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arxiv: 2606.03885 · v1 · pith:LNODPGLEnew · submitted 2026-06-02 · 💻 cs.LG

Attribution via Distributional Paths for Information Revelation

Kieran A. Murphy , Shameen Shrestha This is my paper

Pith reviewed 2026-06-28 11:26 UTC · model grok-4.3

classification 💻 cs.LG
keywords feature attributionintegrated gradientsexplainable AIdistributional pathsprobe distributionscompletenessimage classificationtabular regression
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The pith

Reveal-IG attributes model predictions by integrating expected output changes along paths through structured probe distributions instead of raw inputs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard path methods such as Integrated Gradients traverse trajectories directly in input space and integrate the model's raw response at each point along the chosen path. Reveal-IG lifts the path into a space of structured probe distributions that progressively reveal information about the input. Attributions are then computed from changes in the model's expected output along this distributional trajectory. The construction preserves completeness with respect to the expected model response and directly supports multiscale image probes as well as feature-wise uncertainty in tabular data.

Core claim

Reveal-IG defines attribution as the integral of changes in expected model output along a path in the space of probe distributions. By traversing distributions that gradually reveal information rather than raw input values, the method retains the completeness axiom, accommodates multiscale and uncertain probes without equal weighting of all scales, and eliminates the path artifacts that arise when early baseline-adjacent points contribute on equal footing with the input itself.

What carries the argument

The distributional path through a family of structured probe distributions, along which the integral of the gradient of expected model output is taken.

If this is right

  • Attributions sum exactly to the difference between the expected model output at the baseline distribution and at the input distribution.
  • Multiscale image probes receive resolution-appropriate weighting without manual adjustment of the path.
  • Feature-wise uncertainty in tabular data is incorporated directly into the probe distributions rather than treated as post-processing.
  • Synthetic tests show the method avoids the path artifacts that affect input-space trajectory methods.
  • Signed attributions remain stable across runs and outperform other methods on sign-aware evaluation metrics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same distributional-path construction could be applied to other path-based explanation techniques to obtain completeness with respect to expectations.
  • Domains with high input uncertainty, such as sensor data or noisy measurements, could adopt the framework to produce attributions that reflect that uncertainty by design.
  • Automatic or learned selection of probe families might remove the remaining manual choice of distribution family while preserving the artifact-free property.
  • Information-theoretic measures of revelation along the path could quantify how much new information each scale or feature contributes to the prediction.

Load-bearing premise

A family of structured probe distributions can be chosen so that the integral along the distributional path produces attributions free of new artifacts and without requiring post-hoc tuning of the probe family for each model or dataset.

What would settle it

A synthetic diagnostic in which Reveal-IG attributions on a controlled example display path artifacts of comparable magnitude to those seen in input-space Integrated Gradients or fail to sum exactly to the change in expected model output.

Figures

Figures reproduced from arXiv: 2606.03885 by Kieran A. Murphy, Shameen Shrestha.

Figure 1
Figure 1. Figure 1: (a) SHAP reveals feature information in discrete steps, averaging contributions along all such paths. We introduce Reveal-IG, a method that gradually reveals feature information, traversing a continuous path analogous to the path of Integrated Gradients (IG) in the space of feature values. (b) IG evaluates along a single path from a baseline to the point being explained, x ⋆ . Reveal-IG integrates over a s… view at source ↗
Figure 2
Figure 2. Figure 2: Attribution fields in two dimensions. (a) For a selection of functions (left column), we evaluate attributions according to gradients, SHAP, IG, and Reveal-IG. The difference of attribution components, a1 − a2 is displayed as a heatmap. (b) By systematically varying the function, we obtain response curves for the attribution methods. A bump in the function’s output is rotated around the origin and the attr… view at source ↗
Figure 3
Figure 3. Figure 3: For a random selection of ImageNet validation images, we show signed saliency maps for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Attribution over the path. (a) We show the fractional rate of change of the attributions, |∆a(t)|/ P t |∆a(t)|, averaged over 100 images. (b) Contribution to final attribution maps across segments of the trajectory for a randomly selected image. the explained input, rather than being dominated by regions near the baseline. It also echoes the synthetic diagnostics, where early path dependence produced shado… view at source ↗
Figure 5
Figure 5. Figure 5: Reveal-IG completeness convergence. The completeness gap, measured as | Pai − (Eqend [f(x)] − Eqstart [f(x)])|, with ai the attribution for component i, for (a) ResNet-50 on eight ImageNet samples and (b) an MLP trained on the California Housing dataset, evaluated for 20 samples. Shaded regions display standard error. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of Reveal-IG with different σ endpoints, including the adaptive (per-image) endpoint, whose values are displayed inside the corresponding attribution maps in the right column. C Extended synthetic attribution results In [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) The manner of feature information revelation compared schematically for SHAP, the subdivided variant discussed in Sec. 3.1, and Reveal-IG. For SHAP, the feature contributions are averaged over all paths (here, two possibilities). For k = 2, one path is shown out of the six possibilities. The insets’ shaded regions visualize the distribution over feature values used for the expectation in that step’s ca… view at source ↗
Figure 8
Figure 8. Figure 8: For a random selection of images from the localization set with accompanying ImageNet-S [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: For the same random selection of images from the ImageNet validation set shown in Fig. 3, [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: For the same random selection of images from the ImageNet validation set shown in [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: For the same random selection of images from the ImageNet validation set shown in [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
read the original abstract

Feature attribution methods explain predictions by assigning importance scores to input features. Path-based methods such as Integrated Gradients are especially appealing because they satisfy \textit{completeness}: attributions sum to the change in model output between a reference state and the input. Yet most path methods define this trajectory in input space, explaining a model through pointwise perturbed inputs along a chosen path. An input-space path integrates the model's raw response at each point it passes through, with no control over the resolution at which a feature is queried; the early, baseline-adjacent part of the trajectory contributes to the explanation on equal footing with the input itself. Here, we lift path attribution from input space to a space of structured probe distributions around the example of interest, and call our method Reveal-IG. Rather than traversing raw input values, Reveal-IG progressively reveals information about the input and attributes changes in the model's expected output along this distributional path. The result is a path-attribution framework that retains completeness with respect to the expected model response, and naturally accommodates multiscale image probes and feature-wise uncertainty in tabular data. Synthetic diagnostics show that Reveal-IG avoids path artifacts that affect input-space methods, and across ImageNet classification and tabular regression it produces stable, signed attributions -- leading on metrics that use attribution sign while remaining competitive on the rest.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes Reveal-IG, which lifts Integrated Gradients from input-space paths to paths in a space of structured probe distributions. Rather than integrating the model's response along a trajectory of raw inputs, the method integrates changes in expected model output as information about the input is progressively revealed through a family of probe distributions. The central claims are that the resulting attributions satisfy completeness with respect to the expected model response, naturally support multiscale image probes and feature-wise uncertainty, avoid common path artifacts, and produce stable signed attributions that lead on sign-aware metrics while remaining competitive on others, as shown in synthetic diagnostics and experiments on ImageNet classification and tabular regression.

Significance. If the derivations and empirical results hold, Reveal-IG offers a principled way to control the resolution and uncertainty at which features are queried during attribution, addressing a limitation of standard input-space path methods. The preservation of completeness, the handling of multiscale and uncertain data, and the reported stability on sign-aware metrics would constitute a useful technical contribution to the feature attribution literature.

major comments (2)
  1. [Method and Experiments] The central construction relies on the existence of a well-behaved probe distribution family that introduces no new artifacts and requires no post-hoc tuning. The paper should provide a concrete sensitivity analysis (e.g., in the experimental section) showing that attribution rankings and sign-aware metrics remain stable across reasonable choices within the family, or else clarify the selection procedure.
  2. [Synthetic diagnostics] Synthetic diagnostics are invoked to show avoidance of path artifacts, but the specific artifacts tested, the quantitative metrics used, and the comparison baselines must be stated explicitly with numerical results (e.g., in a table) so that the claim can be verified independently.
minor comments (2)
  1. Notation for the distributional path and the expectation operator should be introduced once and used consistently; cross-references to the completeness proof would help readers.
  2. Figure captions should explicitly state the probe family and any hyperparameters used so that the visualizations can be reproduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation and recommendation for minor revision. The comments highlight useful ways to strengthen verifiability. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Method and Experiments] The central construction relies on the existence of a well-behaved probe distribution family that introduces no new artifacts and requires no post-hoc tuning. The paper should provide a concrete sensitivity analysis (e.g., in the experimental section) showing that attribution rankings and sign-aware metrics remain stable across reasonable choices within the family, or else clarify the selection procedure.

    Authors: We agree that explicit robustness checks are valuable. In the revised version we will add a dedicated sensitivity analysis subsection (and accompanying table) in the experimental section. It will report attribution ranking stability and sign-aware metric values across a range of probe-family parameters (different multiscale widths and uncertainty levels) on both the ImageNet and tabular tasks, together with a brief description of the default selection rule used in the main experiments. revision: yes

  2. Referee: [Synthetic diagnostics] Synthetic diagnostics are invoked to show avoidance of path artifacts, but the specific artifacts tested, the quantitative metrics used, and the comparison baselines must be stated explicitly with numerical results (e.g., in a table) so that the claim can be verified independently.

    Authors: We accept the request for greater explicitness. The revised synthetic-diagnostics section will enumerate the concrete artifacts examined (saturation near baselines, discontinuity at feature boundaries), define the quantitative metrics (e.g., attribution variance under path perturbation, sign-consistency score), list the baselines (standard IG, SmoothGrad, and a random-path variant), and present the numerical results in a compact table. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is a direct mathematical lift of IG to distributional paths

full rationale

The paper defines Reveal-IG by lifting the standard Integrated Gradients path integral from input space to a space of structured probe distributions, with the central claim being that the integral of expected-output changes along this distributional path yields attributions that retain completeness w.r.t. the expected model response. No equation reduces the final attribution to a fitted parameter, a quantity defined only in terms of itself, or a result justified solely by self-citation. The construction is presented as a straightforward change of integration domain that preserves the original completeness axiom without introducing new fitted elements or ansatzes smuggled via prior work. Synthetic diagnostics and empirical comparisons are offered as external validation rather than as part of the derivation itself. This is the most common honest finding for a mathematically coherent extension of an existing method.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of a suitable family of probe distributions whose expected-output integrals satisfy completeness; the abstract does not introduce new free parameters or invented entities beyond the standard IG completeness axiom.

free parameters (1)
  • probe distribution family
    Choice of how the structured probe distributions are parameterized around each input; this choice is required to define the path but is not numerically fitted in the abstract.
axioms (1)
  • domain assumption The integral of changes in expected model output along the distributional path equals the difference between expected output on the full input and on the baseline.
    This is the completeness property transferred from input space to distributional space; it is invoked to guarantee that attributions sum correctly.

pith-pipeline@v0.9.1-grok · 5761 in / 1411 out tokens · 61503 ms · 2026-06-28T11:26:23.242983+00:00 · methodology

discussion (0)

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