Learning for Highly Faithful Explainability
Authors: Yuhan Guo
Lizhong Ding
Shihao Jia
Yanyu Ren
Pengqi Li
Jiarun Fu
Changsheng Li
Ye Yuan
Guoren Wang
Venue: ICLR 2026 Poster (2026)
Keywords: Explainability; Faithfulness; Learning to Explain
Primary area: interpretability and explainable AI
TL;DR: This work overcomes three key challenges in "Learning to Explain" paradigm by jointly optimizing a model-agnostic objective and filtered prior explanations to generate more faithful explanations.

Abstract: \textit{Learning to Explain} is a forward-looking paradigm recently proposed in the field of explainable AI, which envisions training explainers capable of producing high-quality explanations for target models efficiently. Although existing studies have made attempts through self-supervised optimization or learning from prior explanation methods, the \textit{Learning to Explain} paradigm still faces three critical challenges: 1) self-supervised objectives rely on assumptions about the target model or task, restricting their generalizability; 2) methods driven by prior explanations struggle to guarantee the quality of the supervisory signals; and 3) depending exclusively on either approach leads to poor convergence or limited explanation quality. To address these challenges, we propose a \textit{faithfulness}-guided amortized explainer that 1) theoretically derives a self-supervised objective free from assumptions about the target model or task, 2) practically generates high-quality supervisory signals by deduplicating and filtering prior explanations, and 3) jointly optimizes both objectives via a dynamic weighting strategy, enabling the amortized explainer to produce more faithful explanations for complex, high-dimensional models. We re-formalize multiple well-validated faithfulness evaluation metrics within a unified notation system and theoretically prove that an explanation mapping can simultaneously achieve optimality across all these metrics. We aggregate prior explanation methods to generate high-quality supervised signals through deduplicating and faithfulness-based filtering. Our amortized explainer leverages dynamic weighting to guide optimization, initially emphasizing pattern consistency with the supervised signals for rapid convergence, and subsequently refining explanation quality by approximating the most faithful explanation mapping. Extensive experiments across various target models and image, text, and tabular tasks demonstrate that the proposed explainer consistently outperforms all prior explanation methods across all faithfulness metrics, highlighting its effectiveness and its potential to offer a systematic solution to the fundamental challenges of the \textit{Learning to Explain} paradigm.

Published as a conference paper at ICLR 2026
LEARNING FOR HIGHLY FAITHFUL EXPLAINABILITY
Yuhan Guo, Lizhong Ding,, Shihao Jia, Yanyu Ren, Pengqi Li, Jiarun Fu, Changsheng Li,
Ye Yuan, Guoren Wang
School Computer Science and Technology
Beijing Institute of Technology
No. 5 Zhongguancun South Street, Haidian District, Beijing, China
$2202311880bi1 edu. en, lizhong, oong com, f1120221561, renyanyu, 3220242275, 3120235197, les} edu, on, yuan-ye@bit. edu. en, wanggrbite126.. com
ABSTRACT
Learning to Explain is forward-looking paradigm recently proposed in the field of explainable AI, which envisions training explainers capable of producing high- quality explanations for target models efficiently. Although existing studies have made attempts through self-super optimization or learning from prior ex- planation methods, the Learning to Explain paradigm still faces three critical challenges: 1) self-supervised objectives rely on assumptions about the target model or task, restricting their generalizability; 2) methods driven by prior ex- planations struggle to guarantee the quality of the supervisory signals; and 3) de- pending exclusively
either approach leads to poor convergence limited ex- planation quality. To address these challenges, we propose a faithfulness--uuiee amortized explainer that 1) theoretically derives self self-supervised objective free from assumptions about the target model or task, 2) practically generates high- quality supervisory signals by deduplicating and filtering prior explanations, and 3) jointly optimizes both objectives via a dynamic weighting strategy, enabling the amortized explainer produce more faithful explanations for complex, high- dimensional models. We re-formalize multiple well-validated faithfulness eval- uation metrics within a unified notation system and theoretically prove that an explanation mapping can simultaneously achieve optimality across all these met- rics. We aggregate prior explanation methods to generate high-quality supervised signals through deduplicating and faithfulness-basee filtering. Our amortized ex- plainer leverages dynamic weighting to guide optimization, initially emphasizing pattern consistency with the supervised signals for rapid convergence, and sub- sequently refining explanation quality by approximating the most faithful expla- nation mapping. Extensive experiments across various target models and image, text, and tabular tasks demonstrate that the proposed explainer consistently outper- forms all prior explanation methods across all faithfulness metrics, highlighting its effectiveness and its potential to offer systematic solution to the fundamental challenges of the Learning Explain paradigm.
INTRODUCTION
The widespread deployment of deep models has raised substantial concerns regarding their explain- ability (Li et al. 2025 Fu al. 2026 Zhang et al. 2025), motivating the community to propose a variety of explanation methods across different eXplainable AI (XAI) paradigms (Jethani et al.] 2222]. Among these, the Learning Explain paradigm (Madsen al.) (024) puts forward an appealing future: training a neural network as an explainer for the target model by optimizing a learning objective, thereby generating high-quality explanations in inference through a single for- ward pass (Yoon et al.) 2019: Bhalla et al., (202)). This paradigm is often referred to as amortized explanation methods, as it shifts the computational burden of interacting with the target model the training of the explainer, thereby reducing the cost of generating explanations at inference time.
"Corresponding author.

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Published as a conference paper at ICLR 2026
Explanations cannot be learned from scratch without guidance: they necessarily rely prior the- oretical assumptions or supervisory signals. Self-supervised optimization-bar basood methods (Bhalla et al. 2023 Schwab & Karlen 2019) allow the explainer to interact with the target model during training, optimizing a self-supervised loss function designed to measure explanation quality. Prior- explanation-driien methods (Jethani al.] [022] Covert et al. 2023 Barkan al., (023) employ existing XAI algorithms to generate a set of attributions for the target model, and then train the
explainer to model the mapping from inputs explanations. However, the Learning to Explain paradigm has not been widely adopted, primarily because three major challenges in improving the performance of amortized explainers: The objective functions of self-suuervised optimization- based methods are limited by ideal assumptions about the target model or the task setting (Chen) et al. 2018). 2) Prior-explanation-rivee drivee methods face difficulties to ensure the quality of the su- pervisory signals (Barkan et al.) (023). 3) Explainers trained solely on self-supervised objectives struggle with convergence and scale poorly to high-dimensional or complex models (Schwab & Karlen 2019). whereas those relying only prior explanations cannot surpass the quality of the labels they imitate (Situ et al. 2021).
To address these challenges, introduce the critical concept of faithfulness (Bhatt et al. 2020 Dasgupta & Moshkovitz (202) from XAI into the Learning to Explain paradigm and propose Deep architecture-basse Faithful amortized explainer (DeepFaith). Faithfulness serves as a quantitative metric that assesses whether explanation accurately reflects the model's true decision-makinn makinn process (Li et al.] 2023), thereby directly indicating explanation quality. From the perspective of faithfulness, theoretically construct self-supervised optimization objective that requires no assumptions about the target model or task, practically design a methodology for generating high- quality supervisory signals by filtering prior explanations through faithfulness criteria, and develop a dynamic joint optimization strategy that integrates the self-supervised objective with faithfulness- filtered supervisory signals. Together, these novel designs enable our amortized explainers gen- erate explanations that are more faithful than prior methods, even for complex models and high- dimensional tasks.
Our technical approach and contributions to the XAI field can be summarized in three aspects:
(1) We are the first to introduce a self-supervised objective that directly optimizes explanation faith- fulness within the Learning to Explain paradigm. By re- fe-rommalizing ten widely used and well- validated faithfulness metrics, we propose and theoretically prove the existence of an optimal faith- ful explanation mapping that simultaneously achieves optimality across all these metrics.
(2) We are the first to provide a systematic solution for enhancing the quality of supervisory signals in the Learning to Explain paradigm. We aggregate explanations generated by multiple methods for the target model, increase the diversity of supervisory signals through similarity- -base deduplicating, and improve their faithfulness via p-quantile filtering across multiple metrics.
(3) We are the first to complementarily integrate the two main approaches within the Learning Explain paradigm. We design a dynamic weighting-based joint optimization strategy: during the carly stage of explainer training, fitting the supervisory labels enables rapid convergence to a basic explanatory capability, followed by approximating the theoretically optimal mapping to further enhance explanation quality.
To validate the effectiveness of these contributions, we evaluate DeepFaith on 12 explanation tasks spanning image, text, and tabular modalities, as well as across diverse models to be explained. Comparative experiments demonstrate that DeepFaith consistently outperforms baseline methods in terms of faithfulness. Through ablation studies, we further validate the effectiveness of each com- ponent in our proposed method. In addition, the visualizations provided in the appendix illustrate that Fath produces clear and intuitive explanations, along with comparison of runtime.
2 RELATED WORK
Self-Supervised Optimization-base Methods Methods that train explainers by optimizing self- supervised objectives rely on assumptions about the target model or task setting, constructing a self- supervised loss function to measure explanation quality. During training, the explainer interacts with the target model, improving explanations by minimizing this loss. For example, VerT (Bhalla et al. 2023) assumes features strictly divide into signal and noise, training the explainer to learn the spars-
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est separating mask. However, since deep models encode higher-order interactions, this assumption rarely holds in practice. Similarly, L2X (Chen et al. 20188) is grounded in an information -ooomation-theorticcc assumption that tasks involve clearly separable features; it trains the explainer by maximizing the mutual information between feature subsets and predictions, facing the same limitation as VerT. CXPlain (Schwab & Karlen 2019) assumes input features capture all potential factors influencing the prediction, treating feature removal effects as causality and training the explainer to learn the causal importance of features for the output. Yet, real-world confounders are highly unobservable, and removing correlated features can easily produce spurious causal effects. Moreover, because the self- supervised objective nests the target model, its highly non-convex nature makes explainers difficult to converge when dealing with complex models or high-dimensional tasks.
Methods These approaches leverage existing explanation methods as prior references by generating explanations of the target model under different inputs before train- ing and using them as supervisory signals. The explainer is then trained by fitting the mapping from inputs to explanations. L2E (Situ et al. [021] neuralizes multiple XAI algorithms via knowledge distillation, enabling explainers to produce fast and stable explanations. However, prior explana- tion methods cannot guarantee high-quality explanations for all samples, and low-quality supervi- sory signals negatively affect explainer training. FastSHAP (Jethani et al. (022) and ViT Shapley (Covert al. 2023) adopt the Shapley Value (Lundberg & Allen (017)) as high-quality prior and train explainers to approximate the true Shapley Values. Nevertheless, Shapley Values fail to attribute non-independent features and nonlinear interactions, making them unreliable as the sole prior source. Moreover, since fitting supervisory explanation signals essentially mimics existing XAI methods, the explainer's performance inherently bounded by the quality of the explanations in the dataset, hindering further improvement.
Prior-Explann Sroo--ExllanationDriiieei
3 THEORETICALLY OPTIMAL FAITHFULNESS OBJECTIVE
In this section, building on deep insights into the theory of faithfulness, we propose a model- and task-agnostic self-supervised objective within the Learning Explain paradigm. Let f X + y paradign. denote the model to be explained, where the input space X' C IRaxd consists of instance æ = (#1, ...,,., zn)) with each element I; E Rdd. In our experiments: for vision, is an image of patches, each representing the d-dimensional pixels in patch; for NLP. x is a sequence of n tokens with ny as the ddddimensional embedding of the i-th token; for tabular data, x is a row with n scalar features (d = 1). The model output (x) aims to approximate y E y C R. e.g., the predicted probability for the target class in classification. We use [n] to denote the set {1, .,...,,,, n), and use (i) to denote the vector (1, .,...,). n.).
We begin with the observation that current faithfulness metrics follow two distinct views: one evalu- ates the accuracy of attribution values from a saliency perspective (Bhatt et al. 2020 Alvarez Melis & Jaakkola 2018). while the other assesses the relative importance of input elements from a permu- tation perspective (Samek et al.) 2015 Rieger & Hansen 2020). Thus, it is essential to distinguish between explanations under these two perspectives before conducting the analysis.
Definition 1 (Saliency Explanation). A saliency explanation method is defined as a mapping Sj :
X + [0, 1 that, given an input x and model f. outputs saliency vector = ($1, $2........ sn) E [0, 1]", where each 8; quantifies the contribution of x, (e.g., a patch, token, or scalar feature) to the prediction ÿ -xx)..
Definition (Permutation Explanation). A permutatiion explanationn method is defined as a mapping 11, X + S,, where G,, = ((T())) (2).... <(n)) = [m]]] [deotte all permutations of [n]. Given x and model f. I outputs æ E Gn. indicating that (() contributes no less to the model's prediction than (x(i+))-
Remark. Two types of explanations can be interconverted via simple functions: B(s) argsort, {s1, $2...., sn} represents the descending-orde index of s, mapping a saliency explana- tion to a permutation explanation; while E(T) converts a permutation explanation into a saliency explanation, where E(m); = (n (i) 1)/n. Since a saliency explanation assigns specific importance score to each F,, while a permutation explanation does not, B(s)) cannot be recovered back through Σ.
For clarity, we use 7(i) denote the i-th element in vector ा.
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Table 1: We re-formalize ten widely-used and well-validated faithfulness metrics under our notation
system, including FC (Bhatt et al., 2020), FE (Alvarez Melis & Jaakkola 2018), INF (Yeh et al.) 2019), and MC for saliency explanations, as well as DEL and INS (Petsiuk & Saenko 2011)), NEG and POS (Barkan et al.) 2023), RP, and IROF (Rieger & Hansen (2220) for permutation
explanations. 1 indicates that higher values correspond to greater explanation faithfulness, while + indicates that lower values correspond to greater faithfulness.
Faithfulness Metric
Input
Formula
Output
Faithfulness Correlation (FC) 1
8, 8.2.5
(Eiez 4) ()) (A [x (ill
[-1.1]
Faithfulness Estimate (FE)
Syi (220) N.)
(Ejer Sy(al ). (A [f(a()). f(2()) (T)D
Monotonicity Correlation (MC) 1
8, (I.
*/EEE a5) a (A (f()). f(x [)D
[-,,
Infidelity (NF) 1
8:2, (I: P(NADE
AeEE M) (f()), f(x [.)))
[-1,1]
Deletion Score (DEL) L
x:a,f x;
f(x 0,11 +(})] di
[0.1]
Insertion Score (INS) f
Si
[(x), u (1 m(1) di
[0.1]
Negative Perturbation (NEG)
w:a,f f minn f yys (2 My (2
1 Sunn A
[(x), f(x NU F()) di
[0.1]
Positive Perturbation (POS)
I A-
f(x). fir U,2 =())
[0.
Region Perturbation (RP)
(1t) Ex
((210)) M2 11 (()))) )
[].
Iterative Removal Features (IROF)
No 2
[aatt), s(x w 01 (2/ (1))
dy [0.1]
As shown in Table we select ten widely used and well-validated faithfulness evaluation metrics, uncover and extract their shared functional components, and abstract them to enable unified theo- retical analysis. The functional components we define are as follows:
Input Perturbation 2: \ I (I C [n) denotes input z with sub-elements { / I} removed (via noise substitution (Rong et al. 2022), baseline replacement (Bhatt al.) 2020 Bach et al. 2015),
or linear interpolation (Rieger & Hansen 2020)). And x:" U denotes inserting E I into the baseline input x (e.g., blurred input, noise, or zero vector).
Perturbation Effect y x y' + [0. 1] (e.g.. ly - -y(2) or (y 22) Yeh et 2019 measures the discrepancy between model predictions before and after perturbation.
Preservation Effect A : y x y - [o, 1] (e.g.. /y |Rieger & Hansen 2020 or target class confidence) measures the degree to which the original prediction is preserved, which strictly decreasing with respect to A.
Correlation 1 mh [-1, measures correlations between m-dimenssooal vectors, such
as Pearson or Spearman coefficients Alvvrre Melis & Jaakkola 2018 Nguyen & Martinez 2020).
Please refer to Appendix D for more specific examples. We re-formalize four saliency perspective faithfulness metrics under our notation system in Table [ Specifically, FC enumerates all subsets of [n]] as perturbation index sets I (computed using Monte Carlo sampling to ensure feasibility): FE evaluates N samples, each with a specific I: MC defines a fixed perturbation sequence {Z, [- on one sample; and INF samples N index sets from distribution P. which we instantiate as P([m)) Uniform(221) (2irl), a discretized version of the original INF.
By uncovering that the core idea behind FC, FE, MC, and INF is to evaluate the correlation between the local sum of saliency explanations over perturbed indices and the corresponding perturbation effects, we propose a saliency explanation mapping with optimal faithfulness across these four. Proposition 1. Given model being explained and its input space X, for a fixed correlation measure I and perturbation effect A, suppose there exists a saliency explanation mapping Sj such that Vx E X and VII, S [m]]
S7 97-arge argmaxx S;
{EEEEI, SaaeeSS
then the saliency explanations generated by S always achieve optimal faithfulness under the FC, FE, INF, and MC evaluation metrics.
Proof. Please refer to Appendix for for detailed proof.
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Samule
Fak Pairs
Esplaration
Nodd Buiny Exytainct
Aun
Salunoy
Tuffiiass Dvaal
Cooc
(P P-uaart
Loc
Sulleery Replasations
Salaay Explanations
Optiiticing
Figure I: DeepFaith learning framework. We meticulously design a high-quality supervised expla- nation signal generation workflow that leverages K existing explanation methods with deduplicating and filterin. We further introduce a training pipeline for a deep neural explainer (an L-layer Trans- former encoder the figure) that optimizes LLC (Eq. (2) theoretically grounded by Theorem [ and LPC (Eq. empirically guided by the supervised signals. Image modality is shown as example.
For permutation perspective metrics, we formalize four empirical metrics (DEL, INS, NEG, POS) and re-formulate two existing ones (RP, IROF) in Table DEL and INS respectively remove fea- tures from the original input x or insert features into a baseline input x², using the area under the curve (AUC) of preservation effects as faithfulness scores; NEG and POS remove features as- cending order π or descending order until t-th removal leading to prediction changes significantly (e.g., class flips), with AUC used quantify the over-all preservation effect; RP perturbs features in descending order of importance and averages the prediction drop; IROF uses the same order as RP and computes the mean area over the curve (AOC) of preservation effects across N samples.
Although RP, IROF, DEL, INS, NEG, and POS evaluate permutation explanations in ways that differ substantially from FC, FE, INF, and MC, we theoretically show that they share an underlying consistency, and prove that S in Proposition [ can induce optimal permutation explanation mapping on all six permutation. based faithfulness metrics.
Theorem 1. Under the conditions of Proposition ! given a fixed preservation effect A that is strictly decreasing with A, ler (-) ([57(-) denote the permutation explanation mapping in- duced by S₁, then for any sample (x) always achieve optimal faithfulness under the DEL, INS, NEG, POS, RP and IROF evaluation metrics.
Proof. Please refer to Appendix A for the proof.
Remark. Through Proposition and Theorem T we find that the saliency explanation mapping S7 achieves optimal faithfulness under both types of explanation evaluation, indicating that diverse faithfulness metrics share common underlying mathematical essence. Therefore, Equation (1) can be regarded as the consistent objective function the most faithful explanation mapping.
We can construct self-supervised optimization objective for the Learning to Explain paradigm by employing a Monte Carlo approximation of the ideal S7- Let de
[0, 1| denote neural
network parameterized by 0. Given sample set = ||]] C X, DeepFaith approximates the ideal most faithful explanation mapping Sj by optimizing the Local Correlation loss LLC:
LLC(po: D.f)
1
Σ r (EEEZ, (0()))) (Z)))= RED
(2)
2/D
where A, 7 and are user-defined, and Z, P([n)). Since we make no assumptions about the target model or task but instead start from explanation faithfulness itself, Equation (1) imposes strict requirements on Sy. making an ideally defined yet practically intractable explanation mapping. However, our self-supervised objective does not attempt to solve S7 directly; rather, provides clear optimization direction for DeepFaith by approximating S7.
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Algorithm Dynamic Joint Optimization Strategy for DeepFaithh
1: Input: Training dataset D, target model f, supervised signals 2, initial explainer parameters
Pe variance threshold e, monitoring window e, scaling factor C? 1, and learning rate 1
2: Initialize: dynamic weight (x +- I, convergence flag CF = 0, and set lg = 0
3: while not converged do
4: c
COBJ 4 ( c
(1- a (1) 1
b Compute total loss
5:
0g
(++1) 0/ 1/ 6o OBB
(t)
Update explainer parameters
6:
Pfc. t- Var(Crc (((t-++1)
(1)
> Compute variance LPC over last e iterations
7:
if CFCF then
8:
if ofc < then
9:
CF + t, +
Set Convergence Flag
10:
end if
end if
12:
if opc > Ce then
13:
CF + 0, ((+1) +1
Reset Convergence Flag
14:
end
15:
if CFF- = then
16:
(++11)
Gradually decrease a
1+exp(- )
17: end if
18:
end while
4 HIGH--AIIHFULNESS SUPERVISED EXPLANATION SIGNAL
In this section, we propose, for the first time, the generation of high-quality supervised explanation signals for the Learning to Explain paradigm, based on curation by explanation faithfulness.
As illustrated in Figure 1 to increase the diversity of supervisory signals and collect more faithful explanations for each sample, we first aggregate multiple prior explanation methods to generate set of imput-saliency explanation pairs as supervised explanation signals. Given sample set D and
K saliency explanation methods {5()) [==1 (e.g., Occlusion (Matthew D. Zeiler
2013). Saliency
(Simonyan al. (2014), DeepLIFT (Shrikumar al. 2017). Score-CAM (Wang al. 2020) and
Grad-CAM++ (Chattopadhyay et al. 2018)), we generate K saliency explanation { for each sample !², These explanations are then processed via deduplicating and filtering:
(x)) )=
Deduplicating: We compute the pairwise cosine similarity between K saliency explana- tions a given sample ,(()) and identify duplicate groups based on a similarity threshold 6. The first explanation in each group retained, while the others are removed. After dedu- plicating, the number of distinct saliency explanations is denoted as k<(i) S K. This dedup step aims to prevent highly similar explanations from introducing bias into the training of the explainer and to enhance the diversity of the signals.
Filtering: For each of the k-O (the faithfulness of saliency explanation can be evaluated from permutation perspective via }) to get their evaluation scores (r1, r2,.... P10). We determine filtering threshold (Fi, F2....... F10) by computing the p-quantile (or the (1 - -)-uuatelle for metrics where (+) lower is better) of all dedup scores under each metric. Finally, we retain fltter < dedup explanations satisfying Vj [10], r. 2 F, (or ry Fy for metrics where lower is better).
dedup retained explanations, we use all ten faithfulness metrics
After our explanation processing steps, the remained ones can be regarded as high- supervised explanation signals. For each input a((1), we replicate it (() filter times and pair each copy with its corresponding saliency explanation to construct the input- explanation pair set
Z z= { s0 (x(1)) i DD].j
(t)

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Oct
18
Garme St of
8
26a
42-
Dovectsc Gredirts
4000
Figure 2: In the ImageNet+DeiT explanation task, we compute 10 faithfulness metries for each explanation method on single sample. Red and green regions de- note the filtered-out range and retained range.
Figure 3: In the ImageNet+DeiiT expla- nation task, the values of Lpc, LLC, and over 100 training epochs of DeepFaith. We also report the training dynamic of op- timizing LLC alone as LLC-
DeepFaith optimizes the proximity between the explanations generated by do and the high-quality saliency explanation through the Pattern Consistency loss Lrc:
LPc( 2)
Σ
(1 (c)
Z
(2
where T can be any correlation measure and is not necessarily the same as the one used in Eq. (2)
5 FAITHFUL AMORTIZED EXPLAINER TRAINING STRATEGY
Many studies the current Learning to Explain paradigm have shown that solely optimizing self-supervised objective merely fitting supervisory signals derived from prior explanations each has inherent limitations. However, jointly optimizing both objectives is not straightforward. This is because the local and global optima of the two objectives differ, leading to inconsistent gradi- ent directions: optimizing one can easily degrade the other. To address this, we adopt a dynamic weighting- bbased strategy for explainer optimization, illustrated in Algorithm Let the dynamic weight be a E [0, IJ. the overall optimization objective of DeepFaith can be expressed as:
CoBs(ős; D. Z) = aCrc Z) + (1 a:) (b0 f)
(4)
At the beginning training, we set a = 1 so that the explainer initially prioritizes acquiring basic explanatory capability by fitting the supervised signals. During training, we continuously monitor the value of Lpc. the variance of LPC over consecutive iterations falls below a threshold e, we consider LPC to have converged and gradually decrease so that LLC dominates the optimization, further improving explanation quality. To ensure that optimizing LLC does not converge to a poor local minimum, the variance of Lrc continues to be monitored. If it exceeds Cc, the optimization direction of LLC is deemed to have deviated, and a = is reset to 1, allowing LpC to again dominate the optimization.
EXPERIMENTS
In this section, we report the observations during the generation of the supervised explanation sig- nals, as well as the performance of DeepFaith across various explanation tasks. We also provide ablation experiments to verify the necessity of combining LrC and Lı.c, as well as the deduplicat- ing and filtering of generating supervision signals. Visualizations of DeepFaith explanations and comparisons of runtime provided in Appendices H and Our code is available at this Github Repository
Experimental Setting To validate its capabilities across multiple target models and tasks, Deep- Faith is tested on image, text, and tabular modalities using various model architectures. These dataset-model combinations yield diverse settings with varying complexity, forming comprehen- sive and challenging benchmark for explanation quality. Dataset details are in Appendix B All experiments were conducted Ubuntu 22.04 with eight NVIDIA RTX A6000 GPUs.

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Table Comparison of average faithfulness between DeepFaith and other baseline methods across 12 explanation tasks. We report the average rank of each method under 10 faithfulness evaluation metries, where Red denotes the optimal.
ImageNet EfficeenNet
Method
ResNet
Deepiaich (ouns)
3.4
2,9
4.4
4.4
3.3
2.1
2.9
2.7
1.8
1,8
Integrated Grads
7.8
7.6
4.8
6.4
7.0
5.4
3.3
5.6
4.9
5.9
288
5.2
Gradienr SHAP
NIA
4.2
Deepl
Saliency
13.2
11.0
12.8
10.7
11.1
10.6
4.7
5.8
28
4.9
Occlusion
8,5
6.5
8,4
8.9
9.6
10,9
4.6
3.6
2,9
27
3.3
5,9
Feature Ablation
NIA
NIA
NIA
NIA
NIA
NIA
8.5
3.5
4.5
Kernel SHAP
4.2
10,9
12.1
7,0
5.9
8.9
6,4
3.9
3.9
8,9
Input Gradient
5.7
12.3
12.2
5.3
12.9
10.7
NIA
NIA
N/A
NIA
NIA
NAA
Guided Backprop
12.3
6.5
7.6
11.4
10.3
10.4
NIA
N/A
N/A
NIA
NIA
N/A
Grad-CAM
72
NIA
Cr++-CAM+
5.0
10.0
74
4,9
7.8
8.3
XIA
NAA
N/A
NIA
NIA
N/A
Expected Grads
6.9
K4
7.1
7.1
9.5
6.4
VIA
N/A
N/A
N/A
NAA
N/A
DeepL SHAP
8.7
NIA
N/A
LRP
10.2
NIA
Image modality: Following Latec (Klein et al.] 2024), we use ImageNet (Dng et al,
2009 and UCSD OCT Retina (OCT) (Kermany et al. 2018), explaining ResNet50 (He
et al.
2016), EfficientNeth0
TTan & Le 2019). and Deil
(Touvron et al. 2024).
Text modality: IMDb Movie Review (IMDb) (Maas al. 2011) and AGNews
Zhang
et al. 2016) are used with LSTM and vanilla Transformer (Vaswani et al. 2017).
Tabular modality: We use NHANES Age Prediction (NAP) (National Center for Health
Statistics 2019) and Wholesale Customers Data (WCD) (Cardoso 2013) from UCI, with MI.P-based predictors.
For the image modality, we generate supervised signals from and compare against the following baseline methods: Occlusion, LIME (Ribeiro et al. 2016), Kernel SHAP and DeepL.FT SHAP (Lundberg & Allen 2017). Saliency, Input Gradient (Shrikumar al. 2017). Guided Backprop (Springenberg et al. (2155). Grad-CAM (Selvaraju et 20.77) Score- CAM, Grad-CAM++, Inte- grated Grads (Sundararajan al.) (017), Expected Grads (Erion et al. 202T), DeepLIFT, and LRP (Binder et al. 2016). For the text and tabular modalities, we adopt Integrated Grads, Gradient SHAP Lundberg & Allen 2017). DeepLIFT, Saliency, Occlusion, Feature Ablation (Kokhlikyan et al,
2020). LIME. and Kernel SHAP. Parameter settings are listed in Appendix
Generating Supervised Explanation Signals Given a specific dataset and target model, DeepFaith generates high-quality input-saliency explanation pairs before training. Taking the task of explaining DeiT's predictions on ImageNet as an example, we use 14 widely adopted explanation methods from Captum (Kokhlikyan et 2020) generate patch-level explanations for 20,000 validation samples. Each explanation is evaluated using 10 faithfulness metrics (detailed in Appendix D
Figure 2 illustrates the häthfuuleess-asee filtering process of the supervised explanation signals for one sample. For each evaluation metric, we compute the p-quantile and remove explanations deemed unfaithful by any of the metrics. Detailed processes for all explanation tasks are provided in Appendix
Training Faithful Saliency Explainer We use a multi-layer Transformer Encoder the explainer for its strength in processing sequential inputs. It encodes patch-based images, tokenized text, or tabular rows, followed by normalized linear layer projecting to an n-dimensional saliency expla- nation. Task-specific configurations and hyperparameters of DeepFaith are in Appendix
We split the supervised explanation signals into training (80%) and test (20%) sets and train the explainer, with the training loss curves shown in Figure 3 During the early stage of training, the explainer optimizes LpC to the prior explanation methods, and subsequently maintains low Lpc throughout training under the constraints of the training strategy described in Algorithm [ Once LPc is confirmed to have converged, the explainer gradually optimizes LLC. intermittently setting = 1 to adjust the optimization direction. Despite oscillations, LLC steadily converges over this process, whereas optimizing the local-corellttoo loss alone, Lic exhibits pronounced oscillations and fails converge.
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Table 3: DeepFaith is compared against other Learning Explain methods across four different settings. The table reports the average test set scores on ten faithfulness evaluation metrics, as well as the average rank of each explainer across all metrics under each setting.
Setting
Explainer
FC
FEF
MCT
RP
INS
DEL.
NEG:
POSL
IROFt
INPt
Mean Rank
DeepFaith
0.788
0.763
0.952
0.957
0.844
0.031
0.770
0.031
0.844
0.238
1.3
L2X
0.129
0.141
0.899
0.346
0.832
0.749
0.819
0.748
0.302
0.142
3.5
NAP+MLP
CXPlain
0.017
0.308
0.501
0.290
0.153
0.647
0.722
0.301
0.445
0.143
3.7
FasSHAP
0.071
0.097
0,800
0.149
0.849
0.714
0.837
0.710
0.126
0.041
3.7
VerT
0.772
0.484
0.560
0.454
0.564
0.467
0.551
0.603
0.160
2.8
DaepFaith
0.363
0.597
0.629
0.648
0.919
0.197
0.906
0.256
0.650
0.275
1.6
L2X
0.012
0.303
0.336
0.367
0.765
0.621
0.740
0.618
0.320
0.071
4.2
AgNows+LSTM
CXPlain
0.097
0.258
0,402
0.328
0.589
0.189
0.189
0.371
0.030
3.6
FastHAP
0.419
0,251
0,500
0.505
0.800
0,546
0.780
0,551
0.395
0.062
3.2
VerT
0.077
0.519
0.526
0.710
0.838
0.362
0,204
0.762
0.092
2.4
DeepFuith
0.135
0.534
0.942
0.744
0.863
0.248
0.655
0.242
0.742
0.015
1.4
L2X
0.015
0.121
0.393
0.501
0.642
0,505
0.644
0,433
0.482
0.009
3.5
OCT+ResNel
CXPlain
0.004
0.239
0.611
0.356
0.554
0,525
0.508
0.513
0.349
0.008
4.2
FasSHAP
0.013
0.119
0.211
0.302
0.808
0.698
0.605
0.656
0.297
0.022
4.1
VerT
0.015
0.397
0.783
0.540
0.763
0,466
0.707
0.226
0.528
0.028
1.8
DecpFaith
0.026
0.447
0.884
0.486
0.568
0.127
0.417
0.295
0.672
0.014
1.6
L2X
0.004
0.101
0.267
0.198
0.486
0,526
0.520
0,481
0,385
0.014
3.9
ImageNet+Deil
CXPlain
0.003
0.023
0.341
0.237
0.186
0.172
0.211
0.192
0.431
0.017
3.6
FasSHAAP
0.006
0.012
0.227
0.358
0.451
0.439
0.485
0.457
0.461
0.027
3.2
VerT
0.005
0.131
0.505
0.414
0.363
0.323
0,365
0.367
0.588
0.019
2.7
For each explanation task, we compare the faithfulness of DeepFaith against other baseline expla- nation methods. Each explanation is scored using all ten faithfulness metrics and averaged across all test samples (see Appendix G for full results). To concisely summarize the overall explanation quality of each method, we rank all explanation methods under each metric and report their average rankings. Table 2 presents the evaluation results across all explanation tasks. DeepFaith consis- tently achieves the highest faithfulness across various modalities, demonstrating that our method enables the explainer to surpass the faithfulness of the baseline methods used during training and remains effective for complex models and nigh-dimensional feature tasks.
To further validate the advantages of DeepFaith over prior Learning to Explain methods, we con- ducted comparisons on four explanation tasks (NAP+MLP, AGNews+LSTM, OCT+ResNet, and ImageNet+DeiTT evaluating DeepFaith alongside four explainer baselines applicable across multi- ple modalities: VerT (Bhalla et al.) 2023), L2X (Chen et al.) 2018), CXPlain (Schwab & Karlen, 2019), and FastSHAP (Jethani et al. 2022). Table 3 reports the averaged test-set scores across ten faithfulness metrics.
In every task, DeepFaith achieves the highest faithfulness multiple metrics and consistently obtains the best average ranking. These results demonstrate that our method provides a clear im- provement over existing Learning to Explain approaches.
Ablation Study We selected four representative explanation tasks to organize ablation experiments, aiming evaluate the individual contributions of each loss in DeepFaith as well as the effects of deduplicating and filtering when generating supervised explanation signals. For each setting, the explainer trained for an equal number of epochs (100) under five ablation configurations: using the full loss function (COBs), only the pattern consistency loss (Crc), only the local consistency loss (LLc), using both losses with deduplicating only (COR)). and with filtering only (CbB.).
Table presents the results of the ablation experiments, revealing a consistent pattern across all four settings: DeepFaith trained with LoBJ achieves the highest faithfulness across all metrics. When only LrC or LL.C is used, DeepFaith degrades into either prior-explanation-divee or self-supervised Learning to Explain method, with the latter exhibiting poor faithfulness due to op- timization convergence difficulties. This aligns with the design rationale of our dynamic joint op- timization strategy. In the ablations concerning the generation of supervised explanation signals, applying only deduplicating or only filtering leads to reduced explainer performance, with the for- mer showing particularly lower faithfulness due to the lack of faithfulness-baat selection, thereby validating the effectiveness of our proposed approach.
Sensitivity Study of Hyperparameters We introduces several hyperparameters in different compo- nents of FeepFaith: the subset sampling size k in the computation of LLC; the similarity threshold

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Table Ablation study of DeepFaith on explanation tasks across four different settings. The table reports the average scores over test set on ten faithfulness evaluation metrics, where LOBJ denotes the explainer trained with both loss terms.
Setting
Ablation
FC1
FE 1
MC
RP f
INS 1
DEL 4
NEG
POS 4
IROF 1
INF
Cora
0.217
0.475
0.897
0.643
0.944
0.356
0.917
0.368
0.638
0,089
Lyc
0.032
0.231
0.655
0.540
0.913
0.463
0.904
0.521
0.534
0.031
OCT-DeiT
Cye
0.104
0.240
0.169
0.763
0.830
0.809
0.813
0.162
0.023
0.097
0.341
0.669
0.585
0,923
0.447
0.906
0.476
0.552
0.059
Cora
0,156
0.392
0.711
0.602
0,931
0.421
0.910
0.444
0,576
0.067
CoB
0.026
0.447
0.884
0.486
0.568
0.127
0.417
0.295
0.672
0.014
Cpc
0.022
0.364
0.823
0.456
0.501
0.185
0.406
0.366
0.638
0.008
ImageNettDeiiT
CLe
-0.047
-0.051
0.033
0.373
0.552
0.380
0.397
0.414
0.493
-0.037
Cora
0.023
0,390
0.839
0.464
0.523
0.170
0.409
0.348
0.647
0.010
0.024
0.406
0.856
0.472
0.545
0.156
0.412
0.331
0.655
0.011
Cosı
0.162
0,495
0.203
0.759
0,806
0.189
0.799
0.205
0.742
0,047
Cpc
0.058
0.358
0.195
0.718
0.784
0.192
0.775
0.344
0.655
0.038
IMDb-Transformer
Cye
0.023
0.235
0.167
0.316
0:667
0.708
0.738
0.652
0.223
0.013
Cos
0.089
0.402
0.196
0.733
0.791
0.191
0.783
0.310
0.678
0.040
0.115
0.427
0.198
0.746
0.796
0.190
0.789
0.276
0.701
0.042
Cow
0.788
0.763
0.952
0.957
0.031
0.770
0.238
Cpc
0.674
0.671
0.558
0.424
0.358
0.514
0.227
0,541
0.361
0.025
NAP+MLP
CLe
0.748
0.515
0.535
0.426
0.360
0.442
0.512
0.124
0.638
0.135
Cpe 0.703
0.694
0.623
0.552
0.479
0.393
0.363
0.414
0,482
0.079
COrI
0,731
0.717
0.755
0.690
0.601
0.273
0.498
0,286
0.603
0.132
5 and filtering quantile p when constructing the supervised explanation set; and the hyperparameters
e, e, and C in Algorithm|| for explainer training. Studying the sensitivity of these hyperparameters essential for understanding whether DeepFaith can generalize stably under different parameter settings, thereby reducing reliance on manual tuning.
Using the OCT+ResNet explanation task an example, conducted a comprehensive hyperpa- rameter sensitivity analysis. The detailed experimental configurations and results are provided in Appendix D The findings show that varying these hyperparameters leads to only minor changes in performance, and in practice it suffices to keep them within reasonable ranges. This demonstrates that Fath exhibits low sensitivity to its hyperparameters and maintains stable generalization.
CONCLUSION
Learning to Explain paradigm has charted promising yet challenging path for XAI researchers, and DeepFaith takes a crucial step along this trajectory. From the perspective of explanation faithful- ness, we propose improvements to the two main existing approaches within the Learning to Explain paradigm and introduce strategy to integrate them, bridging inherent limitations and offering a potential systematic solution. The baseline explanation methods used by DeepFaith to generate su- pervised signals can be replaced with any newly proposed techniques, and the explainer architecture can comprise any deep neural network capable of handling sequential inputs. This flexibility implies that DeepFaith can continuously evolve alongside advancements in XAI.
ACKNOWLEDGMENTS
This work was supported by the Joint Funds of the National Natural Science Foundation of China under (Grant No. U22A2099), the General Program of the National Natural Science Foundation of China under (Grant No. 62376028), the Excellent Young Scientists Fund (Overseas) of the National Natural Science Foundation of China, the National Key Scientific Instruments and Equipment De- velopment Project under (Grant No. 62427808), and the National Key Research and Development Program of China under (Grant No. 2022YFB2703100).
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A PROOF OF PROPOSITION 1 AND THEOREM! 1
A.1 PROOF OF PROPOSITION
Proof. By definition (Fq.) 1 Sj maximizes the correlation
[Eez, Sy(z))) (AIf(z), (Afl), 2.)l) :=1
over all valid saliency mappings Sy, for every choice of sample v E X and every collection of index sets {I We show optimality for each metric in turn.
Faithfulness Correlation (FC) for given is precisely the correlation evaluated over the full family of index sets I S [n]] Since Si maximizes for every such collection, no other saliency mapping can achieve a strictly larger FC value. Hence S attains the optimal FC.
Faithfulness Estimate (FE) is the empirical correlation computed across dataset (x((1) I 1-/=1 using the mapping Sy. By Eq. (1. S maximizes for every possible choice of {x!1) J= i= therefore, S7 yields the largest possible FE on any finite sample set and thus is FE-optimal.
Monotonicity Correlation (MC) and Infidelity (INF) share the same functional form as FC/FE: they are correlations т computed over particular collections of index sets (MC typically over ordered or monotone collections, INF over random draws Z₁ ~ P(n)))). Since S maximizes 7 for all choices of collections (including those specific to MC and INF), it must also maximize MC and INF,
A.2 PROOF OF THEOREM 1
Proof. III,, given an input sample Iet = = (x) and x² [x) denote the permutation
explanations generated by different mappings, and let s* = S7(x) be the corresponding optimal
saliency explanation. In addition, we denote (I, = A[s(x), [(x Z)] for simplicity.
Given any two index sets Ia, In satisfying Ejez. of 2 EjEz, 83 (i.e., the total saliency assigned to Ia is no less than that of Ip), suppose for contradiction that A (Ia Af, meaning that removing Io causes a larger change in the model output despite receiving a lower total saliency score.
Then, by the definition of the correlation measure т, there must exist another saliency assignment such that Ejer, 8j Ejez, 8j while achieving higher correlation between the saliency ordering and the corresponding perturbation effects, i.e..
DjEZ. 23 T (2EE (2mnte))) >
(()n)))))))))))
which directly contradicts the optimality of SJ as defined in Eq. T since S7 is the maximizer of the same correlation measure over all valid saliency mappings. Therefore, the assumption A A (In) < Aʃ, (Tx) must be false, and we can conclude that
A Ia Is,
Σ JEI
+ 1. (Ia) (In).
JEZz
Now consider the index sets - and U3=11 (j), which correspond to the top-i features
selected by n² and π, respectively. Since the permutation explanation x' s(s**) is obtained by sorting features in descending order of their saliency scores, it follows that for all S n, we have
Σj=1 * (()) (j) 2 Σj=1 "*)' i.e., the cumulative saliency of the top-i features selected by n² always at least as large as that selected by any other permutation æ. By the monotonic relationship just proven, this implies
A (U,===()) =()=
A
By aggregating this result over samples RP (2((0) I.N. JN Since A- is strictly decreasing with respect to A, i.e., larger perturbation
J we can directly get RP (1 f) 2
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effect corresponds to smaller A
value, we have
A Lay Iim
sj D (Tx S
JEZn
JEZL
from which it follows immediately that DEL(T";I, f) < DEL( f) and = S POS(T; z. f); by the same way, one can derive NEG(T";;, Z NEG(T: and (2) f) 2 (I (x
Finally, given a baseline input x representing the uninformative state, we have the identity
Ü ==1
m())
U j=1
which establishes the equivalence between the insertion and deletion processes. Together with the above ordering property, this leads to IN 2 IN,
B DATASETS INFORMATION
Table 5: FeepFaith performs explanation tasks on datasets from three modalities. In NAP, the model predicts age group from body measurements; in WCD, it forecasts Channel using product sales data.
Dataset
Sample Num
Description
ImageNet is large-scale visual dataset encompassing real-world concepts such as an- imals, objects, and scenes, serving as foundational dataset in the era of deep learning.
ImageNet
20,000
The OCT dataset comprises layered structural images of tissues such as the retina or cornea, used medical image analysis and disease diagnosis, typically including high-resolution cross-scctional or 3D volumetric data.
OCT
1,000
AGNews is news article classification dataset containing English news headlines and content, covering four major categories (Worl,, Sports, Business, Science), commonly used for text classification tasks.
AGNews
127,600
IMDb is a movie review sentiment analysis datasct containing English reviews labeled binary sentiment (positive/negative..
IMDb
50,000
The National Health and Nutrition Examination Survey (NHANES), administered by the Centers for Disease Control and Prevention, collects extensive health and nutri- tional information from diverse U.S. population.
NAP
2,278
The data set refers to clients a wholesale distributor. includes the annual spending in monetary units (m.u.) on diverse product categories.
WCD
440
Table 5 presents the explanation tasks of DeepFaith across three distinct data modalities, including ImageNet (Deng et al. 2009) and OCT (Kermany et al., 2018) for image-basee tasks, AGNews
Zhang et al. 2016) and IMDb (Maas | [011]) for text classification and sentiment analysis, as
well as NAP National Center for Health Statisties 2019) and WCD (Cardoso) 2013) for tabular
prediction problems related to health and consumer behavior.
Specifically, ImageNet is employed for large-scale image recognition and object classification, while OCT is used for medical image analysis and disease-related pattern identification. AGNews and IMDb respectively support topic classification and sentiment analysis in the NLP domain. Mean- while, NAP and WCD capture structured information in public health and retail contexts, enabling the evaluation of explanation quality on tabular data. Together, these datasets form a diverse and representative benchmark suite, allowing us to systematically assess the generality, robustness, and croas-modality applicability of explanation methods such DeepFaith.
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C BASELINE EXPLANATION METHODS
Table 6: Parameters of baseline explanation methods for experiments on text and tabular modality,
well whether each method is model-agnostic.
Method
Parameters
Model Agnostic
Integrated Grads
num steps=20, baseline=0
True
Gradient SHAP
num samples=5
Truc
DeepLIFT
baselines=0, eps=le-9
True
Saliency
None
True
Occlusion
strides=l, sliding window=1
Truc
Feature Ablation
perturbations per eval=1
True
LIME
num samples=100, perturbations per eval=1
Truc
Kernel SHAP
num samples=100, perturbations per eval=1
True
Table 7: Parameters of baseline explanation methods for experiments on the image modality, as well as whether each method is -adelsa.iostic.
Method
Parameters
Model Agnostic
Occlusion
strides=25, sliding window=50
True
LIME
num samples=1000 perturbations per eval=5
True
Kernel SHAP
samples= 1000, perturbations per eval=5
True
Saliency
None
True
Input x Gradient
None
True
Guided Backprop
None
True
Grad-CAM
None
False
Score-CAM
None
False
Grad-CAM++
None
False
Integrated Grads
num steps=30, baselines=0
True
Expected Grads
num samples=40, stdevs=0.001
True
DecpLIFT
baselines=0, eps=le99 None
True
DeepLIFT SHAP
True
LRP
eps= le-4, gamma=0.25
False
Tables 7 and 6 detail the parameters for each bascline explanation method used across the three modalities. For Occlusion (Matthew D. Zeiler 2013), the sliding window and strides must be specified. LIME (Ribeiro al. (016) and Kernel SHAP require setting the nun samples and the number of perturbed features per evaluation. For Integrated Grads (Sundararajan et al., (2017). num steps the discretization granularity along the integration path from the baseline the input, while baselines defines the reference input from which integration starts. Expected Grads (Erion al.) (021] requires both the num samples and stdevs, the standard deviation of Gaussian noise added to each sampled baseline. DeepLIFT (Shrikumar et al. 2017) attributes contributions relative to baselines input, with eps preventing division- division-by-zero.
L.P (Binder et al., (016), eps serves the same numerical stability purpose, and gamma adjusts the amplification of positive contributions. Gradient SHAP (Lundberg & Allen 2017) only requires specifying num samples, while Feature ( requires defining the number of perturbed features. For Saliency (Simonyan et al.] 2014). Input x Gradient (Shrikumar et al. (017). Guided Backprop (Springenberg et 20.5) Grad-CAM (Selvaraju al. 2017)). Score- CAor (Wang et al.) 2220), Grad-CAM++
Ablation (Kokhlikyan et al. | 2020)
(Chattopadhyay et al.) 2018). and DecpLIFT SHAP (Lundberg & 20177] we adopt the default
parameters provided by Captum (Kokhlikyan al. 2020).
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D FAITHFULNESS EVALUATION METRICS
Table Variants of the perturbation effect A, presevation effect and correlation 7, along with their corresponding formulations and descriptions.
Function
Variant
Formula
Description
Amizas
f(x) ftr 2)
Difference model prediction before after perturbation.
Avariance
Vax
[s(x]) - -f(x (IN))
Variance of the predicted class score under perturbations.
Airrett
f(x \I)
Prediction value retained after perturba-
[= [Z)
Aatio
fi (t)((s))
Ratio prediction values before and after perturbation.
Tpenseon
(a T) (0- 63/1|a alaab Blla
Classical Pearson correlation coefficient.
Tepearman
"puarnn (o). (36)
Classical Spearman correlation. coefficient Classical mean squared error.
Φे Σ
Ei (a. 6,
Table 8 reports several specific forms of the perturbation effect A, preservation effect A and cor- relation used in our faithfulness evaluation methods. Note that assume perturbing the originally predicted features will lead to decrease in the model output; therefore, A E [0. 1].
Table 9: Parameters of ten faithfulness metrics for three explanation tasks on ImageNet.
Table 10: Parameters of ten faithfulness metrics for three explanation tasks on OCT.
Metrie
Iz
Metric
[
FC
Tpuarson
3136
50
FC
Arsious
Tpeasson
3136
100
FE
Aminns
Tpearson
Ariine
Tposrson
MC
variance
Tspearman
MC
Anriamon
Tepearman
RP
minns
RP
Amiina
INS
cazges
3136
INS
Aarget
3136
DEL
Larget
3136
DEL
Aparget
3136
NRG
targes
3136
NEG
A target
3136
POS
Lazget
3136
POS
Aurget
3136
IROF
ralio
3136
IROF
3136
INF
milnus
Tpeasson
INF
Aminns
100
Table 11: Parameters of ten faithfulness metrics for four explanation tasks on text modality.
Table 12: Parameters of ten faithfulness metrics for two explanation tasks on tabular modality.
Metric
[
Metric
I.
FC
Amiine
Tpenssoon
10
100
FC
Amious
Tearsson
30
FE
minuss
Tpearson
Aminus
Tpearson
MC
puriaane
Tepeseziion
MC
Avariance
Tepearman
RP
minax
Aminus
sarget
10
INS
A
target
DEL
A larged
10
DEL
Atarget
NEG
sarget
10
NEG
A Aurget
POS
sarget
10
POS
Atarget
IROF
ratio
10
IROF
vatio
Amiuus
Tpeamson
100
INF
A
Tpearson
30
As shown in Table 9 we use the same evaluation metric parameters for the three explanation tasks on ImageNet, with those for the three tasks on OCT given in Table [0] For the four explanation tasks in the text modality, the tabular modality are listed Table [2] We use the same perturbation scheme- casemmeebaseliee... value replacement-wiin with identical baseline values across all experiments.
the parameters in Table [I] while those for the two tasks in
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E GENERATING SUPERVISED EXPLANATION SIGNALS
Table 13: Similarity threshold and p-quantile used by DeepFaith for deduplicating and filtering supervised explanation signals.
OCT
ImageNet
AGNews
IMD6
NAP
WCD
Threshold
DeiT
EfficienNNer
ResNet
DeiT
EfficientNet
ResNet
L.TTM
Transformer
LSTM
Transformer
MLP
MLP
Similaritty Thoeshold
0.90
0.90
0.88
0.90
0.85
0.90
0.60
0.65
0.60
0.60
0,90
0.93
P-Quantile
0.13
0.13
0.14
0.13
0.14
0.13
0.20
0.22
0.21
0.19
0.15
0.15
1all Dedopicated
Fileeed
Betention
0.6-
0.4
OCT-Dal
dct eticoneniee
OCT OcTvieetter
Imspetire- Delf
inapstie diitunndie
imagetiet dapdle
(MDRe LOM
Altlonss Parsfimer
HAP-MEP
WCDWMLP
Figure 4: For the 12 explanation tasks we selected. DeepFaith performs deduplicating and filtering on the explanations generated by all baseline methods. Total denotes the total number of explana- tions, Deduplicated denotes the proportion remaining after deduplicating, and Filtered denotes the proportion remaining after further quality-based filtering on top deduplicating.
Table 13 reports the similarity thresholds (for deduplicating) and p-quantiles (for filtering) used by FeepFaith when generating supervised explanation signals for 12 explanation tasks. Figure 4 illustrates, for each task, the proportion of explanations retained after deduplicating and filtering, relative to all generated explanations.
F EXPLAINER TRAINING CONFIGURATIONS
Table 14: The hyperparameters and training parameters of the explainer model (a multi-layer Trans- former encoder) are with varying complexities for different explanation tasks ensure general- ization. nr runs denotes the number of samples used for our local consistency loss.
OCT
ImugeNet
AGNews
IMDb
NAP WCD
Config
Dei'T
EMficienNNet ResNet
Dei'T
EfficientNet
LSTM
Transformer
LSTM
Transformer
seg
196
196
196
196
196
300
500
200
8
embed dim
768
768
768
768
768
512
512
64
n head
12
8
8
8
8
max
1000
1000
1000
100
hidden
1024
1024
1024
2048
1024
1024
1024
1024
1024
128
128
layers
8
drop prob
0.01
0.5
0.01
0.01
0.05
0.05
0.01
0.01
0.01
0.01
0.01
0.01
epochs
100
100
50
20
learning
le-5
le:5
le:5
le:5
lc.5
le:5
le:5
lc-5
weight decay
le-5
le-5
le:5
1e:5
1e.5
1e:5
le:5
1e-5
We set the hyperparameters in Algorithm T for all explanation tasks as follows: 1c 5, C = 10, and
5,
100 for LLC in Equation (2)
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Published as a conference paper at ICLR 2026
G FAITHFULNESS COMPARISON
In this section, we report the faithfulness comparison of DeepFaith and other baseline explanation methods across explanation tasks, including the average over all test samples for each faithfulness evaluation metric and the average ranking across all metrics, including FC (Bhatt al. 20200), FE (Alvarez Melis Jaakkola 2018), INF (Yeh et al. 2019), and MC for saliency explanations, as
Table 15: Faithfulness comparison of DeepFaith and baseline methods on OCT+DeiT task.
Method
FC
FE
MC
RP
INS
DEL
NEG
POS
IROF
INF
Mean Rank
DeepFaith
0.217
0.475
0.897
0.643
0.944
0.356
0.917
0.368
0.638
0.089
3.4
Occlusion
0.034
0.602
0.850
0.520
0.903
0.479
0.924
0.486
0.517
0.009
8,5
LIME
-0.155
0.132
0.394
0.531
0.689
0.466
0.650
0.469
0.527
0.024
12.3
Kernel SHAP
0.018
0.649
0.928
0.683
0.888
0,314
0.853
0.300
0.678
0.038
4.2
Saliency
0.006
0.105
0.287
0.314
0.740
0.685
0.764
0.691
0.310
0.004
13.2
Input Gradient
-0.002
0.575
0.759
0,604
0,920
0.395
0.887
0.312
0,598
0.030
5.7
Guided Backprop
0.009
0.075
0.424
0.339
0.690
0.660
0.774
0.682
0.336
0.026
12.3
Grad-CAM
0.030
0.464
0.784
0,582
0.877
0.414
0.869
0.374
0.577
40,008
8.6
Scorc-CAM
0.479
0.663
0.154
0.597
0.769
0.399
0.709
0.390
0.591
0.079
7.0
Grad-CAM++
0.047
0.571
0.822
0.599
0.921
0.397
0.874
0.358
0.594
0,058
5.0
Integrated Grads
0.272
0.788
0.438
0.547
0.858
0.449
0.664
0.429
0.542
0.114
7.8
Expected Grads
0.439
0.724
0.214
0.597
U.761
0,399
0.701
0.377
0.591
0.060
6.9
DeeplIFT
0.322
0.696
0,182
0.610
0.784
0.384
0.762
0.391
0.605
0.165
5.8
DeepLIFT SHAP
0.060
0.530
0,810
0,584
0.908
0.413
0.866
0.390
0.579
0.043
6.9
LRP
-0.010
0.012
0.944
0.410
0.707
0.589
0.696
0.617
0.408
0.019
12.0
Table 16: Faithfulness comparison of DeepFaith and baseline methods on OCT+EfficintNeet task.
Method
FE
MC
RP
INS
DEL.
NEG
POS
IROF
INF
Mcan Rank
FaepFaith
0.060
0.784
0.959
0.759
0.572
0,240
0.339
0.161
0.747
0.029
2.9
Occlusion
0.106
0.501
0.525
0.639
0,845
0.360
0.825
0.312
0.633
0.022
6.5
LIME
0.098
0.463
0.624
0.636
0.841
0.364
0.867
0.391
0,631
-0.001
8.1
Kernel SHAP
-0.031
0.054
0..44
0.691
0.403
0.303
0.252
0.272
0.685
-0.007
10.9
Saliency
-0.007
0.021
0.106
0.564
0.528
0.434
0.392
0.289
0.559
0.021
11.0
Input Gradient
0.011
-0.181
-0.618
0.452
0.531
0.551
0.397
0.479
0.448
-0.008
12.3
Guided Backprop
0.107
0.542
0.710
0.634
0.853
0.365
0.915
0.382
0.629
0.007
Grad-CAM
0.041
0.498
0.248
0.731
0.353
0.270
0.287
0.196
0.72
-0.033
8.2
Score-CAM
0.015
0.516
0.627
0.728
0.406
0.271
0.162
0.196
0.718
-0.018
7.9
Grad-CAM++
0.007
0.099
0.363
0.710
0.350
0.295
0.287
0.224
0.702
-0.019
10.0
Integrated Grads
0.074
0.522
0.116
0.735
0.347
0.259
0.282
0.176
0.725
-0.051
7.6
Expected Grads
-0.004
0.390
0.056
0.737
0.379
0.262
0.245
0.175
0.726
0.001
8.0
DecpLIFT
0,092
0.471
0.599
0.638
0.847
0.362
0.858
0.373
0.632
-0.008
7.8
DeT SHAP
0.050
0.495
0.228
0.751
0.351
0.260
0.303
0.187
0.740
-0.026
7.3
LRP
0.065
0.726
0.981
0.727
0.727
0.270
0.490
0.171
0.717
0.001
4.5
Table 17: Faithfulness comparison of DeepFaith and bascline methods on OCT+ResNet task.
Method
FC
FB
MC
RP
INS
DEL
NEG
POS
IROF
INF
Mcan Rank
DeepPaith
0.135
0.534
0.942
0.744
0.863
0.248
0.655
0.242
0.742
0.015
4.1
Occlusion
0.072
0.523
0.766
0.677
0.930
0.316
0.888
0.372
0.677
0.028
8.4
LIME
0.062
0.413
0.738
0.672
0.931
0.320
0.908
0.364
0.672
-0.010
Kernel SHIP
-0.029
0.318
0,900
0.651
0.734
0.343
0.490
0.409
0.645
-0.029
12.1
Saliency
0.011
0.111
0.327
0.551
0.675
0.443
0.576
0.368
0.549
-0.003
12.8
Input x Gradient
0.010
0.013
0.818
0,502
0.673
0.490
0.573
0.438
0.500
0.012
12.2
Guided Backprop
0.039
0.452
0.769
0.685
0.932
0.307
0.922
0.333
0.686
0.008
7.6
Grad-CAM
0.139
0.638
0.375
0.730
0.667
0.261
0.457
0.148
0.723
0.007
7.6
Score-CAM
0.108
0.697
0.810
0.717
0.939
0.275
0.659
0.236
0.710
-0.001
6.0
Grad-CAM++
0.100
0.619
0.256
0.728
0.898
0.266
0.544
0.184
0.720
0.015
Integrated Grads
0.155
0.730
0.358
0.741
0.692
0.250
0.509
0.136
0.733
0.024
Expected Grads
0.158
0.661
0.368
0.731
0.668
0.260
0.465
0.135
0.724
-0.010
7.1
DeepLIFT
0.075
0.425
0.771
0.683
0.932
0,308
0.908
0.357
0.683
-0.002
8.1
DeepLIFT SHAP
0.103
0.696
0.351
0.737
0.808
0.253
0.582
0.152
0.732
0.015
5.6
LRP
0.109
0.684
0.852
0.724
0.932
0.268
0.727
0.242
0.718
0.011
5.4
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Published as a conference paper at ICLR 2026
well DEL and INS PPetsiuk & Saenko 2018), NEG and POS
(Barkan al. 2023). RP, and
IROF (Rieger& & Hansen 2020) for permutation explanations.
Table 18: Faithfulness comparison of DeepFaith and baseline methods on ImageNet+DeiiT task.
Method
FC
FE
MC
RP
INS
DEL
NEG
POS
IROF
INF
Mean Rank
DeepFaith
0,060
0.784
0.959
0.759
0.572
0.240
0.339
0.161
0.747
0.029
2.9
Occlusion
0.106
0.501
0.525
0.639
0,845
0.360
0.825
0.312
0,633
0.022
6.5
LIME
0.098
0.463
0.624
0.636
0.841
0.364
0.867
0.391
0.631
-0.001
8.1
Kernel SHAP
-0.031
0.054
-0.044
0.691
0.403
0.303
0,252
0.272
0.685
-0.007
10.9
Saliency
-0.007
0.021
0.106
0.564
0.528
0.434
0.392
0.289
0.559
0.021
11.0
Input Grudient
0.011
-0.181
-0.618
0.452
0.531
0.551
0.397
0.479
0,448
-0.008
12.3
Guided Backprop
0.107
0.542
0.710
0.634
0.853
0.365
0.915
0.382
0.629
0.007
Grad-CAM
0.041
0.498
0.248
0.731
0.353
0.270
0.287
0.196
0.720
-0.033
Score-CAM
0.015
0.516
0.627
0.728
0.406
0.271
0.162
0.196
0.718
-0.018
7.9
Grad-CAM+
0.007
0.099
0.363
0.710
0.350
0.295
0.287
0.224
0.702
-0.019
10.0
Integrated Grads
0,074
0,522
0.116
0.735
0.347
0.259
0.282
0.176
0.725
-0.051
7.6
Expected Grads
-0.004
0.390
0.056
0.737
0.379
0.262
0.245
0.175
0.726
0.001
8.0
DecpLIFT
0.092
0.471
0.599
0.638
0.847
0.362
0.858
0.373
0.632
-0.008
7.8
DIT SHAP
0,050
0.495
0.228
0.751
0.351
0.260
0.303
0.187
0.740
-0.026
LRP
0.065
0.726
0.981
0.727
0.727
0.270
0.490
0.717
0.001
Table 19: Faithfulness comparison of DeepFaith and baseline methods on ImageNet+=EffiieenNNeet
task.
Method
FC
FE
MC
RP
INS
DEL
NEG
POS
IROF
INF
Mean Rank
DeepFaith
0,021
0.217
0.835
0.591
0.525
0.174
0.405
0.156
0,749
0.004
4.4
Occlusion
0.007
-0.017
-0.525
0.333
0.499
0.360
0.445
0.415
0,476
0.028
9.6
LIME
-0.088
0.112
0.921
0.461
0.593
0.231
0.542
0.306
0.657
0.012
6.6
Kernel STIAP
0.003
0.102
0.928
0.535
0.554
0.158
0.400
0.245
0.772
0.019
5.9
Saliency
-0.016
-0.022
-0.161
0.410
0,423
0,283
0.350
0.338
0.559
0.011
11.1
Input Gradient
-0.053
-0.073
-0.802
0.344
0.423
0.349
0.380
0.393
0.446
-0.015
12.9
Guided Backprop
-0.022
-0.012
0.279
0.321
0.535
0.372
0.496
0.430
0.469
Grad-CAM
-0.009
0.122
0,282
0.595
0,404
0.099
0.255
0.182
0.852
6.6
Score-CAM
0.005
0.103
0.389
0.559
0.466
0.135
0.291
0.233
0.808
+0.005
7.2
GradCCA+++
0.004
0.087
0.234
0.538
0.457
0,156
0.295
0.241
0.782
0.014
7.8
Integrated Grads
-0.016
0.192
0.287
0.590
0,397
0.103
0.274
0.186
0.848
-0.030
7.0
Expected Grads
-0.037
0.137
0.263
0,492
0.460
0.201
0.334
0.286
0,717
-0.014
9.5
DeepLIFT
-0.050
0.164
0.890
0,450
0.575
0.243
0.537
0.304
0.639
0.027
6.9
IIT SHAP
-0.066
0,112
0.287
0.588
0.397
006
0.248
0.195
0.843
-0.035
8.7
LRP
0.005
0.139
0.964
0.555
0.506
0.138
0.363
0.231
0.794
0.010
5.0
Table 20: Faithfulness comparison of DeepFaith and bascline methods on ImageNet+ResNet task.
Method
FC
FE
MC
RP
INS
DEL
NEG
POS
IROF
INF
Mean Rank
DeepFaith
0.031
0.254
0.938
0.677
0.577
0.106
0.471
0.182
0.871
0.019
3.3
Occlusion
0.023
0.053
0.125
0.457
0.507
0.285
0.393
0.366
0.633
0.015
10.9
LIME
0.202
0.942
0.573
0.562
0.498
0.280
0.776
-0.004
8.5
Kernel SHAP
0.761
0.579
0.435
0.164
0.344
0.255
0.775
8.9
Saliency
0.006
0.030
0.005
0.627
0.365
0.115
0.268
0.220
0.840
0.003
Input x Gradient
0..41
-0.012
-0.337
0.640
0.373
0.101
0.257
0.204
0.856
-0.041
10.7
Guided Backprop
-0.012
0.066
0.414
0.492
0.513
0.250
0.407
0,340
0.668
0.028
10.4
Grad-CAM
0.042
0.199
0,569
0.655
0.367
0.088
0.271
0.199
0.870
-0.026
7.0
Score-CAM
0.041
0.268
0.697
0.628
0,380
0.116
0.282
0.230
0.846
0.009
7.1
Grad-CAM++
0.057
0.104
0.626
0,627
0.449
0.116
0.284
0.212
0.835
-0.017
8.3
Integrated Grads
0.023
0.244
0.570
0.666
0.368
0.078
0.256
0.162
0.882
0.035
5.4
Expected Grads
0.012
0.253
0.560
0.654
0.352
0.090
0.259
0.180
0.872
0.045
6.4
DcepLIFT
-0.001
0.181
0.910
0.510
0.526
0.232
0.456
0.327
0.693
0.040
8.4
DeTpLIFT SHAP
0.019
0.178
0.604
0.629
0.362
0.114
0.267
0.207
0.839
-0.003
9.3
LRP
0.036
0.946
0.648
0.450
0.374
0.186
0.868
0.004
4.5
Tables
15
I6 and 17
present the experimental results for the three explanation tasks on the OCT
dataset, while Tables 18
19 and 20 report those the ImageNet dataset.
20

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Published as a conference paper at ICLR 2026
In all cases, FeepFaith achieves the optimal average ranking, indicating that its generated explana- tions exhibit strong generalization from a faithfulness perspective across test set samples.
Table 21: Faithfulness comparison of DeepFaith and baseline methods on IMDD+LSTM task.
Method
FC
FE
MC
RP
INS
DEL
NEG
POS
IROF
INF
Mean Rank
DeepFaith
0.172
0.486
0.360
0.812
0.872
0.151
0.869
0.182
0.813
0.038
2.3
Integrated Grads
0.201
0.492
0.048
0.798
0.832
0.167
0.827
0.195
0.798
0.324
3.3
Gradient SHAP
0.081
0.277
0.054
0.796
0.832
0.168
0.828
0.207
0.797
0.278
4,4
Dee
0.031
0.088
0.154
0.517
0.840
0.442
0.846
0.501
0.521
0.081
6.1
Saliency
0.093
0.256
0.050
0.706
0.835
0.255
0.840
0.328
0,709
0.161
5.2
Occlusion
0.087
0.311
0.049
0.794
0.832
0.169
0.829
0.209
0.795
0.313
4.6
Feature Ablation
0.042
0.082
0.018
0.765
0.832
0.199
0.829
0.233
0,766
0.082
6.4
LIME
0.020
0.056
-0.844
0.408
0.890
0.551
0.864
0.530
0.410
0.036
7.7
Kernel SHAP
0.094
0.250
0,994
0.452
0.913
0,508
0.900
0.411
0,453
0.060
5.0
Table 22: Faithfulness comparison of DeepFaith and baseline methods IMDD+ task.
Method
FC
FE
MC
RP
INS
DEL
NEG
POS
IROF
INF
Mean Rank
DeepFaith
0.162
0.495
0.203
0.759
0.806
0.189
0.799
0.205
0.742
0.047
2.1
Integrated Grads
0.061
0.208
0.037
0.634
0.766
0.307
0.762
0.355
0.625
0.128
5.6
Gradient SHAP
0.117
0.347
0.066
0.739
0.760
0.210
0.747
0.219
0.722
0.301
4.0
DeepI.IFT IFF
0.019
0.062
0.073
0.338
0.800
0.599
0.774
0.577
0.332
0.058
6.4
Saliency
0.050
0.167
0.060
0.577
0.770
0.363
0.768
0.406
0.570
0.107
5.9
Occlusion
0.119
0.352
0.071
0.740
0.760
0,210
0.747
0.218
0.723
0.308
3.6
Feature Ablation
0.110
0.324
0.060
0.729
0.760
0,220
0.748
0.236
0.712
0.258
5.1
LIME
0.021
0.064
0.075
0.299
0.817
0.638
0.767
0.592
0.294
0.040
6.8
Kernel SHAP
0.102
0.178
0.979
0.283
0.819
0.655
0,803
0.566
0.276
0.052
5.5
Table 23: Faithfulness comparison of DeepFaith and baseline methods on AGNews+LSTM task.
Method
FC
FE
MC
RP
INS
DEL
NEG
POS
IROF
INF
Mean Rank
DeepFaith
0.363
0.597
0.629
0.648
0.919
0.197
0.906
0.256
0.650
0,275
2.9
Integrated Grads
0.492
0.597
0.052
0.571
0.838
0.375
0.825
0,383
0,573
0,313
4,9
Gradient SHAP
0.302
0.623
0.019
0.787
0.879
0.161
0.868
0.176
0.786
0.434
2.9
Deep
0.032
0.095
0.077
0.373
0.846
0.568
0.825
0.564
0.377
0.074
7.9
Saliency
0.497
0.597
0.052
0.571
0.838
0.375
0.825
0.383
0.573
0.316
4.7
Occlusion
0.313
0.671
-0.001
0.727
0.882
0.122
0.871
0,214
0.726
0.362
2.9
Feature Ablation
0.226
0.311
0,028
0.539
0.844
0.407
0.831
0.416
0.541
0.217
6.6
LIME
0.061
0.202
0.269
0.657
0.908
0.284
0.890
0.296
0.663
0.067
4.6
Kernel SHAP
0.112
0.245
0.952
0.445
0.853
0.496
0.838
0.498
0.449
0.111
6.4
Table 24: Faithfulness comparison of DeepFaith and baseline methods on AGNews=Fransformer
task.
Method
FC
FE
MC
RP
INS
DEL
NEG
POS
IROF
INF
Mean Rank
DeepFaith
0.111
0.318
0.464
0.663
0.901
0.277
0.864
0.194
0.651
0.082
2.7
Integrated Grads
0.119
0.290
0.015
0.400
0.808
0.545
0.776
0.529
0.370
0.154
5.9
Gradient SHAP
0.091
0.402
0.065
0.627
0.811
0.321
0.780
0.319
0.601
0.249
4.2
DeepLIFFT
0.036
0.095
0.222
0.464
0.813
0.474
0.785
0.477
0,444
0.110
5.9
Saliency
0.121
0.290
0.015
0.400
0.808
0.545
0.776
0.529
0.370
0.154
5.8
Occlusion
0.099
0.500
0.028
0.787
0.811
0.163
0.782
0.163
0.755
0.290
2.7
Feature Ablation
0.027
0.204
0.019
0.391
0.775
0.554
0.739
0.557
0.363
0.099
8.5
LIME
0.081
0.231
-0.038
0.655
0.816
0.285
0.789
0.282
0.633
0.175
4.5
Kernel SHAP
0.102
0.236
0.993
0.609
0.897
0.328
0.858
0.271
0.599
0.123
3.9
Tables 21 and 22
present the experimental results for the two explanation tasks on the IMDb dataset,
while Tables 23
and 24
report those the AGNews dataset. DeepFaith outperforms all base-
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Published as a conference paper at ICLR 2026
line explanation methods the two IMDb tasks and matches the overall faithfulness of the best- performing baseline on AGNews. These results demonstrate that DeepFaith also provides highly faithful explanations for data in the text modality.
Table 25: Faithfulness comparison of DeepFaith and baseline methods on NAP+MLP task.
Method
FC
FE
MC
RP
INS
DEL
NEG
POS
IROF
INF
Mcan Rank
DccpFaith
0.788
0.763
0.952
0.957
0.844
0.031
0.770
0.031
0.844
0.238
1.8
Integrated Grads
-0.173
-0.186
0.077
-0.052
0.821
0.875
0.823
0.875
-0.064
-0.154
2.8
Grudient SHAP
-0.178
-0.189
0.043
-0.052
0.817
0.875
0.819
-0.064
-0.153
DicpLifft
-0.75
-0.187
-0.033
-0.052
0.814
0.875
0.817
0.875
-0.064
-0.146
4,4
Saliency
-0.173
-0,186
0.077
-0.052
0.821
0.875
0.823
0.875
-0.064
-0.154
2.8
Occlusion
-0.171
-0.188
0.132
-0.052
0.816
0.875
0.819
-0.064
-0.151
3.3
Feature Ablation
-0.173
-0,188
0.098
-0.052
0.816
0.875
0.819
0.875
-0.064
-0.151
3.5
LIME
-0.175
-0.189
0.052
-0.052
0.814
0.875
0.817
0.875
-0.064
-0.148
4.7
Kernel SHAP
-0.180
-0.187
0.531
-0.052
0.820
0.875
0.822
-0.064
-0.158
3.9
Table 26: Faithfulness comparison DeepFaith and baseline methods on WCD+MLP task.
Method
FC
FE
MC
INS
DEL
NEG
POS
IROF
INF
Mean Rank
DeepFaith
0.961
0.961
0.679
0.364
0.723
0.551
0.575
0,455
0.306
0,929
1.8
Integrated Grads
0.142
0.132
0.534
0.074
0.536
0.492
0.526
0.477
0.066
0.197
5.2
Gradient SHAP
0.169
0.130
0.523
0.070
0.534
0.496
0,522
0,488
0,063
0.202
7.3
DeepLIFT
0.184
0.152
0.666
0.089
0.548
0.539
0.467
0.081
0.218
2.3
Saliency
0.160
0.132
0.534
0.074
0.536
0.492
0,526
0.477
0.066
0.200
4,9
Ocelusion
0.168
0.136
0.672
0.072
0.536
0.495
0.524
0.486
0.064
0.198
5.9
Feature Ablation
0.175
0.141
0.654
0.073
0.538
0.493
0.526
0.484
0.066
0.211
4.5
LIME
0.186
0.159
0.551
0.089
0.547
0.479
0.537
0.468
0.080
0.220
2.7
Kernel SHAP
0.071
0.049
-0.056
0.048
0.515
0.516
0.500
0.512
0.042
0.181
8.9
Tables 25 and 26 present the experimental results of explaining MLPs on the UCI dataset. Many bascline explanation methods score poorly on correlation-basee faithfulness metrics such as FC and FE, their perturbation procedures overly complex relative to the simplicity of the explained model. contrast, DeepFaith directly improves correlation seaeedttoo----eedddd faithfulness by optimizing the local correlation loss, achieving comprehensive superiority over the baseline explanation methods.
H VISUALIZATIONS OF EXPLANATIONS
Imput
DespFaith
GndCAM
GrdCAM++
Stme-CAM
Occlusion
Kemel
Salieney
Expected
Despl.FT
Samplel
INS1
DEL
0,158
0.162
0.432
0.398
0.489
0,699
0.338
0.101
0.239
Sample?
INS1
0.641
DEL
Sample1
INS1
0.841
0.593
0.438
0.610
0.536
0.67%
0.525
DEL
Figure 5: Saliency explanations generated by Feep for DeiT on the ImageNet dataset, along with those produced by baseline methods for the same inputs.
22

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Published as a conference paper at ICLR 2026
Input
DeepFails
GradCAM
OndCAM-
Occlesion
Kernel
Saliency
Expected
DeepLiFT
Sample4
INS1 DELJ
0.946
0.885
0.574
0.842
0.921
0,572
0.161
0.491
0.189
0.274
0.137
0.236
0.29%
0.221
0,636
0.266
0.293
0.305
0.345
0,259
Sumples
INS1 DEL
0.958
0.879
0.687
0.844
0.706
0,664
0.114
0.354
0.315
0.404
0.544
0,403
0.406
0.401
0.239
0.388
Sample6
INST
0.896
0.798
0.745
0.727
0,659
0.664
0.338
0.459
0.482
0.728
DEL
0.309
0.337
Figure 6: Saliency explanations generated by DeepFaith for EfficientNet the OCT dataset, along with those produced by baseline methods for the same inputs.
Predicted Label: sport (1.00) Word Importance:
(s
radcliffe withdrawal not due injury world record holder paula radcliffe tearful
withdrawal from the women s olympic marathon yesterday was not due to injury the
british team says
Figure 7: Attribution by DeepFaith for an LSTM predicting sport the AGNews dataset.
Predicted Label: science (0.99) Word Importance: (s
0.5
new web domain names get preliminary nod ap ap two new internet domain names post
and travel could appear online as early as next year as the internet key oversight board
announced preliminary approval on wednesday
Figure 8: Attribution by DeepFaith for LSTM predicting science news the AGNews dataset.
Predicted Label: business (0.86) Word Importance: (s
0.5
microsoft settles antitrust cases with novell ccia microsoft corp monday announced
antitrust settlements with novell inc and the computer and communications industry
association ccia ending years of legal wrangling
Figure 9: Attribution by DeepFaith for an LSTM predicting business news on the AGNews dataset.
Predicted Label: world (0.99) Word Importance: (s
0.5
africa must move away from conflicts mbeki lusaka africa must move away from conflicts
begin to pool its resources develop impoverished continent reduce poverty
south african president thabo mbeki said on sunday
Figure 10: Attribution by DeepFaith for an LSTM predicting world news on the AGNews dataset.
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Published as a conference paper at ICLR 2026
Predicted Label: positive (0.99) Word Importance: (s
0.5
whenever ida lupino appeared or directed a film in the s s and $ you were guaranteed great entertainment even if the picture was black and white ida was able to capture
audiences and keep them spellbound until the very end of her pictures in this film as mrs helen gordon high sierra along with robert ryan howard wilton golden gloves she keeps you guessing just how the relationship is going to turn out and just how poor mrs gordon will able to have a normal and happy marriage with love and real affection if you liked ida lupino who could play the roles as a criminal in woman prison and prison warden who was hated this is the film for you to enjoy truly believe that ida lupino was not given the true credit she deserved for her great talents in the movie industry
Figure 11: Attribution by DeepFaith for Transformer predicting review the positive category on the IMDb dataset.
Predicted Label: negative (0.99) Word Importance: (s
0.5
when you make film with a killer kids premise there are two effective ways to approach it
you can either make it as realistic as possible creating believable characters and situations or you can make it as fun as possible by playing it for laughs something which the makers of silent night deadly night did for example
equally controversial subject killer santa the people who made bloody birthday however do neither of those things they simply rely on the shock value of the image of a kid with gun or a knife or a noose or an arrow in his her hand the result both offensive and stupid the whole film looks like bad idea that was rushed through production and then kept from release for several years it redeemed tiny bit by good performances from the kids but it s very sloppily made
Figure 12: Attribution by DeepFaith for a Transformer predicting a review as the negative category on the IMDb dataset.
Outpet Scake 3.07
Ouggr ASRE VT
Oupsa Chand 1-0.0
Osger Cleand 0090
EXRL
Regani
(U0)
8X17
Firass
3.0
Fizco
MIA
1
8:34
BMI
1190
0.155
Ckose
0,37
Dibet
230
6,115
15.00
0:445
11.7
330
Delicsses
Figure 13: DeepFaith attributing four feature vectors predicted as different classes on the NAP (left) and WCD (right) datasets, respectively.
linuressSaandovvssataa the saliency maps produced by DeepFaith and baseline explanation meth- ods on two image-modality datasets, together with their faithfulness scores INS and DEL. Deep- Faith not only achieves superior faithfulness metries but also provides explanations that are more aligned with human interpretability.
For example, on the OCT dataset shown in Figure 6 DeepFaith explanations fully cover the rele- vant feature regions while highlighting finer-graines critical features. For samples 4 and 5-each corresponding to different ocular diseases the highlighted areas produced by DeepFaith concen- trate precisely on the abnormal lesion regions. For sample 6, which is labeled as healthy, DeepFaith highlights are evenly distributed across the feature region. The model decision rationale revealed by the explainer aligns closely with human understanding.
24

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Published as a conference paper at ICLR 2026
I RUNTIME COMPARISONS
Table 27: Average runtime (in ms) of DeepFaith and baseline methods for explaining single sample the image modality.
OCT
ImageNet
Method
DeiT
EfficientNet
ResNet
DeiT
EfficientNet
ResNet
DeepFaith
0.609
2.406
2.103
3,103
1.207
2.403
Integrated Grads
78.425
48.764
103.721
95.132
52.537
110,638
DeepLIFT
3.618
14.649
15.003
14.918
14.417
15.428
Saliency
3.874
6.526
8.548
11.264
6.543
9,254
Occlusion
96.147
67.728
170.348
115.435
72.366
185.721
LIME
145.517
135.273
93.352
121.143
100.769
137.326
Kernel SHAP
69.891
65,862
63.114
68.946
71.627
69.642
Input Gradient
3.747
2.584
3.134
3.839
1.964
3,378
Guided Backprop
3,438
2.561
3.372
4.849
1.978
3,673
Grad-CAM
4.139
9.163
9.617
13.756
8.739
10.539
Score-CAM
553.973
1037.456
3628.819
3609.633
1266.827
4203.115
Grad-CAM++
4.389
3.957
3.769
6.048
3.652
4.548
Expected Grads
57.642
65.432
122.261
124.935
65,934
127.967
DeepLIFT SHAP
14.293
29.317
86.179
57.848
34.158
98.453
LRP
7.519
6.867
8.539
17.548
7.716
8.134
Table 28: Average runtime (in ms) of DeepFaith and baseline methods for explaining single sample text and tabular modality.
IMDb
AGNews
NAP
WCD
Method
LSTM
Transformer
LSTM
Transformer
MLP
MLP
DeepFaith
1.217
0.563
1.137
0.433
0.117
0.173
Integrated Grads
3.125
21.926
53,941
58,473
2.839
0.219
Gradient SHAP
0.781
1.302
2.938
3.983
0.331
0.135
DeepLIFT
2.446
0.539
3.101
0.849
0.272
0.193
Saliency
1.278
0.238
5.894
0.682
0.254
0.137
Occlusion
10.872
0.587
61.725
25.734
0.563
0.293
Feature Ablation
21.921
0.253
60.987
25.768
0.337
0.293
LIME
59.067
15.954
79.311
112.438
16. 125
22,443
Kernel SHAP
152.933
20.539
79.645
106.965
37.575
49.441
DeepFaith differs from conventional post-hoc attribution methods by incurring one-time cost for generating supervised explanation signals and training its explainer. Once trained, however, it deliv- ers explanations with low latency, making it well-suited for time-critical applications.
Across image, text, and tabular modalities, DeepFaith consistently produces explanations faster than sampling-bast based methods such LIME, Kernel SHAP, and Occlusion, which require repeated perturbations and evaluations. It also outperforms most gradient-based approaches, including In- tegrated Grads, Grad-CAM, and Grad-CAM++, by avoiding repeated backpropagation through the explained model. This advantage becomes more pronounced for complex architectures, where the runtime of many baselines scales with model size, while DeepFaith remains largely unaffected due to its decoupling from the architecture of the target model.
The results demonstrate that DeepFaith's ' inference speed not only competitive but often superior across different backbones and modalities. Moreover, its consistent efficiency ensures that the same explainer design can be deployed in varied domains without sacrificing latency, enabling real-time interpretability in settings where both speed and explanation quality critical.
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Published as a conference paper at ICLR 2026
J SENSITIVITY STUDY OF HYPERPARAMETRES
Table 29: Sensitivity study of DeepFaith. The baseline (first row) uses the original recommended hyperparameters (6,p,e, e, C). 1/4 hyperparameter while keeping others fixed.
after each hyperparameter indicates increasing/deereasing that
Method
PCT
FET
MCT
RPT
INST
DEL,
NEG1
POST
IROFT
INFT
AAP
DeepPaith&,p..ccm
0.135
0.534
0.942
0.744
0.863
0.248
0.655
0.242
0.742
0.015
0
DeepFaith p...c..
0.140
0.497
0.919
0.706
0.783
0.266
0.628
0.266
0.717
0.016
3.513%
shepPaithss.....c..
0.123
0.563
0.870
0.753
0.940
0.225
0.698
0.223
0.774
0.014
1.246%
DeepFaiths,pt..cc
0.147
0.511
0.954
0.679
0.863
0,272
0.619
0.258
0.693
0.016
2.083%
DeepPaithssp...cc.
0.122
0.575
0.891
0.817
0.797
0.235
0.705
0.218
0.799
0.014
1.01%%
s.p.pt..
0.118
0,588
0.924
0.709
0.884
0.276
0.672
0.270
0.664
0.036
0.410%
0.135
0.552
0.913
0.744
0.864
0.247
0.654
0.241
0.743
0.016
0.214%
DeepFaitha,p..cce &p...
0.136
0.557
0.905
0.743
0.863
0.248
0.654
0.243
0.740
0.016
0.292%
DeepFaith& & &....c..kk
0.117
0.589
0.930
0.710
0.885
0.276
0.673
0.269
0.665
0.037
0.605%
DeepFaith smepFaith&pp..ccmm 6.p..
0.143
0.522
0.913
0.727
0.847
0.245
0.626
0.236
0.721
0.005
2.636%
0.260
0.674
0.929
0.720
0.910
0.270
0.697
0.264
0.688
0.008
5.859%
To empirically validate the sensitivity of DeepFaith hyperparameters, conducted study the OCT+ResNet explanation task, testing the impact varying the similarity threshold 8, quantile p, monitoring window size and scaling factor C' on DeepFaith (with set to small positive value close to 0, using e = 10-5 as in Appendix Fb. The configurations are as follows:
DeepFaiths.p..cc the original configuration from the paper, = 0.88, = 0.14, = 5, C' = 10 and k 100.
DeepFaith at similarity threshold increased to 0.95, representing stricter deduplication policy.
DeepFaithssppe.cct similarity threshold decreased to d = 0.70, representing a more per- missive deduplication policy.
DeepFaith spthe, filtering quantile increased to p 0.2, representing a stricter filtering policy.
SrepFFathhsp..e.co filtering quantile decreased to p 0.05, representing more permis- sive filtering policy.
DeepFaatths,.ettr p.t window size increased to 10, making the algorithm less sensitive variance changes in LPc.
DeepFaith pp.e,,... window size reduced 3, making the algorithm more sensitive to variance changes in LPc.
DeepFaatthsp...ct..t scaling factor increased to 20, increasing the magnitude of a- updates.
DeepFaith DecpFaithspee.c..ut c updates.
scaling factor reduced to C 5, decreasing the magnitude of a-
DeepPaiths,p..coe sampling frequency 10, resulting in faster training but lower sampling precision.
DeepFaiths,,.s p sampling frequency l = 200, leading to slower training but higher sampling precision.
We report the performance of these variants of DeepFaith across 10 faithfulness evaluation metrics
Eieuo Ft- pon
and compute the overall faithfulness deviation AF
where F; and Fori
Exc P.u.
denote the score the i-th faithfulness metric for the current variant and for DecpFaith s.e.. respectively. The experimental results are reported in Table
The experimental results in the table show that DeepFaith exhibits similar explanation faithfulness across different hyperparameter settings for d, P. e, C. and k with overall faithfulness deviation
26

---

Published as a conference paper at ICLR 2026
that is relatively small (< 6%). This demonstrates that DeepFaith is sufficiently robust to the introduced hyperparameters. In practice, we recommend keeping the parameter ranges within reasonable scope, without requiring excessive manual tuning.
K REPRODUCIBILITY STATEMENT
We have made every effort to ensure that the results presented in this paper are reproducible. All code have been made publicly available in a giithub repository to facilitate replication and verification. The experimental setup, including training steps, model configurations, and hardware details, is described in detail in the paper.
Additionally, public datasets used in the paper, such ImageNet (Deng al. 2009), OCT Ker- many et al. 2018). AGNews (Zhang et al. 2016). IMDb (Maas et al. 201 NAP (National Center for Health Statistics 2019) and WCD (Cardoso 2013). are publicly available, ensuring consistent and reproducible evaluation results.
L LLM USAGE STATEMENT
Large Language Models (LLMs) were used to aid in the writing and polishing of the manuscript. Specifically, we used an LLM to assist in refining the language, improving readability, and ensuring clarity in various sections of the paper. The model helped with tasks such as sentence rephrasing, grammar checking. and enhancing the overall flow of the text.
It is important to note that the LLM was not involved in the ideation, research methodology, or experimental design. All research concepts, ideas, and analyses were developed and conducted by the authors. The contributions of the LLM were solely focused on improving the linguistic quality of the paper, with no involvement in the scientific content or data analysis.
The authors take full responsibility for the content of the manuscript, including any text generated or polished by the LLM. We have ensured that the LLM-generated text adheres to ethical guidelines and does not contribute plagiarism scientific misconduct.
27


Reviews:
[{"review_id": "YYsHWfuXXt", "reviewer": "Reviewer_kSSW", "summary": "This paper introduces **DeepFaith**, a method for generating explanations of neural network predictions within the “learning-to-explain” framework. The authors argue that previous approaches fall into two main categories: (1) *Self-supervised methods* that interact directly with the model to optimize a faithfulness objective, but rely on strong assumptions about the model; and (2) *Signal-based methods* that generate explanations using post-hoc techniques and then train a separate explainer model on these explanations, but do not explicitly optimize for faithfulness. DeepFaith is proposed as a hybrid approach that aims to leverage the strengths of both paradigms. It does so by generating a large set of explanations using diverse post-hoc methods and then guiding training using faithfulness-driven objectives. The authors justify this design by proving that different notions of faithfulness, including saliency-based and perturbation-based attribution measures, are aligned, supporting the idea of optimizing toward a unified faithfulness objective. In practice, DeepFaith is trained using two dynamically weighted objectives: the first encourages learning general explanation patterns, while the second shifts training toward optimizing faithfulness through a specific loss function. The method is evaluated across a wide range of vision and language benchmarks, where it consistently outperforms standard post-hoc explanation methods in terms of faithfulness metrics.", "questions": "1. What justifies the claim that self-supervised approaches necessarily rely on assumptions about the model? Which assumptions are unavoidable, and why?\n\n2. Why is it essential to generate explanation signals at all, rather than simply optimizing the faithfulness loss directly? What would change, conceptually or empirically, if we skipped the explanation generation step?\n\n3. There is a substantial line of work on self-explaining models that produce explanations during inference. If DeepFaith were instead trained using a self-explaining architecture that generates explanations optimized via the faithfulness-based objective, how would this fundamentally differ from the proposed approach here, beyond the potential trade-off in accuracy?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The idea of combining both the “learning from explanation signals” paradigm and the optimization via faithfulness objectives is interesting and, to the best of my knowledge, novel (though I may not be aware of all prior work in this area, which are many). However, the paper would benefit from stronger motivation and additional empirical evidence supporting the need for this approach (see Weaknesses).\n\n2. The unification of various notions of saliency and attribution appears potentially useful in certain contexts.\n\n3. The paper is generally well-written and easy to follow.\n\n4. The authors present extensive experiments across a wide range of models, showing that their method achieves improved faithfulness compared to post-hoc approaches.", "weaknesses": "1. While the authors compare their method against post-hoc explanation techniques, they do not include comparisons to self-supervised approaches that directly optimize a faithfulness objective without relying on explanation signals. As a result, it remains unclear whether generating these explanation signals is necessary at all and the theoretical analysis does not justify this design choice.\n\n2. The paper argues that self-supervised methods that directly optimize a faithfulness loss inherently rely on assumptions about the model, but this claim is insufficiently supported. The authors should clarify why such assumptions are required and provide concrete reasoning or evidence to motivate this statement.\n\n3. Regarding the theoretical contributions: the presented proofs are relatively straightforward and unsurprising. The claim of unifying multiple attribution metrics and explanation methods is not entirely novel - prior work has already shown that many attribution methods optimize a shared class of objectives (e.g., Yu et al., NeurIPS 2019, among many others). The authors should better articulate what distinguishes their analysis from these earlier results and explain what new insights it provides.", "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": "LL5pcwO31U", "reviewer": "Reviewer_NUZJ", "summary": "The paper introduces DeepFaith, an amortised explainer that generates faithful explanations for a target model’s predictions in a single forward pass. The goal is to address two long-standing problems in Learning to Explain (LtE):\n- self-supervised explanation models tend to be unstable, and often make task/model assumptions (e.g. separability of features), and frequently fail to converge for high-dimensional models.\n- distilled explanation models (student networks trained to imitate a teacher explainer) inherit teacher bias/noise and are upper-bounded by teacher quality.\n\nDeepFaith is built around three components:\n- Theoretical unification of faithfulness: The paper rewrites 10 widely used faithfulness metrics under one formal framework using perturbation operators and correlation measures. It then shows that a single optimal faithful explanation mapping exists, jointly optimal across these metrics. It shows that the ranking induced is also optimal for perturbation-based ranking metrics. \n- Local Correlation loss ($L_{LC}$): The explainer is trained to align its predicted importance scores with the actual effect of perturbing/removing subsets of features on the model’s output. In other words, subsets that the explainer says are important should, in fact, cause the model’s prediction to drop when those features are masked.\n- Curated supervision + dynamic training ($L_{PC}$): Instead of blindly distilling a single attribution method, DeepFaith constructs a pseudo-labelled supervision set as follows: for each input, it gathers explanations from many attribution methods, deduplicates near-duplicates, and keeps only those that are highly faithful on that exact input across several metrics. The explainer is first trained to imitate these curated high-faithfulness maps, and then gradually shifted toward the self-supervised tasks using a dynamic controller that adapts. The controller increases reliance on the self-supervised loss once the supervised loss stabilises, and can revert if training destabilises.\n\nDeepFaith is evaluated on 12 (dataset, model) pairs across three modalities and multiple architectures. Across 10 standard faithfulness metrics, DeepFaith achieves the best average rank on all tasks and outperforms the attribution methods it partly learned from. Ablation studies show that removing any of the key pieces degrades performance. The paper argues that DeepFaith therefore delivers (i) explanations that are more faithful to model behaviour, (ii) in a single forward pass at inference time, and (iii) across multiple data modalities and network architectures.", "questions": "Right now, you curate supervision using all 10 faithfulness metrics, and you evaluate on those same 10. Can you train DeepFaith while excluding one or two metrics from the curation filter, and then report performance specifically on those held-out metrics?\nIf DeepFaith still outperforms baselines on those unseen metrics, it would strengthen your claims.\n\nCan you include at least one amortised explainer baseline per modality? If not, at least justify clearly why they are not comparable. Right now, this missing comparison is a significant experimental gap.\n\nThe theory assumes a relationship between removal-based and insertion-based perturbation effects and essentially treats them as monotonic and compatible. In practice, these can be instantiated with different perturbation baselines (e.g., zeroing, blurring, masking).\nDid you enforce a consistent perturbation operator across all metrics in your experiments, or are you making any assumptions? It would be helpful to state it explicitly.\n\nFor the Local Correlation loss $L_{LC}$:\n- How many feature subsets are sampled per input/batch to estimate the correlation, and how sensitive is performance to that number?\n- Do you observe high gradient variance or unstable optimisation when using $L_{LC}$ alone?\n- You show training dynamics for the whole method (including $\\alpha$ adapting over time); can you also share curves for the $L_{LC}$-only variant to illustrate the claimed instability in isolation?\n\nIf I train DeepFaith for a DeiT classifier on ImageNet, how well does it explain an EfficientNet classifier on the same ImageNet labels without retraining?\n\nDid you run any preference checks with human annotators or domain experts? If you didn’t, can you comment on whether the high-faithfulness explanations ever look spurious? In general, I would encourage the authors to conduct a human study or a small qualitative preference experiment.\n\nHow sensitive is performance to the hyperparameters?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper proposes a single mathematical lens that captures 10 commonly used faithfulness metrics and argues that there exists an optimal explanation mapping that is jointly optimal across all of them. It claims that correlation-style metrics and perturbation-style metrics are not fundamentally competing criteria but can be satisfied simultaneously. \n\nRather than naively distilling from a single teacher explainer, the paper proposes a per-sample curation pipeline: generate many explanations, deduplicate them, and select only those that empirically score best across multiple metrics for that specific input. This is a clever way to ensure the distilled model surpasses the teacher's abilities.\n\nDeepFaith combines a supervised imitation loss and a self-supervised faithfulness loss with an adaptive weighting schedule. The training controller monitors the stability of the supervised loss and shifts the weight toward self-supervision once the model is stable, then bounces back to supervision if it destabilises. This offers an explicit control loop to manage convergence. Prior LtE methods tend to be either pure distillation (stable but capped) or pure self-supervision (principled but unstable).\n\nThe paper doesn’t restrict itself to a single modality; it claims a single template that applies to CNNs, ViTs, LSTMs, Transformers, and MLPs across images, natural language, and tabular data.", "weaknesses": "Missing comparisons to prior LtE/amortised explainers: The paper positions itself as advancing the Learning-to-Explain paradigm, i.e., training a neural explainer that produces explanations in a single forward pass. But in the experiments, the baselines are almost entirely classic post-hoc attribution methods (Integrated Gradients, GradCAM++, Occlusion, Kernel SHAP, LIME, etc.).\n\nIt's missing are head-to-head comparisons against other amortised / LTE-style methods:\n- L2X \n- CXPlain\n- FastSHAP\n- VerT / selection-and-rationale models for vision/text that jointly learn to point and predict.\n\nThese methods are discussed in related work, but they are not quantitatively included in the results tables. Currently, the only measured comparisons are to non-amortised attribution methods; if DeepFaith cannot clearly outperform other learned explainers, it would weaken the paper's contributions.\n\nDeepFaith’s curated supervision set is built by:\n- Generating multiple candidate explanations from K attribution methods for each input.\n- Computing all 10 faithfulness metrics for each candidate explanation on that specific input.\n- Keeping only the top explanations by those metrics (after deduplication).\n- Training the explainer to imitate those survivors, then refining.\n\nAt test time, DeepFaith is evaluated on those same 10 metrics.\n\nThis creates a risk of training on the test: DeepFaith is at least partially optimised to produce explanations that look good under exactly the metrics it’s later ranked by. Yes, self-supervision introduces a new structure by forcing local correlation between model behaviour and perturbations. But without an experiment that uses held-out metrics, it’s hard to conclude DeepFaith is genuinely, broadly more faithful rather than just better at exploiting the metrics.\n\nThe theory relies on assumptions about monotonic relationships between removal and insertion effects and consistent perturbation baselines. In practice, faithfulness metrics vary widely in how they perturb features. If two metrics use different perturbation baselines, it’s not apparent that a single explanation can be jointly optimal for both. The paper should be explicit about whether all metrics were instantiated using a shared perturbation scheme or whether there are any assumptions.\n\nEach DeepFaith explainer is trained separately for each target model. The paper doesn’t test whether an explainer trained on one model can be reused for another model in the same domain (e.g., training on DeiT and applying it to EfficientNet on ImageNet). If there’s no transfer at all, then amortisation helps inference latency but does not reduce the number of explanation models.\n\nAll evaluation metrics are model-faithfulness metrics: does ablating important features change the model’s output in the expected direction? The paper also leans on real-world motivation, where humans must interpret the explanations. There’s no human study, or even a small qualitative preference experiment, in the main results to demonstrate that DeepFaith explanations are more clinically meaningful than others.\n\nThe curated supervision pipeline depends on thresholds:\n- cosine similarity thresholds for deduplication,\n- p-quantile cutoffs for filtering which explanations count as faithful,\n- and dynamic controller hyperparameters for toggling $\\alpha$.\n\nThe main results don’t present a sensitivity study.", "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": "sGwxtfgVan", "reviewer": "Reviewer_JuTS", "summary": "The authors propose a faithfulness-guided amortized explainer that jointly optimizes self-supervised and prior-based objectives, and the experiments show improved faithfulness and efficiency across different datasets.", "questions": "The authors may refer to the weaknesses and address them in the rebuttal.", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper proposes a explainer that integrates self-supervised and prior-based objectives, offering a unified perspective for the Learning to Explain paradigm.\n\n2. Experiments across image, text, and tabular datasets and the paper is clear-written.", "weaknesses": "1. In the Introduction, the authors identify three key challenges: generalization, supervision quality, and convergence. However, the descriptions of these problems remain somewhat abstract. Specifically, the statement “self-supervised objectives rely on assumptions about the target model” could be better supported with a concrete example, such as the failure of L2X under correlated features, to make the motivation more convincing.\n\n2. In Algorithm 1, they presents a variance-based switching rule for adjusting α, but the paper provides no theoretical guarantee of stability or convergence. And Fig 3 still shows noticeable oscillations during training, suggesting limited robustness of the proposed mechanism.\n\n3. The experiments include many baselines for image, but text and tabular tasks only use a few baselines. This imbalance makes the evaluation heavily vision-centric. Adding some representative methods for text and tabular data would strengthen fairness.\n\n4. The explanation units are different across modalities, and no experiment examines cross-modal transfer or unified explainer training. Therefore, the claim that the framework generalizes across modalities is not yet empirically supported.", "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": "fmPsAQb1Zp", "reviewer": "Reviewer_FfQQ", "summary": "This paper addresses key challenges in the \"Learning to Explain\" paradigm by proposing DeepFaith, a framework for training highly faithful amortized explainers. The authors identify that existing methods are limited by restrictive assumptions in self-supervised objectives or by the low quality of supervisory signals from prior explanation methods.  To overcome this, DeepFaith introduces a three-part solution: (1) a theoretically-derived, model-agnostic self-supervised objective based on a unified view of faithfulness metrics; (2) a novel pipeline for generating high-quality supervisory signals by aggregating, deduplicating, and filtering explanations from existing methods based on their faithfulness; and (3) a dynamic joint optimization strategy that combines both objectives to ensure rapid convergence and high final explanation quality. Extensive experiments across image, text, and tabular data show that DeepFaith consistently outperforms prior explanation methods across a suite of ten faithfulness metrics.", "questions": "- What was the rationale for choosing a Transformer Encoder architecture for the explainer across all modalities, including tabular data where simpler architectures might be more common? \n- Regarding Algorithm 1, how sensitive is the dynamic weighting strategy to the choice of the hyperparameters $\\epsilon$, $e$, and $C$? \n- The ablation study in Table 3 shows that training with only $\\mathcal{L}_{LC}$ performs very poorly. Does this suggest that the self-supervised objective alone is insufficient to guide the explainer to a good solution from a random initialization?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 2, "contribution": 3, "strengths": "- This paper provides a clear motivation and problem definitions. The introduction clearly differentiates faithfulness from plausibility and articulates the gap between qualitative interpretability and quantitative fidelity. \n-  This paper provides strong theoretical grounding for the self-supervised objective.  The paper makes a laudable effort to build its self-supervised objective on a firm theoretical foundation, rather than relying on heuristics or task-specific assumptions. The authors reformalize ten different, widely used faithfulness metrics into a unified notational system, distinguishing between \"saliency\" and \"permutation\" perspectives. The paper theoretically proves that an optimal explanation mapping exists that simultaneously maximizes performance across all ten considered faithfulness metrics. \n-  This paper provides a novel faithfulness-aware learning framework.  It defines synthetic supervision using controlled feature perturbations (Sec. 3.1; Fig. 2), bridging causal interpretability with optimization. The faithfulness loss integrates causal relevance with sparsity and smoothness priors, balancing interpretability and fidelity.\n-  This paper provides a comprehensive empirical evaluation. The authors consider image, text, and tabular datasets and various architectures, such as ResNet,  Deit, Transformer, and LSTM, demonstrating improvement across explainers (GradCAM, IG, LRP), confirming generalizability.", "weaknesses": "- This paper lacks an analysis of the computational cost of training.  The paper emphasizes the fast inference speed of the amortized explainer but does not quantify or discuss the potentially massive upfront computational cost required for training. The signal generation phase involves running $K$ different explanation methods (including computationally expensive ones like Kernel SHAP and Score-CAM) on thousands of training samples, and then computing 10 faithfulness metrics for each generated explanation.  This pre-processing cost is likely to be very high but is not reported, making it difficult to assess the overall efficiency of the framework.   The training process involves calculating $\\mathcal{L}_{LC}$, which requires $K$ perturbations and forward passes through the target model for each sample in a batch. This adds significant overhead compared to simply training on a static dataset of prior explanations. Total training times are not provided.  While DeepFaith is shown to be fast at inference, the comparison can be misleading. Many of the fastest baselines (e.g., Saliency, Input x Gradient) are also the ones that perform most poorly on faithfulness, while the methods that are more faithful (e.g., Integrated Gradients, Kernel SHAP) are much slower. A plot of faithfulness vs. runtime would provide a more nuanced view of the trade-offs.\n\n- There are still some writing issues, for example, the citation is mixed with the body text, making it hard to read. The notation $\\bar{\\pi}$ in the formula for the NEG metric in Table 1 is undefined.  The notation in Table 1 is very compact. The formula for Faithfulness Correlation (FC), for instance, implies a correlation over all $2^n$ subsets of features, \nwhich is computationally intractable and differs from the Monte Carlo sampling used in the actual loss function $\\mathcal{L}_{LC}$.      \n   \n- This framework introduces a new set of sensitive hyperparameters that require manual tuning for each task, somewhat undermining the goal of full automation. Table 12 shows that both the `Similarity Threshold` for deduplication and the `p-quantile` for filtering were set to different values for each of the 12 explanation tasks. The paper provides no methodology for how these values were chosen, suggesting a manual, trial-and-error process that is contrary to the overarching goal of automating explainability. The performance of the filtering pipeline is contingent on the initial set of $K$ baseline methods. The paper uses a large set of 14 methods for images and 8 for other modalities, but does not analyze how the results would change with a smaller or different set of priors.", "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)