Interpretable Generalization (IG)

• Interpretable Generalization is a research theme that connects model transparency with out-of-sample performance, robustness, and transfer.
• It formalizes the tradeoff between predictive accuracy and interpretability using methods like kernel learning, structural constraints, and logical regularization.
• IG frameworks employ model-by-design principles and diagnostic metrics to yield interpretable architectures that often enhance generalization in diverse applications.

Interpretable Generalization (IG) denotes a family of research programs that explicitly connect interpretability with out-of-sample performance, robustness, or transfer. The term is not used uniformly. In kernel learning, it is formulated as an equilibrium between predictive fit and consistency with a prior interpretation model (Zhao et al., 2018). In interpretable modeling, it refers to structural or logical constraints that keep learned effects human-inspectable while preserving or improving generalization (Yang et al., 2024, Tan et al., 2024, Barbiero et al., 1 Aug 2025, Agarwal et al., 2024). In cybersecurity, IG is also the proper name of an intrinsically interpretable intrusion-detection mechanism based on coherent class-exclusive patterns (Pai et al., 2024, Chung et al., 16 Jul 2025, Huang et al., 16 Jul 2025). A recurrent source of confusion is acronym overlap: in attribution research, “IG” often means Integrated Gradients rather than Interpretable Generalization (Merrill et al., 2019, Kamalov et al., 22 Sep 2025).

1. Scope, terminology, and recurrent ambiguity

Recent literature uses “Interpretable Generalization” in several non-identical senses. Some papers treat it as a formal tradeoff between interpretability and generalization performance; others treat it as a design principle for model classes, regularizers, or concept bottlenecks; still others use it as the name of a specific pattern-mining mechanism for cyberattack identification. This suggests that IG is better understood as a research theme than as a single standardized object.

Usage	Core idea	Representative papers
Formal learning objective	Balance empirical fit with an interpretability criterion relative to prior knowledge	(Zhao et al., 2018)
Model-by-design interpretability	Constrain structure so the learned model remains decomposable into inspectable effects or semantic supports	(Yang et al., 2024, Tan et al., 2024, Barbiero et al., 1 Aug 2025, Agarwal et al., 2024)
Intrusion-detection mechanism	Learn coherent normal and anomalous patterns and use them directly as auditable evidence	(Pai et al., 2024, Chung et al., 16 Jul 2025, Huang et al., 16 Jul 2025)
Acronymic overlap with attribution	Generalize or stabilize Integrated Gradients explanations	(Merrill et al., 2019, Kamalov et al., 22 Sep 2025, Yang et al., 2023, Rodrigues et al., 2024)

A common misconception is that IG names a single algorithm. The literature instead contains a plurality of definitions, each tied to a different problem setting. Another misconception is that interpretability is always treated as post-hoc explanation. Several IG papers reject that premise and require interpretability to be native to the learned mechanism rather than appended afterward (Yang et al., 2024, Pai et al., 2024, Barbiero et al., 1 Aug 2025).

2. Formal theories of the interpretability–generalization relationship

A foundational formulation appears in kernel learning, where interpretability is defined relative to an interpretation model $P(x)$ rather than to human readability alone. The quantitative index is the interpretation distance

$E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$

with

$u_P(f)=\int_X |f(x)-P(x)|\,dv.$

Under this view, generalization performance seeks proximity to target outputs $y$, whereas interpretability seeks proximity to $P(x)$; the paper explicitly frames the problem as an equilibrium between the two objectives (Zhao et al., 2018).

This equilibrium modifies standard Tikhonov regularization. Instead of optimizing only empirical squared loss and RKHS norm,

$$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$

the proposed universal learning framework adds an interpretability penalty: $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$ The same work derives probability upper bounds for the sum of interpretability loss and generalization-related loss, and states that if the hypothesis space $H$ is a compact convex subset of $L^2(X)$, then the optimization problem has a unique solution. Its interpretable LSSVM instantiation adds an interpretability regularization term to the primal objective and reports that ILSSVM generally reduces interpretation distance relative to LSSVM, while predictive performance is often similar and sometimes better on Friedman1, Friedman2, Plane1, Plane2, Multi1, Multi2, Gabor1, and Gabor2 (Zhao et al., 2018).

A more recent foundational program defines interpretability as inference equivariance: a function is interpretable to a user if the function’s and the user’s inference mechanisms are equivariant. The formal picture is a commutative diagram between model variables, translated human-readable variables, and outputs. This work places particular weight on a lossless latent space $C \subseteq \mathbb{R}^K$ with $E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$0 and $E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$1, on conditional interpretability

$E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$2

and on the reparametrization

$E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$3

It further states that inference equivariance is verifiable in $E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$4 steps iff the task is conditionally interpretable given a lossless latent space $E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$5 with $E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$6, and $E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$7 is a sound translation for all $E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$8 and task $E_P(f)=\int_X \Big(f(x)-P(x)-u_P(f)\Big)^2\,dv$9 (Barbiero et al., 1 Aug 2025).

A third formalization defines interpretability relative to another model through generalized distillation. In that framework, a model $u_P(f)=\int_X |f(x)-P(x)|\,dv.$0 interprets a black-box model $u_P(f)=\int_X |f(x)-P(x)|\,dv.$1 by reducing uncertainty about $u_P(f)=\int_X |f(x)-P(x)|\,dv.$2’s decision boundary. The central index is

$u_P(f)=\int_X |f(x)-P(x)|\,dv.$3

with classifier entropy defined combinatorially from the number of decision cells and class assignments. For Piece-Wise Linear Neural Networks, the paper gives upper, lower, and average entropy bounds and derives corresponding interpretability bounds, thereby treating interpretability as a model-to-model information-gain quantity rather than as a human-centered notion (Agarwal et al., 2020).

3. Structural model classes and exact decompositions

A prominent strand of IG research argues that interpretability should arise from model structure. In tree ensembles, the central result is that when shallow decision trees are used as base learners, the ensemble can be exactly rewritten as an additive model whose terms are easy to inspect. A tree ensemble

$u_P(f)=\int_X |f(x)-P(x)|\,dv.$4

can be rearranged into a leaf representation and then purified into a functional ANOVA decomposition

$u_P(f)=\int_X |f(x)-P(x)|\,dv.$5

Because a tree of maximum depth $u_P(f)=\int_X |f(x)-P(x)|\,dv.$6 contains leaves involving at most $u_P(f)=\int_X |f(x)-P(x)|\,dv.$7 distinct split variables, the highest possible interaction order is also $u_P(f)=\int_X |f(x)-P(x)|\,dv.$8: depth-1 trees yield a generalized additive model, depth-2 trees yield a generalized additive model with pairwise interactions, and higher depths yield higher-order additive interaction models (Yang et al., 2024).

The same framework makes the representation identifiable through the functional ANOVA constraint

$u_P(f)=\int_X |f(x)-P(x)|\,dv.$9

implemented operationally by aggregation $y$0 purification $y$1 attribution. At the feature level, the contribution

$y$2

is exactly the Shapley value of feature $y$3. Interpretability is further enhanced by limiting maximum tree depth, imposing monotonicity constraints, limiting the maximum number of bins, restricting allowable feature interactions, and using L1/L2 regularization and early stopping. Post-hoc effect pruning then removes trivial effects with Lasso or L1-regularized logistic regression followed by FBED$y$4 with $y$5 (Yang et al., 2024).

The reported experiments tie these design choices directly to generalization. On the Friedman simulation, the best XGBoost model is depth 2, exactly matching the ground-truth structure of main effects plus one pairwise interaction; deeper trees overfit, while Lasso-based pruning reduces 10 main effects and 45 pairwise interactions to 5 main effects and 1 interaction, with test RMSE improving to about 0.425. On CreditSimu, the best test AUC is achieved by XGB-2, and pruning the constrained model leaves 7 main effects and 15 pairwise interactions. On TaiwanCredit, constrained XGB-2 reduces 18 main effects and 97 pairwise interactions to 15 main effects and 24 pairwise interactions with essentially unchanged AUC. These results are used to argue that the right structural biases can make the model both more interpretable and often better generalizing (Yang et al., 2024).

4. Logic, concepts, and local parts as routes to robust transfer

In visual classification, one line of work derives a logical regularization, L-Reg, from a formal view of classification as logic over semantic supports. Let $y$6 be latent semantic dimensions, and let $y$7 denote subsets sufficient to deduce the relation between $y$8 and $y$9. The regularization target is to minimize entropy on semantic supports and maximize entropy on their complement, leading to the practical objective

$P(x)$0

The stated effect is a reduction in the complexity of both feature distribution and classifier weights, accompanied by Grad-CAM visualizations that shift toward salient class-defining parts such as faces for person, neck and strings or fingerboard for guitar, long neck for giraffe, trunk, teeth, large ears for elephant, nose area for dog, and overall outline shape for horse (Tan et al., 2024).

The empirical evidence for L-Reg is reported across multi-domain generalization, generalized category discovery, and the combined mDG + GCD setting. For GMDG on PACS, VLCS, OfficeHome, TerraIncognita, and DomainNet, average performance changes from $P(x)$1, $P(x)$2, $P(x)$3, $P(x)$4, and $P(x)$5, respectively. For PIM in generalized category discovery, averages change from All $P(x)$6, Known $P(x)$7, and Unknown $P(x)$8. In the combined mDG + GCD setting, GMDG changes from All $P(x)$9, Known $$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$0, and Unknown $$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$1. The paper interprets these results as evidence that minimal, class-specific semantic supports can improve both interpretability and robustness to unseen domains and unseen categories (Tan et al., 2024).

TIDE addresses the same conjunction of interpretability and transfer from a local-concept perspective in single-source domain generalization. It first constructs concept-level region annotations by using GPT-3.5 to list distinctive, intrinsic, class-specific concepts, SDv2.1 to synthesize exemplar images and extract cross-attention maps, and Diffusion Feature Transfer to move those maps to real images in PACS, VLCS, OfficeHome, and DomainNet. Training then combines standard classification with concept saliency alignment and local concept contrastive learning. The concept saliency alignment loss

$$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$2

forces the model’s concept attention to match transferred ground-truth saliency maps, while the local concept contrastive loss

$$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$3

pulls together same-concept features and pushes apart unrelated concepts. TIDE then performs test-time correction by comparing local concept features to stored signatures $$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$4 and iteratively masking irrelevant regions (Agarwal et al., 2024).

The reported accuracies are 80.02 on PACS, 77.08 on VLCS, 74.01 on OfficeHome, and 82.14 on DomainNet, outperforming the second-best approaches by 8.33%, 13.37%, 16.16%, and 8.84%, respectively. The PACS ablation progresses from $$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$5, to $$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$6, to $$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$7, to $$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$8, and finally to 80.02 with test-time correction. CSA improves saliency overlap from 0.19 without CSA to 0.71 with CSA. The paper states that in 72.2% of test samples, correction is not invoked and predictions are correct 93.8% of the time; in the 27.8% where correction is triggered, 52.5% converge to the correct class (Agarwal et al., 2024).

These vision papers converge on a common claim: forcing the model to use the right parts or the right semantic supports can act as a generalization mechanism rather than merely a visualization device. A similar claim is made in the broader foundations work, which emphasizes concept invariance, concept equivariance, compositionality, sparsity, and sound translation as prerequisites for interpretable model design (Barbiero et al., 1 Aug 2025).

5. Representation-centric and geometric diagnostics

Another IG tradition is diagnostic rather than architectural. Instead of building interpretability into the hypothesis class, it studies whether hidden representations exhibit structures predictive of generalization. One approach proposes three representation-based complexity measures: Davies–Bouldin Index for consistency, label-wise mixup for robustness, and margin distribution summaries for separability. The central interpretation is that models with more consistent, robust, and separable internal representations tend to have smaller generalization gaps, echoing neuroscience-inspired ideas of invariant and untangled object manifolds (Natekar et al., 2020).

The DBI measure computes within-class scatter and between-class centroid separation in hidden activations; label-wise mixup evaluates whether same-class interpolations preserve the class label; and the margin-based measure approximates distance to class boundaries through

$$f_{z,\gamma}=\arg\min_{f\in H_K} \left( \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \gamma\|f\|_K^2 \right),$$9

The paper reports that even about 1% of the training samples is enough to estimate useful scores, and that the final competition-winning solution for predicting the generalization gap combines DBI and label-wise mixup by taking their product (Natekar et al., 2020).

A more recent top-down diagnostic program treats representational geometry as a biomarker for future out-of-distribution failure. Using penultimate-layer object manifolds, it compares conventional ID-only summaries against GLUE-based markers such as effective dimension $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$0, effective radius $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$1, and effective utility $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$2. The paper states that smaller $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$3 and smaller $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$4 mean more separable manifolds, while larger $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$5 means more efficient compression for classification; however, in transfer settings, reductions in $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$6 and $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$7 predict weaker OOD performance, which the paper interprets as overcompression and overspecialization (Chou et al., 2 Mar 2026).

The quantitative claims are explicit. In the ImageNet-pretrained weight-selection study, ID test accuracy predicts OOD weight preference with only 37.22% accuracy, whereas the geometry-based prognostic rule is correct in 73.02% of the evaluated comparisons, using 92 out of 126 model-dataset decisions. Across controlled sweeps, geometric markers, especially $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$8 and $$f_{z,\alpha} = \arg\min_{f\in H_K} \left[ \frac{1}{m}\sum_{i=1}^m (f(x_i)-y_i)^2 + \lambda \|f\|_K^2 + \beta\sum_{i=1}^m \Big(f(x_i)-P(x_i)-u_P(f)\Big)^2 \right].$$9, often show correlations around 0.8–0.95 with OOD linear-probe accuracy, while train/test accuracy and simple statistics are usually weak or inconsistent. This literature reframes IG as the capacity to derive interpretable, system-level indicators of future generalization behavior from representation geometry alone (Chou et al., 2 Mar 2026).

6. Cybersecurity: coherent patterns, forensic evidence, and scalable deployment

In cybersecurity, IG is the name of a specific intrinsically interpretable intrusion-detection mechanism. Its core operation is set-theoretic. Each traffic instance is converted into a categorical set after conversion to binary Normal/Anomalous labels, preservation of missing values as 'NotNumber', z-score discretization, column re-encoding, and anti-contradiction filtering. Training computes intersections among same-class instances and discards any intersection that also appears in the opposite class. The resulting class-exclusive evidence sets are Coherent Normal Patterns (CNP) and Coherent Anomalous Patterns (CAP) (Pai et al., 2024).

At inference time, a test instance $H$0 receives a normal score and anomaly score: $H$1

$H$2

Classification then follows three deterministic rules: anomalous if $H$3; anomalous if both scores are zero; and anomalous if

$H$4

The third rule is the mechanism for identifying novel anomalies without prior exposure, because a sample can be flagged as anomalous even when no explicit CAP was observed in training if its normal evidence is abnormally weak (Pai et al., 2024).

The reported results use train-test ratios from 10%-to-90% through 90%-to-10% on NSL-KDD, UNSW-NB15, and UKM-IDS20. At 10%-to-90%, IG achieves Precision 0.93, Recall 0.94, and AUC 0.94 in NSL-KDD; Precision 0.98, Recall 0.99, and AUC 0.99 in UNSW-NB15; and Precision 0.98, Recall 0.98, and AUC 0.99 in UKM-IDS20. The detailed 1|9 results are Accuracy 0.9389, Recall 0.9353, Precision 0.9426, and AUC 0.9402 for NSL-KDD; Accuracy 0.9894, Recall 0.9997, Precision 0.9656, and AUC 0.9988 for UNSW-NB15; and Accuracy 0.9810, Recall 0.9980, Precision 0.9436, and AUC 0.9982 for UKM-IDS20. The paper also states that in UKM-IDS20, IG successfully identifies all three anomalous instances without prior exposure (Pai et al., 2024).

IG-MD extends this mechanism by representing every continuous feature at several Gaussian-based resolutions. For a feature value $H$5, with mean $H$6 and standard deviation $H$7, it computes

$H$8

then rounds to multiple decimal precisions $H$9, producing symbolic codes $L^2(X)$0. Learning and opposite-class filtering proceed separately for each precision, while inference superimposes evidence across precisions: $L^2(X)$1 On UKM-IDS20, precision improves from 0.9436 to 0.9687 at the 1:9 split, and from 0.9125 to 0.9563, 0.8851 to 0.9288, 0.8918 to 0.9412, 0.8847 to 0.9368, 0.8832 to 0.9289, 0.8777 to 0.9298, 0.8949 to 0.9485, and 0.8891 to 0.9335 across the remaining splits. The paper summarizes this as a mean precision improvement from 0.896 to 0.941, while recall remains approximately 1.0 and AUC stays near 0.995–1.000 (Chung et al., 16 Jul 2025).

IG-GPU preserves the exact logic of IG while moving pairwise intersections, subset checking, and inference scoring to the GPU through bit-packed uint64 tensors and PyTorch kernels. On 15k-record subsets, reported speedups range from 37× to 430×, with average speedups of 116× on NSL-KDD, 116× on UNSW-NB15, and 145× on UKM-IDS20. On the full 148,517-record NSL-KDD dataset, IG-GPU achieves Accuracy 0.96662, Recall 0.95728, Precision 0.97315, and AUC 0.96093 in 1101 s, roughly 18 minutes 21 seconds, on a single RTX 4070 Ti. The original CPU IG required down-sampling to around 15k records to avoid memory exhaustion and obtained Recall 0.935, Precision 0.942, and AUC 0.940 (Huang et al., 16 Jul 2025).

7. Acronymic overlap with Integrated Gradients and attribution literature

A distinct but related literature uses “IG” to mean Integrated Gradients. This matters because some papers speak of “generalizing IG” while addressing attribution rather than Interpretable Generalization in the broader sense. The most formal extension is Generalized Integrated Gradients (GIG), which explains functions that are piecewise continuous off a set of orthogonal hyperplanes. GIG preserves ordinary IG on continuous path segments and adds uniquely determined orthant-based attributions at discontinuities, under extended Aumann-Shapley axioms including strong symmetry, insensitivity to remote change, insensitivity to constant variables, and reflexivity. The paper presents GIG as the only correct method, under those axioms, for mixed-type models or games (Merrill et al., 2019).

Path-Weighted Integrated Gradients (PWIG) is another generalization. Standard IG uses

$L^2(X)$2

whereas PWIG inserts a continuous, non-negative weight function $L^2(X)$3: $L^2(X)$4 PWIG reduces to IG when $L^2(X)$5, preserves implementation invariance, Sensitivity(b), symmetry-preserving behavior, and linearity, but does not generally satisfy completeness. In the dementia-classification study on OASIS-1 MRI, the authors use $L^2(X)$6 with $L^2(X)$7, 50 integration steps, attribution clipping at the 60th and 95th percentiles, and a PyTorch CNN with four convolutional blocks and validation accuracy 99.80%. The reported attribution maps highlight cortical and subcortical regions, areas showing atrophy or abnormal morphology in mild/moderate dementia, and more diffuse patterns in non-demented subjects (Kamalov et al., 22 Sep 2025).

Other work in this attribution strand focuses on explanation noise. IDGI argues that standard IG can assign zero attribution to important features when they match the baseline, and proposes Important Direction Gradient Integration to modify the integration direction. Across 11 ImageNet models, IDGI improves IG, GIG, and BlurIG on AUC of AIC, AUC of SIC, and MS-SSIM-based variants; for example, on DenseNet121, IG changes from 0.161 to 0.300 on AIC and from 0.054 to 0.228 on SIC, while on Xception it changes from 0.238 to 0.404 on AIC and from 0.119 to 0.363 on SIC (Yang et al., 2023). Gradient Artificial Distancing is a wrapper around gradient-based methods, including Integrated Gradients, that trains support regression models with artificially increased class separation and intersects their attribution masks; it measures compactness through

$L^2(X)$8

and evaluates causal concentration through an occlusion-based sensitivity ratio $L^2(X)$9 (Rodrigues et al., 2024).

The attribution literature therefore shares with broader IG research a concern for faithful, stable, semantically meaningful explanations, but it addresses a different object: explanations of a fixed predictor rather than the design of predictors whose generalization is itself interpretable. This distinction is central whenever the acronym “IG” appears without expansion.