GradCFA: A Hybrid Gradient-Based Counterfactual and Feature Attribution Explanation Algorithm for Local Interpretation of Neural Networks

Jacob Sanderson; Hua Mao; Wai Lok Woo

cs.LGMar 16, 2026

GradCFA: A Hybrid Gradient-Based Counterfactual and Feature Attribution Explanation Algorithm for Local Interpretation of Neural Networks

Authors: Jacob Sanderson, Hua Mao, Wai Lok Woo

Organizations: Department of Computer and Information Sciences, Northumbria University, Newcastle, UK, NE1 8ST

Abstract

Explainable Artificial Intelligence (XAI) is increasingly essential as AI systems are deployed in critical fields such as healthcare and finance, offering transparency into AI-driven decisions. Two major XAI paradigms, counterfactual explanations (CFX) and feature attribution (FA), serve distinct roles in model interpretability. This study introduces GradCFA, a hybrid framework combining CFX and FA to improve interpretability by explicitly optimizing feasibility, plausibility, and diversity - key qualities often unbalanced in existing methods. Unlike most CFX research focused on binary classification, GradCFA extends to multi-class scenarios, supporting a wider range of applications. We evaluate GradCFA's validity, proximity, sparsity, plausibility, and diversity against state-of-the-art methods, including Wachter, DiCE, CARE for CFX, and SHAP for FA. Results show GradCFA effectively generates feasible, plausible, and diverse counterfactuals while offering valuable FA insights. By identifying influential features and validating their impact, GradCFA advances AI interpretability. The code for implementation of this work can be found at: https://github.com/jacob-ws/GradCFs .

Figures & tables

Fig. 1 : Overview of the GradCFA Pipeline: Beginning with a trained neural network, a query instance, and the observed dataset. The counterfactual set $X^{\prime}$ is initialized with random values sampled from a normal distribution. Individual loss components are calculated and compared with user-defined thresholds $\tau_{char}$ , where each loss component $L$ has its own threshold $\tau_{char}$ . For proximity, sparsity, and plausibility $L$ within $\tau$ is true if $L\leq\tau_{char}$ , and for diversity $L$ is considered within $\tau$ if $L\geq\tau_{char}$ . If thresholds are not met, a penalty is applied. The total loss is computed based on user-defined weighting. User constraints are then applied, gradients are computed to attribute feature importance, and update $X^{\prime}$ . If the final loss after optimization does not meet the threshold, values are perturbed, and optimization is repeated until an acceptable loss is achieved or the maximum number of perturbation attempts is reached, after which the counterfactual set and FAs are returned.

Dataset	Training	Validation	Testing
Credit Approval	0.88	0.86	0.82
Obesity	0.90	0.84	0.85
Fetal Health	0.92	0.93	0.91

TABLE I : Classification accuracy of the predictive model on each dataset across training, validation and testing.

		Ablation Study Combinations							GradCFA		Previous Work			Multi-Class
	GradCFA	1	2	3	4	5	6	7	W/o Pert.	W/o Pen.	Wachter	DiCE	CARE	0	1	2	3	4	5	6
Credit Approval Dataset for Binary Classification
Prox.	0.15	0.14	0.12	0.19	0.16	0.16	0.13	0.23	0.23	0.21	0.03	0.12	0.18	-	-	-	-	-	-	-
Spars	0.18	0.19	0.16	0.21	0.20	0.20	0.17	0.25	0.27	0.24	0.10	0.28	0.56	-	-	-	-	-	-	-
Plaus	0.37	0.68	0.53	0.61	0.46	0.45	0.54	0.42	0.51	0.45	0.56	0.51	0.47	-	-	-	-	-	-	-
Div	0.96	0.86	0.72	0.82	0.92	0.80	0.88	0.94	0.91	0.92	0.35	0.84	0.68	-	-	-	-	-	-	-

TABLE II : Proximity, Sparsity, Plausibility, Diversity and Confidence of GradCFA in Comparison with the results obtained in the experiments conducted in subsections IV A, B, C, E, and F. Proximity, Sparsity and Plausibilty are minimized, while Diversity and Validity are maximized. An overall average of these metrics is given for each experiment.

Panel of Figure 4 — Fig. 2 : Loss curves for (a) credit approval, (b) obesity levels, and (c) fetal health, with perturbation, where the grey dashed lines represent the points of perturbation. The curves demonstrate that after each perturbation the loss is driven further down, indicating the efficacy of the approach in improving the results.

Panel of Figure 5 — Fig. 3 : Loss curves for (a) credit approval, (b) obesity levels, and (c) fetal health without perturbation.

Feature	Query	Counterfactual Values
Age	34.14	28.55	33.44	35.34	37.26	46.75
Debt	2.75	4.2	3.9	3.4	5.1	8.0
YE	2.5	3.28	3.93	2.94	3.54	2.5
Income	200.01	199.00	200.00	205.00	105.00	195.00
Gender	1	1	1	1	0	0
MS	1	1	1	1	1	1

TABLE III : Example Counterfactual Set for Credit Approval.

Feature	Query	Counterfactual Values
Age	19.0	20.0	19.0	21.0	23.0	22.0
Height	1.75	1.68	1.72	1.65	1.66	1.65
Weight	100.0	53.4	51.9	62.3	51.6	61.8
FVFC	2.0	1.9	1.9	1.9	2.0	2.0
NCP	3.0	3.0	3.0	2.9	3.0	3.0
CH2O	2.0	1.9	2.0	2.0	2.0	2.0

TABLE IV : Example Counterfactual Set for Obesity Levels.

Feature	Query	Counterfactual Values
LBE	125.0	128.9	148.0	128.3	141.5	142.2
LB	125.0	132.8	124.9	124.8	132.1	118.2
AC	10.0	5.1	2.8	0.1	5.5	2.2
FM	-4.6e-11	-3e-11	-7.4e-11	-1.1e-11	1.5e-11	1.2e-11
UC	2.3e-10	3e-10	-1.2e-10	4.3e-10	-4e-10	-2e-10
ASTV	41.0	56.9	55.1	52.6	44.2	41.0

TABLE V : Example Counterfactual Set for Fetal Health.

Panel of Figure 9 — Fig. 4 : FA computed with GradCFA for (a) credit approval, (b) obesity levels and (c) fetal health. The results highlight the critical role of prior default and income in credit approval, weight in obesity classification, and active vigilance and calm sleep in fetal health, while other features like age, years employed, dietary habits, and histogram statistics are less influential in generating plausible and feasible counterfactuals.

Panel of Figure 10 — Fig. 5 : FA computed with SHAP for (a) credit approval, (b) obesity levels and (c) fetal health.

Feature	Val.	Prox.	Spars.	Plaus.	Div.
Fixed
PriorDefault	0.37	-	-	-	-
Income	0.54	0.26	0.24	0.87	0.82
Industry	0.62	0.25	0.22	0.61	0.86
CreditScore	0.65	0.24	0.24	0.50	0.88
BankCustomer	0.67	0.23	0.23	0.46	0.88

TABLE VI : Analysis of the FA with the Credit Approval Data.

Feature	Val.	Prox.	Spars.	Plaus.	Div.
Fixed
Weight	0.18	-	-	-	-
MTRANS	0.52	0.33	0.42	0.62	0.71
SMOKE	0.57	0.29	0.37	0.67	0.75
CALC	0.59	0.28	0.35	0.61	0.76
CAEC	0.61	0.28	0.30	0.55	0.78

TABLE VII : Analysis of the FA with the Obesity Levels Data.

Feature	Val.	Prox.	Spars.	Plaus.	Div.
Fixed
D	0.24	-	-	-	-
A	0.45	-	-	-	-
AD	0.51	0.48	0.49	0.77	0.79
B	0.53	0.47	0.47	0.71	0.77
C	0.56	0.47	0.46	0.69	0.80

TABLE VIII : Analysis of the FA with the Fetal Health Data.

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FlowCF: Sparse Counterfactual Explanations for Mixed-Type Tabular Data using Flow Matching

Emmanouil Panagiotou, Eirini Ntoutsi

Freie Universität Berlin · University of the Bundeswehr Munich

Flow Matching Explainable Artificial Intelligence Counterfactual Explanations Tabular ML

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In the field of Explainable AI (XAI), counterfactual (CF) explanations interpret a model's decision by suggesting the changes to the input that would lead to a more favourable outcome. To be useful in practice, such an explanation should change few features and change them as little as possible, properties known as sparsity and proximity. We observe that existing methods remain limited in this respect, especially for numerical features, whether they are model-agnostic and amortised, or gradient-based with full access to the model. In this paper, we propose FlowCF, a model-agnostic generative method that frames CF generation as sparse transport from the factual to the target class. We solve this transport with flow matching, which we extend to mixed feature types with a novel mixed flow operator, and exploit the resulting geometry to optimise for sparsity through a gating network that minimises the number of features the transport changes. Extensive experiments on six benchmark datasets demonstrate that FlowCF produces the best numerical sparsity and proximity, changing 29% of the numerical features where the best baseline changes 89%, at 70% smaller displacement, while remaining comparable on the other desiderata.

Abstract

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