\mathbf{x}_{i}$ based on the scores produced by $\phi(\mathbf{x}_{i})$, and $\chi^{-}(\mathbf{x}_{i},\alpha^{-})$ removes $\lceil s\alpha^{-}\rceil$ fraction of the lowest scoring $td-s$ elements. It can be noted that if $\alpha^{+}=\alpha^{-}=1$, then the RFid metric reduces to the Fid metric. On the other hand, as $\alpha^{+}$ and $\alpha^{-}$ are decreased, fewer input elements are removed, hence requiring lower OOD robustness to ensure the accuracy of the evaluation output. In this work, we adapt the RFid metric for general, non-graphical domains, and introduce improvements in several directions. First, we show through extensive empirical evaluation that a specific finetuning process applied to the to-be-explained classifier enable significantly more precises evaluation of explainers using the RFid metric.
Second, we show both theoretically and empirically, that by appropriate choice of the $\alpha^{+}$ and $\alpha^{-}$ parameters, one can extract the size of the ground-truth explanation by evaluating the RFid metric.

## 3 Robust Fidelity via Model Fine-tuning and Bounded Removals

As discussed in the previous section, a significant limitation of prior explanation evaluation metrics is the loss in accuracy due to the OOD nature of the modified inputs generated by the application of removal strategies. For instance, the probability difference
$P(Y=f(\mathbf{X}))-P(Y=f(\mathbf{X}-\mathbf{X}\odot\mathbf{M}))$ may be large, even for low-quality explanations. This occurs because the modified input $\mathbf{X}-\mathbf{X}\odot\mathbf{M}$ is OOD for the trained classifier $f(\cdot)$,despite $P_{Y|\mathbf{X}}$ and $P_{Y|\mathbf{X}-\mathbf{X}\odot\mathbf{M}}$ being close to each other. Consequently, this yields a high $Fid^{+}$ score despite the explanation’s low quality with respect to the theoretically justified total variation metric. For example, in the empirical evaluations provided in the next sections, we demonstrate that the Fid measure sometimes assigns better evaluations to completely random explainers than to those whose outputs align with ground-truth explanations.

A partial solution in the graph domain addresses this issue by removing only an $\alpha^{+}$ fraction of the explanation subgraph and $\alpha^{-}$ fraction of the non-explanation subgraphs (Zheng et al., ). However, we argue that two issues degrade the evaluation quality of the RFid metric. First, if the original explanation size $\mathbf{M}$ is large (small), then removing an $\alpha^{+}$ ($\alpha^{-}$) of the explanation (non-explanation) part of the input, this would still yield OOD inputs. Second, the classifier may lack robustness and produce unreliable outputs even when the input is only slightly perturbed.

To address the first issue, we modify the RFid metric so that the size of the removed part of the input is upper-bounded by a constant fraction of the entire input, rather than a fraction of the explanation, which can vary depending on the learning task. That is, for a fixed $\beta\in[0,1]$, and RFid parameters $\alpha^{+}_{orig},\alpha^{-}_{orig}\in[0,1]$, we set the upper-bounded RFid parameters as

$$ $\displaystyle\alpha^{+}=\min(\alpha^{+}_{orig},\frac{\beta td}{s})\quad\text{ and}\quad\alpha^{-}=\min(\alpha^{-}_{orig},\frac{\beta td}{s}),$ (5) $$

so that the sampling functions $\xi^{+}$ and $\xi^{-}$ do not remove more than at most $\beta td$ elements of the input.

To address the second issue, we fine-tune the classifier prior to applying the explanation method. This finetuning process is performed by taking into consideration the aforementioned upper bound on the size of the removed input. To elaborate, we introduce a stochastic mask generator $P_{\beta}:(t,d)\mapsto\mathbf{M}_{\beta}$, which takes a the input dimensions $(t,d)$ as input and outputs a mask $\mathbf{M}_{\beta}\in\{0,1\}^{t\times d}$ of size $\beta td$, i.e. with $\beta{td}$ non-zero elements. For instance, in image classification, the mask generator is designed to select random image patches for removal.
Formally, we define the fine-tuning loss function as:

$$ $L=\mathbb{E}_{\mathbf{X},Y}\left[\mathcal{L}\left(f\left(\mathbf{X}-P_{\beta} \odot\mathbf{X}\right),\ Y\right)\right]$ (6) $$

where $\mathcal{L}$ is the loss function used during training (e.g., cross-entropy).
The pipeline of our evaluation method, which incorporates the fine-tuning and upper-bounded removal techniques described above is provided in Algorithm 1. We denote the resulting evaluation metrics, which utilize the finetuning process and the $RFid^{+}$ and $RFid^{-}$ metrics with sampling rates which are truncated based on $\beta$ ( equation 5),
as $FFid^{+}(\psi,\alpha^{+}_{orig},\beta,s)$ and $FFid^{-}(\psi,\alpha^{-}_{orig},\beta,s)$, respectively.

## 4 Empirical Verification of Robustness

To demonstrate the robustness of our proposed F-Fidelity framework, we conduct comprehensive experiments across multiple domains, including image classification, time series analysis, and natural language processing. Our evaluation strategy builds upon the concept introduced by Rong et al. (), which posits that an ideal evaluation method should yield consistent rankings in both MoRF and LeRF settings. We introduce a novel approach for a fair comparison using a degradation operation on a good explanation, such as an explanation obtained by Integrated Gradients (IG) (Sundararajan et al., ), generating a series of explanations with varying levels of random noise. This method provides a clear ground truth (GT) ranking based on noise level, allowing for controlled evaluation.

We evaluate the performance of F-Fidelity against established baselines such as Fidelity (Fidelity), ROAR (Hooker et al., ), and R-Fidelity (Zheng et al., ) across a wide range of sparsity levels, from 5% to 95% at 5% intervals. Throughout our evaluation, we focus on three key Spearman rank correlations: “MoRF vs. GT”, “LeRF vs. GT”, and “MoRF vs. LeRF”. It allows us to assess the methods’ performance under various conditions, from highly sparse to nearly complete explanations. To provide a thorough analysis, we employ both macro and micro correlation metrics:

- •
Macro Correlation (Rong et al., ; Pan et al., ; Zhu et al., ): We compute the AUC with respect to sparsity across the entire 5-95% range for each explanation method. The macro correlations are then calculated using these AUC values, providing an overall performance measure across all sparsity levels.
- •
Micro Correlation: To capture fine-grained performance differences, we calculate micro correlations at each sparsity level. In the main body of the paper, we report the averaged micro correlations across all sparsity levels, as well as the average rank of each method.

### 4.1 Image Classification Explanation Evaluation

Setup. We use Cifar-100 (Krizhevsky et al., ) and Tiny-Imagenet (Deng et al., )(^1^11https://github.com/rmccorm4/Tiny-Imagenet-200?tab=readme-ov-file), as the benchmark datasets.
To obtain a pre-trained model to be explained, we adopt ResNet (He et al., ). More experiments with Vision Transformer(ViT) (Dosovitskiy et al., ) can be found in Appendix D.4. To generate different explanations, we first use two explanation methods, SmoothGrad Squared (SG-SQ) (Smilkov et al., ) and GradCAM (Selvaraju et al., ) to obtain the explanations. Then we use a set proportion of noise perturbations in the image, $\left[0.0,0.2,0.4,0.6,0.8,1.0\right]$. We provided the implementation detail in Appendix C.

Results. As shown in Table 1 and Table 2, F-Fidelity achieves superior performances across different explainers and correlation metrics. Traditional Fidelity and ROAR methods show inconsistent and often poor performance, particularly in MoRF scenarios. Fidelity suffers from the out-of-distribution (OOD) issue, leading to unreliable evaluations when features are removed. ROAR, while addressing the OOD problem through retraining, faces challenges with information leakage and potential convergence issues, resulting in suboptimal correlations. In contrast, for both SG-SQ and GradCAM, F-Fidelity consistently achieves optimal or near-optimal performance in ranking explanations. In Cifar-100, F-Fidelity achieves perfect Macro and Micro correlations for all three cases with SG-SQ. For GradCAM, it shows strong negative correlation (-0.60 to -0.71) in MoRF comparisons, significantly outperforming other methods. Tiny ImageNet results further reinforce its effectiveness with perfect correlations (-1.00) across all metrics for both explainers. Notably, F-Fidelity consistently ranks first in the micro rank evaluation for “MoRF vs. GT” and “MoRF vs. LeRF” correlations across both datasets and explainers, indicating its robust performance across various sparsity levels.

**Table 1: Spearman rank correlation and rank results on Cifar-100 dataset with ResNet.**
|  | Correlation | SG-SQ | GradCam |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Fidelity | ROAR | R-Fidelity | F-Fidelity | Fidelity | ROAR | R-Fidelity | F-Fidelity |  |  |
| Macro<br>Corr. | MoRF vs GT $\downarrow$ | -0.68$\pm$0.08 | -0.66$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | 0.81$\pm$0.03 | 0.99$\pm$0.02 | 0.20$\pm$0.11 | -0.60$\pm$0.00 |
| LeRF vs GT $\uparrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | -0.68$\pm$0.08 | -0.66$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | 0.81$\pm$0.03 | 0.99$\pm$0.02 | 0.20$\pm$0.11 | -0.60$\pm$0.00 |  |
| Micro<br>Corr. | MoRF vs GT $\downarrow$ | -0.36$\pm$0.37 | -0.54$\pm$0.35 | -1.00$\pm$0.01 | -1.00$\pm$0.00 | 0.57$\pm$0.14 | 0.76$\pm$0.07 | 0.09$\pm$0.12 | -0.71$\pm$0.02 |
| LeRF vs GT $\uparrow$ | 0.98$\pm$0.04 | 0.99$\pm$0.04 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 0.99$\pm$0.01 | 0.99$\pm$0.01 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | -0.23$\pm$0.35 | -0.53$\pm$0.34 | -1.00$\pm$0.01 | -1.00$\pm$0.00 | 0.57$\pm$0.14 | 0.75$\pm$0.07 | 0.01$\pm$0.12 | -1.00$\pm$0.02 |  |
| Micro<br>Rank | MoRF vs GT $\downarrow$ | 3.68$\pm$0.46 | 3.26$\pm$0.44 | 1.11$\pm$0.31 | 1.00$\pm$0.00 | 3.00$\pm$0.46 | 3.74$\pm$0.55 | 2.11$\pm$0.79 | 1.00$\pm$0.00 |
| LeRF vs GT $\downarrow$ | 1.11$\pm$0.31 | 1.21$\pm$0.41 | 1.42$\pm$0.67 | 1.42$\pm$0.67 | 2.05$\pm$1.39 | 1.68$\pm$1.08 | 1.21$\pm$0.69 | 1.11$\pm$0.45 |  |
| MoRF vs LeRF $\downarrow$ | 3.68$\pm$0460 | 3.32$\pm$0.46 | 1.11$\pm$0.31 | 1.00$\pm$0.00 | 3.00$\pm$0.45 | 3.74$\pm$0.55 | 2.16$\pm$0.74 | 1.00$\pm$0.00 |  |

**Table 2: Spearman rank correlation results on Tiny-Imagenet dataset with ResNet.**
|  | Correlation | SG-SQ | GradCam |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Fidelity | ROAR | R-Fidelity | F-Fidelity | Fidelity | ROAR | R-Fidelity | F-Fidelity |  |  |
| Macro<br>Corr. | MoRF vs GT $\downarrow$ | -0.69$\pm$0.07 | -0.83$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -0.97$\pm$0.03 | 0.63$\pm$0.03 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |
| LeRF vs GT $\uparrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.03 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | -0.69$\pm$0.07 | -0.83$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -0.97$\pm$0.03 | 0.63$\pm$0.03 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |  |
| Micro<br>Corr. | MoRF vs GT $\downarrow$ | -0.38$\pm$0.48 | -0.50$\pm$0.37 | -0.99$\pm$0.03 | -1.00$\pm$0.00 | -0.42$\pm$0.14 | 0.54$\pm$0.14 | -0.99$\pm$0.01 | -1.00$\pm$0.00 |
| LeRF vs GT $\uparrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.01 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 0.99$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | -0.38$\pm$0.48 | -0.50$\pm$0.36 | -0.99$\pm$0.03 | -1.00$\pm$0.01 | -0.42$\pm$0.14 | 0.55$\pm$0.16 | -0.99$\pm$0.01 | -1.00$\pm$0.00 |  |
| Micro<br>Rank | MoRF vs GT $\downarrow$ | 3.74$\pm$0.44 | 3.21$\pm$0.41 | 1.16$\pm$0.36 | 1.00$\pm$0.00 | 3.05$\pm$0.51 | 3.84$\pm$0.36 | 1.21$\pm$0.41 | 1.00$\pm$0.00 |
| LeRF vs GT $\downarrow$ | 1.11$\pm$0.31 | 1.00$\pm$0.00 | 1.16$\pm$0.49 | 1.16$\pm$0.49 | 1.47$\pm$0.94 | 1.58$\pm$1.04 | 1.16$\pm$0.67 | 1.11$\pm$0.44 |  |
| MoRF vs LeRF$\downarrow$ | 3.74$\pm$0.44 | 3.21$\pm$0.41 | 1.10$\pm$0.31 | 1.00$\pm$0.00 | 3.16$\pm$0.36 | 3.84$\pm$0.36 | 1.21$\pm$0.41 | 1.00$\pm$0.00 |  |

### 4.2 Time Series Classification Explanation Evaluation

Setup. We use two benchmark datasets for time series analysis: PAM for human activity recognition and Boiler for mechanical fault detection (Queen, ). For PAM, we use 534 samples across 8 activity classes, with each sample recorded using a fixed segment window length of 600 from 17 sensors. The Boiler dataset, used for mechanical fault detection, consists of 400 samples with 20 dimensions and a fixed segment window length of 36. We employ IG from the Captum library (^2^22https://github.com/pytorch/captum) to obtain initial explanations. To generate different explanations, we apply noise perturbations to the importance of each timestamp, using proportions of $[0.0,0.1,0.2,0.3,0.4,0.5]$ for PAM and $[0.0,0.2,0.4,0.6,0.8,1.0]$ for Boiler. For R-Fidelity and F-Fidelity, we set $\alpha^{+}=\alpha^{-}=0.5$. Other settings remain consistent with the image classification task to ensure comparability across domains.

Results. Table 3 demonstrates the robust performance of F-Fidelity across different evaluation metrics. Specifically, in the PAM dataset, F-Fidelity and R-Fidelity outperform Fidelity and ROAR in micro correlations and ranks, with F-Fidelity slightly edging out R-Fidelity in “LeRF vs GT” and “MoRF vs LeRF” micro ranks. The Boiler dataset results reveal more significant differences among the methods. F-Fidelity substantially outperforms other methods in “LeRF vs GT” and “MoRF vs LeRF” macro correlations. In micro correlations and ranks for the Boiler dataset, F-Fidelity consistently achieves the best or near-best performance across all metrics. These results underscore the effectiveness and stability of F-Fidelity in evaluating explanations for time series data.

**Table 3: Spearman rank correlations and ranks on time series datasets. The best performance is marked as bold. the “-” means the correlation can’t be obtained because of the same rank of different explanations.**
|  | Correlation | PAM | Boiler |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  | Fidelity | ROAR | R-Fidelity | F-Fidelity | Fidelity | ROAR | R-Fidelity | F-Fidelity |  |
| Macro<br>Corr. | MoRF vs GT $\downarrow$ | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -0.98$\pm$0.03 | -0.99$\pm$0.20 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |
| LeRF vs GT $\uparrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 0.22$\pm$0.03 | 0.36$\pm$0.11 | 0.53$\pm$0.06 | 0.86$\pm$0.07 |  |
| MoRF vs LeRF $\downarrow$ | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -0.27$\pm$0.08 | -0.38$\pm$0.14 | -0.53$\pm$0.06 | -0.86$\pm$0.07 |  |
| Micro<br>Corr. | MoRF vs GT $\downarrow$ | -0.88$\pm$0.39 | -0.97$\pm$0.09 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | - | - | -0.79$\pm$0.31 | -0.78$\pm$0.29 |
| LeRF vs GT $\uparrow$ | 0.74$\pm$0.33 | 0.80$\pm$0.21 | 1.00$\pm$0.01 | 1.00$\pm$0.00 | - | - | 0.69$\pm$0.35 | 0.79$\pm$0.27 |  |
| MoRF vs LeRF $\downarrow$ | -0.65$\pm$0.45 | -0.77$\pm$0.21 | -1.00$\pm$0.01 | -1.00$\pm$0.00 | - | - | -0.81$\pm$0.27 | -0.97$\pm$0.03 |  |
| Micro<br>Rank | MoRF vs GT $\downarrow$ | 1.53$\pm$0.82 | 1.37$\pm$0.58 | 1.00$\pm$0.00 | 1.05$\pm$0.22 | 2.95$\pm$0.51 | 2.73$\pm$0.71 | 1.21$\pm$0.52 | 1.52$\pm$0.50 |
| LeRF vs GT $\downarrow$ | 2.32$\pm$1.09 | 2.37$\pm$0.74 | 1.16$\pm$0.36 | 1.05$\pm$0.22 | 2.59$\pm$0.99 | 2.74$\pm$0.64 | 2.21$\pm$1.00 | 1.68$\pm$0.86 |  |
| MoRF vs LeRF $\downarrow$ | 2.37$\pm$1.09 | 2.42$\pm$0.82 | 1.16$\pm$0.36 | 1.11$\pm$0.31 | 2.95$\pm$0.22 | 2.95$\pm$0.22 | 1.89$\pm$0.31 | 1.05$\pm$0.22 |  |

## 5 Determining the Explanation Size via Fidelity Metrics

In many machine learning tasks, such as image classification and NLP,
the ground truth explanations can be discretized into distinct clusters representing different levels of importance. For instance, in image classification, pixels associated with the target object tend to receive high importance scores. Conversely, pixels corresponding to the background or irrelevant regions receive low scores.
However, in many practical scenarios, even *good* explainers that produce accurate explanation masks — as measured by the Fid and RFid evaluation metrics — may yield explanation scores that are not discretized into distinct clusters. For instance, when using PGExplainer on the MUTAG dataset (Luo et al., ), the explainer achieves over 90% accuracy in correctly ranking the influential edges of the input graph. Yet, the explanation scores are not clustered around discrete values. As a result, the size of the ground-truth explanation cannot be inferred from the explainer’s output since it provides only a ranking of edge importance without a clear separation into important and non-important edges.

In this section, we theoretically demonstrate that our proposed evaluation metric can recover the cluster sizes given an explainer that outputs the correct explanation mask (i.e., correctly ranks the importance of input elements). Thus, provided the explainer outputs an accurate mask function, our metric can recover the explanation size (also known as sparsity).
To provide a concrete theoretical analysis, we first consider a classification problem under a set of idealized assumptions that generalize the above observations on the clustering of explanation scores. In the subsequent sections, we provide empirical evaluations demonstrating the applicability of our theoretical results to real-world settings.

Specifically, let us consider a classification task defined by a joint distribution
$P_{\mathbf{X},Y}$ and a classifier $f:\mathbf{x}\mapsto y$. We assume that the input elements can be partitioned into several *influence tiers*. That is, for any given input $\mathbf{x}$, there exists a partition $\mathcal{C}_{k}(\mathbf{x}),k\in[r]$ of the index set $[t]\times[d]$, where $\mathcal{C}_{k}(\mathbf{x})$ represents the set of indices of the input elements belonging to tier $k$, and $c_{k}=|\mathcal{C}_{k}(\mathbf{x})|$ are the (fixed) tier sizes.
For a given mask $\mathbf{m}$, the probability of correct classification based on the masked input $\mathbf{x}\odot\mathbf{m}$ depends only on the counts of unmasked elements in each influence tier. Formally,

$$ $\displaystyle P(Y|\mathbf{x}\odot\mathbf{m})=g(j_{1},j_{2},\dots,j_{r}),$ $$

where $g:[c_{1}]\times[c_{2}]\times\cdots\times[c_{r}]\to[0,1]$ is a function monotonically increasing with respect to the lexicographic ordering on its input, and $j_{k}\in[c_{k}]$ is the number of elements in $\mathcal{C}_{k}(\mathbf{x})$ whose corresponding mask element in $\mathbf{m}$ is non-zero (unmasked). We further focus on Shapley-value-based explanations, which provide a theoretical foundation for our analysis. Recall that the Shapley value associated with an element $(i,j)\in[t]\times[d]$ of $\mathbf{x}$ is given as (Lundberg, ):

$$ $\displaystyle S_{\mathbf{x}}(i,j)=\sum_{\mathbf{m}:m_{i,j}=0}\frac{\|m\|_{1}!( td-\|m\|_{1}-1)!}{(td)!}(P(\mathbf{x}\odot\mathbf{m}^{\prime})-P(\mathbf{x} \odot\mathbf{m})),$ $$

where $\mathbf{m}^{\prime}$ is the mask obtained from $\mathbf{m}$ by setting $m^{\prime}_{i,j}=1$ (unmasking the $(i,j)$ element). Under the aforementioned influence tier assumption, it is straightforward to verify that input elements within the same influence tier receive equal Shapley values. Specifically, for any $k\in[r]$ and any $(i,j),(i^{\prime},j^{\prime})\in\mathcal{C}_{k}(\mathbf{x})$, we have
$S_{\mathbf{X}}(i,j)=S_{\mathbf{X}}(i^{\prime},j^{\prime})$.

###### Theorem 1 .

For the classification task described above, and a given pre-trained classifier $f(\cdot)$, consider a Shapley-value-based
explainer $\psi(\cdot)$. For $\alpha_{orig}^{+}\in[0,1]$ and $\beta\in[0,\alpha^{+}]$, let

$$ $e(s)=\mathbb{E}_{\mathbf{X},Y}(FFid^{+}(\psi,\alpha_{orig}^{+},\beta,s)),\quad s \in[0,td].$ $$

Then, $e(s)$ is monotonically increasing for $s\in[0,c_{1}]$ and monotonically decreasing for $s\in[\max(\frac{\beta}{\alpha_{orig}^{+}}td,c_{1}),td]$.

The proof is provided in the Appendix.

This theorem shows that $FFid^{+}$ can recover the size of the most influential tier (i.e., the first cluster size) when the explainer’s ranking is close to that of an ideal Shapley-based explainer. Specifically, the value of $s$ in which $FFid^{+}$ changes direction corresponds to the size of an influence tier.
This is verified in the empirical evaluation provided in Section 6.
This result implies that even when an explainer provides continuous scores without distinct clustering, our metric can infer the underlying discrete structure of the ground truth explanations and recover the explanation size.

###### Theorem 1 .

## 6 Emprical Verification of determining the Explanation Size

In this section, we demonstrate empirically that the $FFid$ metric can be used to deduce the size or sparsity of explanations, complementing the theoretical analysis of Section 5. Specifically, we consider the colored-MNIST dataset (Arjovsky et al., ), where the explanation corresponds to the pixels representing the digit in each image. To control the explanation size, we rescale and crop the image samples so that the digit pixels occupy $\gamma\in\{0.1,0.15,0.2,0.25\}$ fraction of the total image area. Our goal is to show empirically that the $FFid$ metric can recover the value of $\gamma$, thus revealing the explanation size. A three-convolution-layer model is used as the pre-trained model.

In the terminology of Section 5, the pixels can be divided into two tiers: those belonging to the digit, which form the explanation, and those belonging to the background, which do not. The explanation size is thus $c_{1}=\gamma td$. According to Theorem 1, we expect $FFid^{+}$ to increase for $s<c_{1}$ and decrease for $s>\max\left(\frac{\beta}{\alpha^{+}}td,\gamma td\right)$. This behavior is illustrated in Figure 1 for various values of $\beta$ and $\gamma$.
Furthermore, when $\frac{\beta}{\alpha^{+}}td<c_{1}$ (e.g., the blue curve in each plot), the point at which $FFid^{+}$ changes direction corresponds to the size of the explanation, $\gamma$. This allows us to recover $\gamma$ by evaluating $FFid^{+}$ over different $\beta$ values, as predicted by Theorem 1.

Figure: (a) $\gamma=0.1,\alpha^{+}=0.5$
Refer to caption: extracted/5899988/experiments/sparsity/finetune_size0.10_F-Fidelity_alpha0.50_MoRF.png

## 7 Related Work

Existing methods for evaluating explanations can be generally divided into two categories according to whether ground truth explanations are available. Comparing to the ground truth is an intuitive way for explanation evaluation. For example, in time series data and graph data, there exist some synthetic datasets for explanation evaluation, including BA-Shapes (Ying et al., ), BA-Motifs (Luo et al., ), FreqShapes,
SeqComb-UV, SeqComb-MV, and LowVar (Queen et al., ; ). In computer Vision and Natural Language Processing, the important parts can also be obtained with human annotation. However, these methods suffer from the heavy labor of ground truth annotation.

The second category of evaluation methods assesses the explanation quality by comparing model outputs between the original input and inputs modified based on the generated explanations Zheng et al. (). For example, Class Activation Mapping (CAM) (Zhou et al., ) first compares the classification performance between the original and their GAP networks, which makes sure the explanation is faithful for the original network. Grad-CAM(Selvaraju et al., ) uses image occlusion to measure faithfulness. In the following work, Grad-CAM++ (Chattopadhay et al., ) uses three metrics to evaluate the performance of explanation methods, “Average Drop $\%$”, “$\%$ Increase in Confidence”, and “Win $\%$”. In Adversarial Gradient Integration (Pan et al., ; Petsiuk et al., ), the authors use “Deletion Score” and “Insertion Score” to measure the faithfulness, where “Deletion Score” is to delete the attributions from the original input and “Insertion Score” is to insert attributions into one blank input according to the explanations.
In (Samek et al., ), the LeRF/MoRF method is proposed to measure if the importance is consistent with the accuracy of the model. However, this group of metrics does not consider the effect of the OOD issues.
In (Hooker et al., ), the author proposed a new evaluation method ROAR to calculate the accuracy, which avoids the OOD problem by using retrain. To overcome the disadvantage of ROAR, ROAD (Rong et al., ) was introduced to solve information leakage and time-consuming issues.

In the field of NLP, various methods are employed for evaluating faithfulness, as outlined in (Jacovi & Goldberg, ). These methods include axiomatic evaluation, predictive power evaluation, robustness evaluation, and perturbation-based evaluation, among others.
Axiomatic evaluation involves testing explanations based on predefined principles (Jacovi & Goldberg, ; Adebayo et al., ; Liu et al., ; Wiegreffe et al., ). Predictive power evaluation operates on the premise that if explanations do not lead to the corresponding predictions, they are deemed unfaithful (Jacovi & Goldberg, ; Sia et al., ; Ye et al., ).
Robustness evaluation examines whether explanations remain stable when there are minor changes in the input (Ju et al., ; Yin et al., ; Zheng et al., ), such as when input words with similar semantics produce similar outputs.
Perturbation-based evaluation, one of the most widely used methods, assesses how explanations change when perturbed (Atanasova, ; Jain & Wallace, ). This approach is akin to MoRF and LeRF, where (DeYoung et al., ) measures prediction sufficiency and comprehensiveness by removing both unimportant and important features.
For further information, please refer to the survey paper (Lyu et al., ).

## 8 Conclusion

In this paper, we introduced F-Fidelity, a robust framework for faithfulness evaluation in explainable AI. By leveraging a novel fine-tuning process, our method significantly mitigates the OOD problem that has plagued previous evaluation metrics. Through comprehensive experiments across multiple data modalities, we demonstrated that F-Fidelity consistently outperforms existing baselines in assessing the quality of explanations. Notably, our framework revealed a relationship between evaluation performance and ground truth explanation size under certain conditions, providing valuable insights into the nature of model explanations.

## Appendix A Detailed Algorithm

In this section, we provided the detailed pipeline of our evaluation method F-Fidelity  as follows:

Figure: Algorithm 1 Computating $FFid^{+}$,$FFid^{-}$

## Appendix B Proof of Theorem 1

We provide the proof by considering the following cases:
Case 1: $s\in[\max(\frac{\beta}{\alpha_{orig}^{+}}td,c_{1}),td]$
We have:

$$ $\displaystyle e(s)$ $\displaystyle=\mathbb{E}_{\mathbf{X},Y}(FFid^{+}(\psi,\alpha_{orig}^{+},\beta, s))$ $\displaystyle=\mathbb{E}_{\mathbf{X},Y}(\frac{1}{n}\sum_{(\mathbf{x}_{i},y_{i} )\in\mathcal{T}}\mathds{1}(y_{i}=f_{r}(\mathbf{x}_{i}))-P(y_{i}=f_{r}(\chi^{+} (\mathbf{x}_{i},\alpha^{+}_{orig},s))),$ $$

where $f_{r}(\cdot)$ represent the finetuned model in Algorithm 1, which is assumed to be robust to up to $\beta td$ removals, i.e., $P(f_{r}(\mathbf{x}\odot\mathbf{m})=Y)=P(Y|\mathbf{x}\odot\mathbf{m})$ if $\|\mathbf{m}\|_{1}\geq td-\beta td$. Consequently,

$$ $\displaystyle e(s)$ $\displaystyle=P_{\mathbf{X},Y}(Y=f_{r}(\mathbf{X}))-P_{\mathbf{X},Y}(Y=f_{r}( \chi^{+}(\mathbf{X},\alpha^{+}_{orig},s)))$ $\displaystyle=g(c_{1},c_{2},\cdots,c_{r})-\sum_{j^{r}:j_{i}\leq c_{i}}P(J^{r}= j^{r})g(c_{1}-j_{1},c_{2}-j_{2},\cdots,c_{r}-j_{r})$ $\displaystyle=g(c_{1},c_{2},\cdots,c_{r})-\mathbb{E}(g(c_{1}-J_{1},c_{2}-J_{2} ,\cdots,c_{r}-J_{r})),$ $$

where $J^{r}$ is a multivariate hypergeometric vector with parameters $(n_{1},n_{2},\cdots,n_{r},\beta td)$, where:

$$ $\displaystyle n_{i}=\begin{cases}c_{i}\qquad&\text{ if }\sum_{i^{\prime}\leq i }c_{i^{\prime}}\leq s,\\ s-\sum_{i^{\prime}<i}c_{i^{\prime}}&\text{ if }\sum_{i^{\prime}<i}c_{i^{\prime }}\leq s\leq\sum_{i^{\prime}\leq i}c_{i^{\prime}}\\ 0&\text{otherwise}\end{cases}.$ (7) $$

To explain the last equation, recall that $FFid^{+}$ first ranks the elements of the input based on Shap values, and chooses the top $s$ element. Then, it randomly and uniformly samples $\beta td$ elements from
the top $s$ elements (as long as $\lfloor\alpha^{+}_{orig}s\rfloor>\beta td$). So, if the $i$-th influence tier satisfies $\sum_{i^{\prime}\leq i}c_{i^{\prime}}\leq s$, then all of its elements will be chosen among the top $s$ influential elements. If $\sum_{i^{\prime}<i}c_{i^{\prime}}\leq s\leq\sum_{i^{\prime}\leq i}c_{i^{\prime}}$, then $s-\sum_{i^{\prime}<i}c_{i^{\prime}}$ elements from the tier would be chosen among the top $s$, and otherwise, no elements will be chosen from the tier. So, in general, $n_{i}$ elements from each tier will be chosen, where $n_{i}$ is defined in equation 7. Next, $FFid$ samples $\beta td$ of these top $s$ elements and masks them. Thus,
the number of elements masked in each tier follows a multivariate hypergeometric distribution, modeling the sampling of $\beta td$ elements from $n_{1},n_{2},\cdots,n_{r}$ elements of types $1,2,\cdots,r$, respectively. As $s$ increases, the choice is diluted by the inclusion of the lowest tier elements in the top $s$ (since only $n_{i}$ for the tier with $\sum_{i^{\prime}<i}c_{i^{\prime}}\leq s\leq\sum_{i^{\prime}\leq i}c_{i^{\prime}}$ increases as $s$ is increased to $s+1$).
So, $J^{r}$ is decreasing (in terms of lexicographic ordering) as a function of $s$, and $c^{r}-J^{r}$ is increasing as a function of $s$. Since $e(s)$ is linearly related to $\mathbb{E}(g(c^{r}-J^{r}))$,
it follows by the fact that $g(j_{1},j_{2},\cdots,j_{r})$ is increasing with respect to the lexicographic ordering that $e(s)$ is decreasing in $s$.
Case 2: $s\in[0,c_{1}]$
The proof follows by similar arguments as in the previous case. We have:

$$ $\displaystyle e(s)$ $\displaystyle=g(c_{1},c_{2},\cdots,c_{r})-g(c_{1}-\lfloor\alpha^{+}s\rfloor,0, 0,\cdots,0),$ $$

It follows by the fact that $g(j_{1},j_{2},\cdots,j_{r})$ is increasing with respect to the lexicographic ordering that $e(s)$ is increasing in $s$.

## Appendix C Detailed Experiment Setup

We explore two architectures, Resnet and ViT for the image classification tasks. We use Resnet-9 (^3^33https://jovian.com/tessdja/resnet-practice-cifar100-resnet) and a 6-layer ViT as backbones for both  Cifar-100  and  Tiny-Imagenet .
In the ResNet architecture, the hidden dimensions are set to $[64,128,128,256,512,512,512,512]$. For the ViT model, we use a patch size of 4, with a patch embedding dimension of 128. The backbone consists of 6 attention layers, each with 8 heads for multi-head attention. The final output hidden dimension of the ViT encoder is 256.
In the training stage, we set the learning rate and weight decay to 1E-4 for Resnet and set the learning rate to 1E-3 and weight decay to 1E-4 for ViT. We use Adam as the optimizer and the training epochs are 100 for Resnet and 200 for ViT. During fine-tuning, we use the same hyperparameters. We report our model accuracy in the Table 4.

**Table 4: The accuracy of the models to be explained in the image classification task.**
|  | ResNet | ViT |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| Dataset | origin | retrain | fine-tune | origin | retrain | fine-tune |
| Cifar-100 | 0.7323 | 0.7001 | 0.7310 | 0.5025 | 0.5071 | 0.4691 |
| Tiny-Imagenet | 0.5585 | 0.5600 | 0.5476 | 0.4255 | 0.4262 | 0.3825 |

**Table 5: The accuracy of the models to be explained in the time series classification task.**
|  | LSTM | Transformer |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| Dataset | origin | retrain | fine-tune | origin | retrain | fine-tune |
| PAM | 0.8773 | 0.8446 | 0.8886 | 0.8783 | 0.8502 | 0.8689 |
| Boiler | 0.7975 | 0.7750 | 0.7425 | 0.8425 | 0.7575 | 0.8325 |

For the time series classification task, we follow the TimeX (Queen et al., ) to use a simple LSTM for both Boiler and PAM datasets. The simple LSTM model contains 3 bidirectional LSTM layers with 128 hidden embedding sizes. We use AdamW as the optimizer with a learning rate of 1E-3 and weight decay is 1E-2. Similarly, we provide the model accuracy in the Table 5.

## Appendix D Extra Experimental Study

### D.1 Ablation Study

To evaluate the effectiveness of our proposed F-Fidelity framework, we conduct ablation studies comparing three evaluation setups: the original Fidelity metric, Fidelity with fine-tuning (Fidelity+Fine-tune), and F-Fidelity. We utilize the CIFAR dataset for these experiments, employing a ResNet architecture as the backbone for the classifier. The explainers are based on SG-SQ.

Figure: (a) MoRF vs GT
Refer to caption: extracted/5899988/experiments/ablation/fig/cfar_resnet_morf.png

As shown in Figure 2, across all three correlation metrics—“MoRF vs GT”, “LeRF vs GT”, and “MoRF vs LeRF”—F-Fidelity consistently outperforms the other methods. Notably, Fidelity+Fine-tune shows a marked improvement over the original Fidelity, indicating that the fine-tuning step enhances the robustness of the evaluation. F-Fidelity further advances this by effectively addressing the OOD issue, resulting in the most faithful and reliable rankings of the explainers.

### D.2 Hyperparameter Sensitivity Study

In this part, we assess the robustness of F-Fidelity to hyperparameter choices. We select a subset of 400 samples with an explanation size ratio of 0.2 from the colored-MNIST dataset (Arjovsky et al., ). we have three key hyperparameters: the number of sampling iterations $T$, the ratio $\alpha^{+}/\alpha^{-}$, and $\beta$. For each hyperparameter, we explored a range of values to understand their impact on the performance of F-Fidelity. We evaluated the method’s performance using three Macro Spearman correlations, with additional detailed results on $RFid^{+}$, $RFid^{-}$, and Micro Spearman correlations provided in Appendix E.4.

Figure: (a) Ablation study on $T$
Refer to caption: extracted/5899988/experiments/ablation/sampling/image_finetune_size0.20_numsampling_global_lerf_spearman_coeffe.png

Figure 3 presents the results of our hyperparameter sensitivity study. The findings demonstrate that F-Fidelity exhibits remarkable stability across a wide range of hyperparameter settings. This consistency is observed across all three Macro Spearman correlations, indicating that the performance of F-Fidelity is not overly sensitive to specific hyperparameter choices.

### D.3 Fidelity and Explanation Size

As mentioned in Section D.2, We conduct experiments on three settings of $\alpha^{+}$ and five settings of $\beta$ in the evaluation stage. As Figure 4 shows, in different settings, the ground truth size can be observed from the flat area in $RFid^{+}$. According to the analysis in Section 5, there are two key points in the x-axis, the explanation size $\gamma$ and the point where the deleting attributions are equal to the explanation size, $\beta\/\alpha^{+}$. Between the two key points, there exists a flat area, which is the best comparison area. Notably, our experiments are based on the assumption that all the explanation parts share the same important weight. In the real world, there is a gap between the ideal results and experiment results, such as the smooth increase and decrease in Figure  4.

Figure: (a) $\gamma=0.1,\alpha^{+}=0.3$
Refer to caption: extracted/5899988/experiments/sparsity/finetune_size0.10_F-Fidelity_alpha0.30_MoRF.png

### D.4 ViT as Backbone for Image Classification.

To further validate the robustness of our F-Fidelity framework across different model architectures, we conducted additional experiments using ViT (Dosovitskiy et al., ) as the backbone for image classification on both Cifar-100 and TinyImageNet datasets. We utilize the SG-SQ (Smilkov et al., ) to generate explanations. For the settings, se follow our main experimental setup. As shown in Table 6, F-Fidelity consistently achieves best correlations across all metrics for both datasets, outperforming other methods. This strong performance on ViT models further emphasizes the versatility and effectiveness of F-Fidelity in evaluating explanations across different deep learning architectures.

**Table 6: Spearman rank correlation results on Cifar-100 and Tiny-Imagenetdataset with ViT.**
|  | Correlation | Cifar-100 | Tiny-Imagenet |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Fidelity | ROAR | R-Fidelity | F-Fidelity | Fidelity | ROAR | R-Fidelity | F-Fidelity |  |  |
| Macro<br>Corr. | MoRF vs GT $\downarrow$ | -0.94$\pm$0.00 | -0.94$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -0.82$\pm$0.02 | -0.83$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |
| LeRF vs GT $\uparrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | -0.94$\pm$0.08 | -0.94$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -0.82$\pm$0.02 | -0.83$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |  |
| Micro<br>Corr. | MoRF vs GT $\downarrow$ | -0.68$\pm$0.40 | -0.91$\pm$0.07 | -1.00$\pm$0.01 | -1.00$\pm$0.00 | -0.74$\pm$0.27 | -0.76$\pm$0.10 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |
| LeRF vs GT $\uparrow$ | 1.00$\pm$0.01 | 0.94$\pm$0.21 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | -0.69$\pm$0.39 | -0.77$\pm$0.44 | -1.00$\pm$0.01 | -1.00$\pm$0.00 | -0.74$\pm$0.27 | -0.76$\pm$0.10 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |  |
| Micro<br>Rank | MoRF vs GT $\downarrow$ | 3.47$\pm$0.94 | 3.16$\pm$0.67 | 1.05$\pm$0.22 | 1.00$\pm$0.00 | 3.26$\pm$0.44 | 3.63$\pm$0.48 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |
| LeRF vs GT $\downarrow$ | 1.16$\pm$0.36 | 1.11$\pm$0.31 | 1.32$\pm$0.57 | 1.32$\pm$0.57 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | 3.58$\pm$0.75 | 3.16$\pm$0.67 | 1.05$\pm$0.22 | 1.00$\pm$0.00 | 3.26$\pm$0.44 | 3.63$\pm$0.48 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |

### D.5 Natural Language Classification Explanation Evaluation

Setup. We use two benchmark datasets for our NLP experiments: the Stanford Sentiment Treebank (SST) (Socher et al., ) for binary sentiment classification and the Boolean Questions (BoolQ) (Socher et al., ) dataset for question-answering tasks. For SST, we utilize 67,349 sentences for training and 872 for testing. BoolQ comprises 9,427 question-answer pairs for training and 3,270 for testing. We employ two popular model architectures: LSTM networks and Transformer-based models. For SST, the token embedding dimension is set to 128, and the hidden dimension is 512. The model has 2 multi-head attention layers, each with 4 heads.
For BoolQ, the token embedding dimension is increased to 256, with 8 layers, each containing 8 heads.
We follow the setting in image classification. Specifically, to generate explanations, we first use IG to obtain initial explanations, then apply noise perturbations to the importance of each timestamp at levels of $[0.0,0.2,0.4,0.6,0.8,1.0]$. We compare our F-Fidelity method against baselines including Fidelity (Fidelity) and R-Fidelity, evaluating performance using both macro and micro Spearman correlations. We use the Adam optimizer (Kingma & Ba, ) with a learning rate of 1E-4, keeping other hyperparameters at their default values. The model accuracy results are shown in Table 7.

**Table 7: The accuracy of the models to be explained in the natural language classification task.**
|  | LSTM | Transformer |  |  |
| --- | --- | --- | --- | --- |
| Dataset | Origin | Fine-tune | Origin | Fine-tune |
| SST2 | 0.8131 | 0.8280 | 0.7362 | 0.7867 |
| BoolQ | 0.6281 | 0.6263 | 0.6737 | 0.6764 |

**Table 8: Spearman rank correlation and rank results on SST2 dataset with LSTM and Transformer.**
|  | Correlation | LSTM | Transformer |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
| Fidelity | R-Fidelity | F-Fidelity | Fidelity | R-Fidelity | F-Fidelity |  |  |
| Macro<br>Corr. | MoRF vs GT $\downarrow$ | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -0.94$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |
| LeRF vs GT $\uparrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -0.94$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |  |
| Micro<br>Corr. | MoRF vs GT $\downarrow$ | -1.00$\pm$0.01 | -1.00$\pm$0.01 | -0.99$\pm$0.03 | -0.93$\pm$0.07 | -0.97$\pm$0.05 | -1.00$\pm$0.01 |
| LeRF vs GT $\uparrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.01 | 0.98$\pm$0.04 | 0.99$\pm$0.02 | 0.99$\pm$0.03 |  |
| MoRF vs LeRF $\downarrow$ | -1.00$\pm$0.01 | -1.00$\pm$0.01 | -0.99$\pm$0.02 | -0.92$\pm$0.09 | -0.97$\pm$0.05 | -0.99$\pm$0.02 |  |
| Micro<br>Rank | MoRF vs GT $\downarrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.05$\pm$0.22 | 2.05$\pm$0.89 | 1.32$\pm$0.46 | 1.05$\pm$0.22 |
| LeRF vs GT $\downarrow$ | 1.05$\pm$0.22 | 1.05$\pm$0.22 | 1.05$\pm$0.22 | 1.16$\pm$0.49 | 1.26$\pm$0.55 | 1.16$\pm$0.36 |  |
| MoRF vs LeRF $\downarrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.11$\pm$0.31 | 2.05$\pm$0.97 | 1.32$\pm$0.46 | 1.11$\pm$0.45 |  |

**Table 9: Spearman rank correlation and rank results on BoolQ dataset with LSTM and Transformer.**
|  | Correlation | LSTM | Transformer |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
| Fidelity | R-Fidelity | F-Fidelity | Fidelity | R-Fidelity | F-Fidelity |  |  |
| Macro<br>Corr. | MoRF vs GT $\downarrow$ | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |
| LeRF vs GT $\uparrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 | -1.00$\pm$0.00 |  |
| Micro<br>Corr. | MoRF vs GT $\downarrow$ | -1.00$\pm$0.01 | -1.00$\pm$0.01 | -1.00$\pm$0.00 | -1.00$\pm$0.01 | -1.00$\pm$0.01 | -1.00$\pm$0.00 |
| LeRF vs GT $\uparrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | -1.00$\pm$0.01 | -1.00$\pm$0.01 | -1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| Micro<br>Rank | MoRF vs GT $\downarrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |
| LeRF vs GT $\downarrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |
| MoRF vs LeRF $\downarrow$ | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 | 1.00$\pm$0.00 |  |

Results. Our experiments in the NLP domain reveal an interesting phenomenon that NLP models demonstrate remarkable robustness to OOD inputs, which is reflected in the performance of various fidelity metrics. Notably, the vanilla Fidelity (Fidelity) method achieves excellent results, often matching or closely approaching the performance of more sophisticated methods like R-Fidelity and our proposed F-Fidelity. This is evident from the near-perfect correlations (-1.00 or 1.00) across most metrics for both LSTM and Transformer models. This strong performance of vanilla fidelity suggests that the OOD problem, which often necessitates more complex evaluation frameworks in other domains, may be less pronounced in NLP tasks. The robustness of NLP models to perturbations in input tokens likely contributes to this phenomenon, allowing simpler evaluation methods to maintain their efficacy. However, it’s worth noting that our proposed F-Fidelity method still demonstrates consistent top-tier performance across all metrics and models, reinforcing its versatility and reliability even in scenarios where simpler methods perform well.

## Appendix E Detailed Experimental Results

### E.1 Image Classification Explanation Evaluation

Experiments on Cifar-100. We provide the detailed experiment results on the Cifar-100 dataset. The Cifar-100 dataset is a collection of 60,000 color images, each sized 32x32 pixels, classified into 100 distinct categories, with 600 images per class. It contains 50,000 training images and 10,000 test images. For the Resnet backbone, in Table 10, we compared different methods on the $Fid+$ and $Fid-$ metrics. From the figures, we found R-Fidelity and F-Fidelity methods have the advantage of distinguishing explanations with larger margin scores.

Similar results can be observed for the ViT backbone. We provide the results in Table 11.

**Table 10: Fidelity results on Cifar-100 dataset with ResNet as the model to be explained.**
|  | Fidelity | ROAR | R-Fidelity | F-Fidelity |
| --- | --- | --- | --- | --- |
| $Fid^{+}$ |  |  |  |  |
| $Fid^{-}$ |  |  |  |  |

**Table 11: Fidelity results on Cifar-100 dataset with ViT as the model to be explained.**
|  | Fidelity | ROAR | R-Fidelity | F-Fidelity |
| --- | --- | --- | --- | --- |
| $Fid^{+}$ |  |  |  |  |
| $Fid^{-}$ |  |  |  |  |

Experiments on Tiny-Imagenet.
Similar to the Cifar-100, we provide the detailed experiment results on Tiny-Imagenet in this section, which is a scaled-down version of the ImageNet dataset, designed for image classification tasks. Tiny-Imagenet contains 200 classes and 500 training images per class, 50 validation images, and 50 test images per class. The image resolution is 64x64. From Table 12 and  13, we observe that compared to R-Fidelity and F-Fidelity, F-Fidelity and R-Fidelity have the best performance.

**Table 12: Fidelity results on Tiny-Imagenet dataset with ResNet as the model to be explained.**
|  | Fidelity | ROAR | R-Fidelity | F-Fidelity |
| --- | --- | --- | --- | --- |
| $Fid^{+}$ |  |  |  |  |
| $Fid^{-}$ |  |  |  |  |

**Table 13: Fidelity results on Tiny-Imagenet dataset with ViT as the model to be explained.**
|  | Fidelity | ROAR | R-Fidelity | F-Fidelity |
| --- | --- | --- | --- | --- |
| $Fid^{+}$ |  |  |  |  |
| $Fid^{-}$ |  |  |  |  |

### E.2 Detailed Results on Time series Datasets

We conduct the experiments on the PAM and Boiler datasets with LSTM architecture. As Table 14 and  15 show, our method distinguishes explanations with a larger margin than R-Fidelity. Moreover, Fidelity and ROAR method fail to distinguish different explanations in the Boiler dataset.

**Table 14: Fidelity results on PAM dataset with LSTM as the model to be explained.**
|  | Fidelity | ROAR | R-Fidelity | F-Fidelity |
| --- | --- | --- | --- | --- |
| $Fid^{+}$ |  |  |  |  |
| $Fid^{-}$ |  |  |  |  |

**Table 15: Fidelity results on Boiler dataset with LSTM as the model to be explained.**
|  | Fidelity | ROAR | R-Fidelity | F-Fidelity |
| --- | --- | --- | --- | --- |
| $Fid^{+}$ |  |  |  |  |
| $Fid^{-}$ |  |  |  |  |

### E.3 Detailed Results on NLP

In Table 16,  17, 18 and  19, with LSTM and Transformer, we find the Fidelity has a consistent result which is quite different than other tasks. Compared to R-Fidelity and F-Fidelity, the results are almost the same both in the SST2 and BoolQ datasets, which indicates in these two cases, the OOD problem can be ignored.

**Table 16: Fidelity results on SST2 dataset with LSTM as the model to be explained.**
|  | Fidelity | R-Fidelity | F-Fidelity |
| --- | --- | --- | --- |
| $Fid^{+}$ |  |  |  |
| $Fid^{-}$ |  |  |  |

**Table 17: Fidelity results on SST2 dataset with Transformer as the model to be explained.**
|  | Fidelity | R-Fidelity | F-Fidelity |
| --- | --- | --- | --- |
| $Fid^{+}$ |  |  |  |
| $Fid^{-}$ |  |  |  |

**Table 18: Fidelity results on BoolQ dataset with LSTM as the model to be explained.**
|  | Fidelity | R-Fidelity | F-Fidelity |
| --- | --- | --- | --- |
| $Fid^{+}$ |  |  |  |
| $Fid^{-}$ |  |  |  |

**Table 19: Fidelity results on BoolQ dataset with Transformer as the model to be explained.**
|  | Fidelity | R-Fidelity | F-Fidelity |
| --- | --- | --- | --- |
| $Fid^{+}$ |  |  |  |
| $Fid^{-}$ |  |  |  |

### E.4 Detailed results of hyperparameter sensitivity study

In this section, we provide the detailed ablation study experiment results on the Colored-Mnist dataset. The experiment settings are described as Section D.2. We provide the detailed $Fid^{+}$, $Fid^{-}$, and three Spearman rank Correlation, same as the subsection E.1.
As Table 20, 21, and  22 show, our method is robust to the choice of hyperparameters. From the $Fid^{+}$ and $Fid^{-}$, the larger sampling number helps reduce the standard deviation. But with large sampling number, the evaluation time increases. In this paper, we select a balance point of $50$ for all the other experiments. For the hyperparameter $\beta$, the best option is near the ground truth explanation size ratio. However, in the real-world setting, it is hard to find the best choice. In our paper, for the fine-tuning efficiency and evaluation performance, we select $0.1$ for all the other experiments. In R-Fidelity, the hyperparameter $\alpha$ is designed for alleviating the OOD problem, where smaller $\alpha$ means less OOD problem. In our method, because of the $\beta$, a larger $\alpha$ is also optional.

**Table 20: The detailed ablation study results on sampling number $T$, with $\beta=0.1$, $\alpha_{1}=\alpha_{2}=0.5$.**
| Sampling<br>Number $T$ | $Fid^{+}$ | $Fid^{-}$ | Local Spearman<br>Correlation |
| --- | --- | --- | --- |
| 10 |  |  |  |
| 30 |  |  |  |
| 50 |  |  |  |
| 80 |  |  |  |
| 150 |  |  |  |

**Table 21: The detailed ablation study results on hyperparameter $\beta$, with $S=50$, $\alpha_{1}=\alpha_{2}=0.5$.**
| $\beta$ | $Fid^{+}$ | $Fid^{-}$ | Local Spearman<br>Correlation |
| --- | --- | --- | --- |
| 0.05 |  |  |  |
| 0.10 |  |  |  |
| 0.15 |  |  |  |
| 0.20 |  |  |  |
| 0.25 |  |  |  |

**Table 22: The detailed ablation study results on hyperparameter $\alpha=\alpha^{+}=\alpha^{-}$, with $T=50$, $\beta=0.1$.**
| $\alpha$ | $Fid^{+}$ | $Fid^{-}$ | Local Spearman<br>Correlation |
| --- | --- | --- | --- |
| 0.2 |  |  |  |
| 0.3 |  |  |  |
| 0.4 |  |  |  |
| 0.5 |  |  |  |
| 0.6 |  |  |  |
| 0.7 |  |  |  |
| 0.8 |  |  |  |

## Peer Reviews

confidence: 3
contribution: 2
initial_rating: 6
presentation: 1
questions: Questions are as below

#### W1:
- a) Provide specific examples of how "removal" is implemented for different data types like images, tabular data, and text.
- b) Give a more detailed explanation of how bounding the removed portion to a fraction of the input, rather than the explanation, helps mitigate OOD issues.

#### W2:
- a) Elaborate on how the random masking process relates to or simulates small perturbations, particularly in the context of image data.
- b) Provide examples or visualizations that demonstrate how this masking approach compares to traditional perturbation methods.
- c) Present empirical evidence or theoretical justification for why their masking approach is an effective way to improve classifier robustness.

#### W3:
- a) Provide empirical evidence or theoretical justification for why their fine-tuning process preserves the original classifier's decision boundaries.
- b) Compare the original and fine-tuned classifiers' outputs on a test set to demonstrate the degree of change.

#### W4:
- a) Provide theoretical or empirical evidence demonstrating the equivalence between explanations of the original and fine-tuned classifiers.
- b) Include a comparison of explanations generated for both classifiers on a set of test examples.

#### W5:
- a) Provide a step-by-step description of how they generate or obtain the ground truth (GT) explanations, including any assumptions made in this process.
- b) Include examples of GT explanations for different data types.

#### W6:
- a) Provide a detailed analysis of why F-Fidelity underperforms on this specific dataset and model combination.
- b) Investigate potential reasons, such as dataset characteristics, model architecture specifics, or hyperparameter settings that might contribute to this result.
- c) Discuss the implications of this finding for the broader applicability of their method.
- d) Consider conducting an ablation study to isolate the factors contributing to this performance difference.

The paper addresses an important aspect of fidelity evaluation and the issue of OOD while doing it. Overall, I like the central theme of the paper and that’s why I am leaning towards mild acceptance but I would like the authors to address the points in the weakness section and the questions in this section.
soundness: 2
strengths: 1) The paper deals with important aspect of fidelity evaluation
2) The authors discuss about OOD issue during fidelity evaluation
3) The authors propose an approach to handle the issues and show the performance in different data types like images, time series and NLP.
summary: The authors propose a fidelity evaluation framework which utilizes an explanation agnostic fine tuning and a random mask generator which ensures that the generates input is not OOD. The efficacy of the proposed method if shown in various data types like images, time series etc.
weaknesses: W1) In section 3, it is mentioned in lines [215 to 222] that the size of the removed part is upper bounded by a fraction of the input and not a fraction of the explanation. It would be helpful to the readers if the authors could explain what they mean by "removed," as it might mean different in tabular data and images. Further, the authors should also explain how their strategy of selecting a fraction of input and not explanation addresses the OOD issue. 

W2) In lines[224:235], the authors use fine tuning to address the problem of robustness of the classifier for small perturbations(mentioned in lines [213:214]). However, at least from the perspective of images, it is unclear how applying a mask of {0,1} on random patches of an image can be considered as a perturbation.

W3) Further, the fine-tuning process mentioned in lines[224:235] seems like retraining the classifier with occlusion (for image classifiers). The authors should explain how their method won't change the decision boundary drastically so that their approach can be called fine-tuning and not training a different classifier altogether.

W4) The authors should explain why explaining the fine-tuned classifier is equivalent to explaining the original classifier (as mentioned in line[224])

W5) For the ease of readers, the authors should explain more about GT and how they extract it(in Section 4)

W6) It needs to be clarified to see why F-Fidelity performs worse than vanilla Fidelity and R-Fidelity for SST2 dataset with LSTM (Table 8). The authors are requested to explain this phenomenon in detail for the ease of readers.

---

confidence: 4
contribution: 2
initial_rating: 5
presentation: 2
questions: The ablation study provided regarding B selection suggests this value can approach 1 (i.e. this is the same as if the value was not implemented) and the correlation scores would be good. Is this true? If so, what use does B have? In addition, what value of B is used and how was it selected? 

What is the intuition for fine tuning with the image perturbation limitation? I do not see why fine-tuning under image perturbed by random masks instead of perturbed explanations is better either. It is not obvious that this skirts the OOD problem. 

What is the value of being able to extract the explanation size? The motivation for this is lacking and it is not clear why it is important or interesting.
soundness: 3
strengths: From their experiments which cover a broad range of applications and datasets, it seems this new method does improve over existing methods in rank correlation tests, indicating its ability to fairly and consistently sort attributions under evaluation. 

The solutions presented are simple.
summary: The authors propose a new attribution evaluation framework which attempts to solve existing issues in current metrics such as the OOD problem from perturbation metrics, and the information leakage of fine-tuning methods like ROAR. To do this, the authors propose limiting the size of the perturbations made to each image and performing fine-tuning on images randomly masked under this perturbation size limitation.
weaknesses: I do not think the intuition behind the solutions is entirely clear and I do not think the presentation of the solutions is clear.  

The choices for multiple hypermeters are not indicated. 

More attribution methods should have been employed for a better representation of the existing space.

---

confidence: 3
contribution: 3
initial_rating: 6
presentation: 2
questions: 1. I couldn't find how Pan et al., 2021, or Zhu et al., 2024 utilized macro correlation in their work. Can you explain how they employed macro correlation and how it relates to your citation of their work?

2. In Section 6, it seems that both MoRF and LeRF conditions would be satisfied equally. This is because deleting or inserting features based on the gamma value would maximize the MoRF-LeRF difference. I'm uncertain whether this experiment effectively demonstrates that F-Fidelity can distinguish explainers that are closer to the ideal Shapley explainer than other metrics. Could you clarify how this experiment supports that claim?

3. Regarding computational resources, I would like to know how much computational effort your method requires. One of the primary reasons ROAR isn't widely adopted is not just due to information leakage but also because of its significant computational cost. It would be helpful if you could provide details on the computational resources required for F-Fidelity and how they compare to those needed for ROAR.

** Typo : in figure 1, the y-axis label is RFid.
soundness: 3
strengths: The paper is well written, especially introduction section and preliminary section.

The paper effectively tackles the OOD problem inherent in traditional removal-based evaluation methods. This is a crucial issue because OOD inputs can lead to unreliable assessments of an explainer's faithfulness.

The authors conducted extensive experiments across broad data, such as images, time series, and natural language processing.

The method is well mitigate limitation of prior methods; Addresses the information leakage issue and OOD issue at once.

The paper provides theoretical analysis demonstrating that F-Fidelity can recover the sparsity of the ideal SHAP explanations.

The paper introduces a novel approach by assuming that an explainer is better the closer it is to an ideal Shapley value explainer. This assumption is appealing because Shapley values provide a theoretically sound basis for feature attribution.
summary: The authors presented F-fidelity, a new metric for evaluating the faithfulness of attribution methods. Traditional evaluation methods such as MoRF and LeRF suffer out-of-distribution(OOD) issue, and ROAR method suffers information leakage issue. F-fidelity overcomes these limitations through two strategies. 1. explanation-agnostic fine-tuning, which fine-tunes the model using stochastic masking operations. 2. a controlled random masking operation to overcome the OOD issue, by applying a random masking operation conditioned on the explainer's output so that removal of input features does not produce OOD samples. The authors conducted controlled experiments with other explainers. Moreopver, they showed that F-fidelity can be used to determine the sparsity of influential input components.
weaknesses: Lack of Visualizations Demonstrating F-Fidelity's Effectiveness. The paper does not include figures or visualizations that illustrate the effectiveness of F-Fidelity. Providing attribution maps or examples where there is a significant discrepancy between F-Fidelity and other evaluation metrics would enhance understanding and make the results more tangible. Visual comparisons could help readers better appreciate the advantages of F-Fidelity over existing methods. For example, Attribution map between samples that have discrepancy between F-Fidelity and MoRF - LeRF.

Novelty issue. Though theoretical availability of extracting the size of the ground-truth explanation is novel, the core difference between F-fidelity and R-Fidelity is introducing an upper bound on the fraction of input elements removed. This extension seems an incremental refinement rather than a fundamental novel idea.

Limited Explanation of Ground Truth. The paper's approach to establishing ground truth rankings involves using Integrated Gradients with systematically added noise levels. However, Integrated Gradients is known to be less faithful than some state-of-the-art explanation methods, such as the LRP (Layer-wise Relevance Propagation) family or LayerCAM. This raises concerns about whether the ground truth used is an appropriate benchmark. As the authors discuss ideal Shapley value explainers in Section 5, utilizing Shapley values as the ground truth might have been more appropriate to align with their theoretical framework.

Insufficient Clarification on the Importance of Macro Correlation. The paper could benefit from a more thorough explanation of why macro correlation between different evaluation methods is important. It was not immediately clear how macro correlation demonstrates the usefulness of F-Fidelity. Including figures or visual aids that depict the relationship between macro correlation and the effectiveness of F-Fidelity would help clarify this point and strengthen the argument.

Limited Variety of Explanation Methods Evaluated. The experiments involve a relatively small number of explanation methods. Comparing F-Fidelity scores across a wider range of explainers would provide a more comprehensive evaluation. For instance, methods like LayerCAM and LRP family are known to have higher fidelity than GradCAM, and GradCAM typically outperforms the pure gradient. Demonstrating whether F-Fidelity can reflect these known differences in fidelity would enhance the paper's validity.

Practical Challenges in Determining Explanation Size (c₁). In the section 6, the size of the most influential tier (c₁) is assumed to be known. However, in real-world applications, c₁ is not readily observable. It would have been beneficial if the authors had demonstrated how c₁ could be estimated or inferred from practical data, such as through experiments on datasets like ImageNet. Providing practical guidance on determining c₁ would make the theoretical contributions more applicable.

Meta-review: Strengths : 
The paper addresses the important issue of out-of-distribution (OOD) inputs in fidelity evaluation and proposes a simple yet effective method to handle this challenge. Through extensive experiments across diverse data types, including images, time series, and NLP, the authors demonstrate that their approach improves rank correlation in attribution evaluations, ensuring more reliable and consistent assessments. The method effectively mitigates limitations of prior techniques by addressing both information leakage and OOD problems.

Weaknesses:
It lacks visualizations, such as attribution maps, to demonstrate the effectiveness of F-Fidelity and highlight its advantages over other evaluation metrics. The novelty of F-Fidelity is questioned, as its primary distinction from R-Fidelity seems incremental. The use of Integrated Gradients for establishing ground truth raises concerns, as it may not be the most faithful method compared to others like LRP or LayerCAM. The importance of macro correlation is not sufficiently explained, and the paper evaluates a limited set of explanation methods, missing comparisons with more established techniques. Additionally, practical challenges in determining the size of the most influential tier (c₁) and clarifications on certain aspects of the methodology (e.g., perturbation masking and fine-tuning) are not fully addressed. There are also issues with the clarity of the intuition behind the solutions, hyperparameter choices, and the paper's presentation of the results.

Decision: Accept (Poster)