Reveal-IG: Distributional Attribution Method

• Reveal-IG is a path-attribution method that replaces direct input interpolation with gradual information disclosure via structured probe distributions.
• It preserves completeness by integrating expected model responses along a distributional path, mitigating artifacts common to standard Integrated Gradients.
• The implementation uses Monte Carlo estimation and adaptive probe calibration to demonstrate robust performance on both image and tabular tasks.

Searching arXiv for the Reveal-IG paper and closely related Integrated Gradients work to ground the article in current literature. arXiv paper located: "Attribution via Distributional Paths for Information Revelation" (Murphy et al., 2 Jun 2026), which introduces Reveal-IG. I also identified directly relevant related IG literature on baseline choice (Tan, 2022), decision-region weighting (Walker et al., 2023), graph adaptations (Simpson et al., 9 Sep 2025), manifold generalization (Costanza et al., 2 Mar 2025), and coarse-to-fine path design (Kim et al., 19 May 2026). Reveal-IG is a path-attribution method that preserves the completeness logic of Integrated Gradients (IG) while relocating the attribution path from raw input space to a space of structured probe distributions centered on the example of interest. Rather than traversing pointwise perturbed inputs, Reveal-IG progressively reveals information about a target example $x^\star$ and attributes changes in the model’s expected output along that distributional path. In this formulation, the object being integrated is not $f(x)$ at a sequence of interpolated inputs, but the expected model response under a parameterized probe family $q_\theta(z\mid x^\star)$ (Murphy et al., 2 Jun 2026).

1. Conceptual basis

Standard path methods such as IG explain a prediction by integrating derivatives along a trajectory in input space from a baseline to the input. Reveal-IG is motivated by the claim that this construction makes the explanation depend on how the model behaves at every intermediate point on that path, including semantically weak or out-of-distribution inputs, and that the early, baseline-adjacent part of the trajectory contributes to the explanation on equal mathematical footing with the neighborhood of the target example. Reveal-IG therefore reframes path attribution as gradual information revelation rather than literal traversal of raw input values (Murphy et al., 2 Jun 2026).

This reframing is explicitly continuous and distributional. Early points on the path correspond to broad, uncertain, low-information probes; later points correspond to concentrated probes that encode finer information about $x^\star$. The method is presented as a continuous analogue of SHAP-style feature revelation: discrete reveal in SHAP becomes smooth reduction of uncertainty in Reveal-IG. The paper’s synthetic diagnostics further argue that this construction reduces path artifacts such as “shadow” effects, in which localized structure encountered earlier along an input-space path disproportionately affects attributions at a distant endpoint (Murphy et al., 2 Jun 2026).

A useful contrast is that standard IG explains the difference between an input and a baseline in input space, whereas Reveal-IG explains how the model’s expected response changes as information about the target example is progressively disclosed. This places Reveal-IG in the broader family of path-based attribution methods, but with a different path semantics from straight-line interpolation, blur-based reveal, or decision-region reweighting.

2. Formal distributional-path framework

Reveal-IG begins from a general path decomposition. For a path $\mathcal S$ in parameter space $\theta$, and a scalar functional $G(\theta)$, the total change along the path is decomposed featurewise as

$$G(\theta^{\mathrm{end}}) - G(\theta^{\mathrm{start}}) = \int_{\mathcal{S}} \nabla_\theta G(\theta)\cdot d\theta = \sum_i \int_{\mathcal{S}} \frac{\partial G}{\partial \theta_i}\, d\theta_i = \sum_i a_i .$$

Reveal-IG instantiates this by lifting the explained quantity from $f(x)$ to

$$G(\theta; x^\star) = \mathbb{E}_{z \sim q_\theta(\cdot \mid x^\star)}[f(z)],$$

so that the central line integral becomes

$f(x)$0

Under a factorized probe family,

$f(x)$1

the coordinates $f(x)$2 define featurewise attribution blocks, and their line-integral contributions sum to completeness with respect to the expected model response (Murphy et al., 2 Jun 2026).

For Gaussian probes, each feature has parameter block

$f(x)$3

and the feature attribution is

$f(x)$4

The paper stresses that the mean-path and variance-path contributions are not heuristic additions; both are required by completeness.

The resulting completeness identity is

$f(x)$5

This is exact for the lifted functional $f(x)$6. It is not necessarily identical to $f(x)$7 unless the endpoint probe collapses to a delta distribution at $f(x)$8 and the start probe coincides with a deterministic baseline.

3. Probe families and path construction

Reveal-IG is domain-specific primarily through the choice of probe family. The paper instantiates this for images and tabular data.

Domain	Probe family	Path endpoints
Images	$f(x)$9	start: $q_\theta(z\mid x^\star)$0; end: $q_\theta(z\mid x^\star)$1
Tabular data	$q_\theta(z\mid x^\star)$2	start: broad empirical-marginal regime; end: concentrated near $q_\theta(z\mid x^\star)$3

For images, the probe is a factorized Gaussian over pixel-channel components,

$q_\theta(z\mid x^\star)$4

The path starts at a normalized image-space prior

$q_\theta(z\mid x^\star)$5

and ends at

$q_\theta(z\mid x^\star)$6

The paper interprets this as a multiscale reveal process: large early variance produces coarse, low-information probes, and decreasing variance yields progressively finer interrogation of the model near the actual image. An adaptive endpoint is also defined by the largest Gaussian noise level preserving at least $q_\theta(z\mid x^\star)$7 of the clean target logit,

$q_\theta(z\mid x^\star)$8

For tabular data, arbitrary continuous perturbations are treated as implausible, so the probe is defined over empirical feature values: $q_\theta(z\mid x^\star)$9 In the experiments, $x^\star$0 is negative squared distance. As $x^\star$1, the probe approaches the empirical marginal; as $x^\star$2 decreases, it concentrates near the observed feature value. The path is parameterized by fractional entropy reduction so that features with different marginal entropies reveal information at matched rates rather than becoming deterministic at unequal speeds (Murphy et al., 2 Jun 2026).

Implementation uses reparameterized gradients for Gaussian image probes and weighted expectations over fixed empirical support for tabular probes. The reported settings are 50 integration steps and 10 Monte Carlo samples per step for images, and 40 integration steps with 40 Monte Carlo samples per step for tabular data.

4. Relationship to Integrated Gradients and neighboring path methods

Reveal-IG remains an IG-family method in the sense that it is still a complete path-attribution framework. The decisive change is that standard IG integrates derivatives of $x^\star$3 along an input-space path, whereas Reveal-IG integrates derivatives of

$x^\star$4

along a path in probe-distribution parameter space. The paper therefore positions Reveal-IG as a distributional-path generalization of IG rather than a perturbation ensemble or baseline-averaging variant (Murphy et al., 2 Jun 2026).

This distinction separates it from several adjacent lines of IG research. "Integrated Decision Gradients" concentrates attribution in the decision region by weighting each path contribution by the derivative of the output logit with respect to path position, addressing saturation but retaining a straight input-space path (Walker et al., 2023). "Spectral Integrated Gradients" constructs a coarse-to-fine path by progressively activating singular components of the baseline-to-input difference, still in input space and with explicit SVD-based path scheduling (Kim et al., 19 May 2026). "Diffusion Integrated Gradients" makes path generation a conditional generative modeling problem and uses diffusion-based guided sampling to produce controllable non-linear attribution paths (Kim et al., 21 Jun 2026). Reveal-IG differs from all three because it changes not only the path geometry but also the object being integrated: expected response under structured uncertainty, rather than pointwise response along a deterministic reveal trajectory.

The method also contrasts with graph and manifold generalizations of IG. "Graph-based Integrated Gradients for Explaining Graph Neural Networks" replaces Euclidean interpolation with accumulation along graph shortest paths and selects graph baselines using a path-entropy criterion (Simpson et al., 9 Sep 2025). "Riemannian Integrated Gradients" lifts IG to compact connected Riemannian manifolds using geodesics, tangent spaces, and parallel transport (Costanza et al., 2 Mar 2025). Those methods adapt IG to non-Euclidean domains, whereas Reveal-IG keeps the input domain fixed but changes the path space to structured probe distributions.

A different orthogonal issue is baseline choice. The maximum-entropy baseline literature argues that many conventional IG baselines are not actually uninformative to the model and proposes

$x^\star$5

as a model-centric reference state (Tan, 2022). Reveal-IG does not eliminate this design problem so much as relocate it: the central design choice becomes the probe family and its start/end distributions rather than a single deterministic reference input.

5. Empirical behavior

The paper evaluates Reveal-IG on synthetic diagnostics, ImageNet classification, and tabular regression. The synthetic analysis is used to visualize path artifacts. In simple functions, IG and Reveal-IG can agree, but in structured landscapes IG exhibits “shadow” effects when localized bumps intersect the straight baseline-to-input path. Reveal-IG weakens these effects because broad early probes average over a neighborhood rather than querying the model at a single off-target point. The paper also interpolates between SHAP and Reveal-IG by subdividing feature revelation into $x^\star$6 uncertainty-reduction steps, arguing that SHAP’s higher-order axis-aligned artifacts diminish as the reveal becomes more continuous (Murphy et al., 2 Jun 2026).

On images, the experiments use 1,000 ImageNet-1K validation images with ResNet-50 and ViT-B/16. Reveal-IG is reported as best or second-best on every image metric across both architectures, with especially strong gains on metrics that use attribution sign. For ResNet-50, the reported values include $x^\star$7 and $x^\star$8, both described as best by a wide margin. For ViT-B/16, Reveal-IG is reported as best on all four listed image metrics. The paper’s interpretation is that Reveal-IG more reliably separates supporting from suppressing evidence (Murphy et al., 2 Jun 2026).

The path-position analysis is one of the method’s clearest empirical signatures. The paper reports that IDG accumulates attribution very early; IG, Guided IG, and Blur-IG accumulate mostly early; Expected Gradients is nearly uniform; and Reveal-IG accumulates mostly late. This is presented as direct evidence that attribution mass shifts toward the stage where the probe has become informative about the target rather than being dominated by baseline-adjacent path segments.

For tabular regression, the datasets are Bike Sharing Demand, California Housing, and Wine Quality, using a two-hidden-layer MLP with 64 units per layer. Results are more mixed than in images, but Reveal-IG is reported as among the best on directional insertion and sufficiency, and best or second-best on sensitivity-max on all three datasets. The paper explicitly notes that KernelSHAP and feature ablation remain highly competitive on perturbation-native metrics such as comprehensiveness and sufficiency.

The computational cost is substantially higher than standard IG. For images, IG with 50 steps is reported at about $x^\star$9 ms, whereas Reveal-IG with 10 Monte Carlo samples per step is about $\mathcal S$0 s, roughly $\mathcal S$1 slower. For tabular data, the cost penalty is much larger; on Bikeshare, Reveal-IG is described as around $\mathcal S$2 s per attribution and about $\mathcal S$3 slower than IG / KernelSHAP / LIME millisecond-scale methods.

6. Limitations, interpretation, and scope

Reveal-IG shifts the main design burden from a single baseline to the family of probe distributions and the path through that family. The paper is explicit that this is both a strength and a limitation. The experiments use factorized probes—independent Gaussian pixel-channels for images and factorized empirical marginals for tabular data—so the method does not model feature correlations in the probe itself. This leaves open whether richer probe families could better capture structure without reintroducing path artifacts (Murphy et al., 2 Jun 2026).

A second limitation is the completeness target. Reveal-IG is exactly complete with respect to

$\mathcal S$4

not necessarily with respect to the deterministic point prediction difference $\mathcal S$5. The paper identifies this explicitly as a conceptual caveat when endpoint probes retain finite variance. Practical computation also introduces numerical completeness gap because the method relies on path discretization, Monte Carlo estimation, and in some settings binary search for endpoint calibration.

The empirical strengths of Reveal-IG are concentrated in sign-sensitive and stability-sensitive evaluations, especially for image models. This suggests that the method is particularly well suited to settings where the distinction between supporting and suppressing evidence is materially important. At the same time, the tabular results indicate that Reveal-IG is not uniformly dominant over perturbation-native approaches.

The term itself should also be scoped carefully. Reveal-IG is the method introduced in "Attribution via Distributional Paths for Information Revelation" (Murphy et al., 2 Jun 2026). It is distinct from several unrelated frameworks named REVEAL in image forensics, multimodal manipulation detection, AI-generated text detection, and reinforcement-learning interpretability (Cao et al., 28 Nov 2025, Zhou et al., 27 May 2026, Wang et al., 21 Apr 2026, Ao et al., 2024). Within the IG literature, its specific contribution is the move from input-space interpolation to attribution over a path of uncertainty-reducing probe distributions, with completeness retained at the level of expected model response.