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arxiv: 2605.19607 · v1 · pith:GEHZLP3Cnew · submitted 2026-05-19 · 💻 cs.CV · cs.AI· cs.LG

Spectral Integrated Gradients for Coarse-to-Fine Feature Attribution

Soyeon Kim , Seongwoo Lim , Kyowoon Lee , Jaesik Choi This is my paper

Pith reviewed 2026-05-20 05:27 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.LG
keywords Spectral Integrated Gradientsfeature attributionIntegrated Gradientssingular value decompositioncoarse-to-fineexplainable AIimage classificationpath-based attribution
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The pith

Spectral Integrated Gradients builds integration paths via SVD to introduce global structure before fine details, yielding cleaner attributions than straight-line paths.

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

The paper introduces Spectral Integrated Gradients to fix a key flaw in standard Integrated Gradients: the straight-line path from baseline to input turns on all features at once and accumulates noisy gradients. SIG instead decomposes the difference vector with singular value decomposition and follows a path that activates the largest singular components first, then progressively smaller ones. This creates a coarse-to-fine ordering that supplies global image structure before local details. Evaluations across multiple image classification datasets show the resulting attribution maps contain less noise and score higher on quantitative metrics than other path-based methods. The approach keeps the axiomatic properties that make Integrated Gradients attractive while changing only the choice of path.

Core claim

Integrated Gradients satisfies its axiomatic properties for any integration path, yet the conventional straight-line path from baseline to input activates every feature simultaneously and therefore collects noisy gradients along the way. Spectral Integrated Gradients replaces that path with one derived from the singular value decomposition of the baseline-to-input difference: the path is parameterized so that singular components are added in descending order of singular value. The resulting attributions therefore receive global structure before fine-grained details, producing maps with visibly reduced noise and higher quantitative scores on standard image-classification benchmarks while the

What carries the argument

Spectral Integrated Gradients, which constructs the integration path by ordering singular components from largest to smallest singular value so that global structure precedes fine details.

If this is right

  • Attribution maps exhibit visibly lower noise levels on image data.
  • Quantitative metrics for attribution quality improve over existing path-based baselines.
  • Axiomatic guarantees of Integrated Gradients remain intact under the new path choice.
  • The coarse-to-fine ordering applies across diverse image classification datasets without retraining.
  • The method requires only an SVD on the input-baseline difference and no change to the underlying model.

Where Pith is reading between the lines

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

  • The same SVD ordering idea could be tested on non-image domains where a natural low-rank decomposition exists.
  • If the singular-value ordering aligns with human visual perception, it might explain why certain explanations feel more intuitive.
  • Future work could compare the learned singular directions against known dataset biases or model failure modes.
  • The approach suggests that other path-based methods might also benefit from ordering features by some measure of global importance rather than uniform activation.

Load-bearing premise

Ordering singular components from largest to smallest singular value will reduce noise and improve attribution quality without introducing new artifacts or violating the axiomatic properties of Integrated Gradients.

What would settle it

If quantitative noise metrics and performance scores on standard image datasets show no consistent improvement over straight-line Integrated Gradients or other path variants, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.19607 by Jaesik Choi, Kyowoon Lee, Seongwoo Lim, Soyeon Kim.

Figure 1
Figure 1. Figure 1: Overview of Spectral Integrated Gradients (SIG). (A) In the logit surface landscape, the linear path (gray line) of IG [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Frequency-domain analysis of integration paths. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Path analysis on ImageNet using the VGG16 clas [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative comparison of attribution maps on ImageNet (InceptionV3), Oxford-IIIT Pet (ResNet18), and Oxford 102 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: RemOve And Retrain (ROAR) test on CIFAR10. SIG [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Extended runtime analysis on faithfulness metrics. [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Additional examples of frequency-domain analysis of integration paths. Supplementary to Figure 2, these examples [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Additional path analysis examples. Supplementary to Figure 3, these results on ResNet18 (left) and VGG16 (right) [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Extended path analysis comparing IG, BIG, EIG, MIG, GIG, and SIG. For each example, the top row displays the [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Qualitative comparison against baselines on ImageNet 2012 using three classifiers. Bold test labels indicate the [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Qualitative comparison on Oxford 102 Flower using three classifiers. Bold test labels indicate the predicted class, and [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Qualitative comparison on Oxford-IIIT Pet using three classifiers. Bold test labels indicate the predicted class, and [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
read the original abstract

Integrated Gradients (IG) is a widely adopted feature attribution method that satisfies desirable axiomatic properties. However, the choice of integration path significantly affects the quality of attributions, and the standard straight-line path introduces all input features simultaneously, often accumulating noisy gradients along the way. To address this limitation, we propose Spectral Integrated Gradients, which constructs integration paths based on singular value decomposition (SVD) of the baseline-to-input difference. By progressively activating singular components from largest to smallest, SIG introduces global structure before fine-grained details, naturally following a coarse-to-fine progression. Through extensive evaluation across diverse image classification datasets, we demonstrate that SIG produces cleaner attribution maps with reduced noise and achieves improved quantitative performance compared to existing path-based attribution methods. Our code is available at https://github.com/leekwoon/sig/.

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

3 major / 2 minor

Summary. The manuscript proposes Spectral Integrated Gradients (SIG), a path-based variant of Integrated Gradients for feature attribution in image classification models. SIG constructs the integration path by applying SVD to the baseline-to-input difference and progressively activating singular components ordered from largest to smallest singular value, aiming for a coarse-to-fine progression that reduces noise compared to the standard straight-line path. The authors report that this yields cleaner attribution maps and improved quantitative performance across diverse datasets, with code released for reproducibility.

Significance. If the central claims hold, SIG could provide a practical enhancement to attribution quality in computer vision without violating IG axioms, potentially aiding interpretability of CNNs. The open-source code is a clear strength for reproducibility and further testing.

major comments (3)
  1. [§3] §3 (Path Construction): The SVD-based path must be explicitly shown to be a continuous, differentiable curve parameterized by a single scalar t ∈ [0,1] from baseline (zero components) to full input. It is unclear whether the progressive activation of singular components (largest to smallest) forms a monotonic trajectory that satisfies the fundamental theorem of calculus underlying the IG proof, or if it introduces piecewise behavior or interpolation artifacts.
  2. [§4 or §5] §4 or §5 (Evaluation): The claim of improved quantitative performance and reduced noise requires concrete metrics (e.g., insertion/deletion scores, faithfulness metrics), statistical tests, dataset names/sizes, and direct comparisons to baselines such as standard IG and other path variants. The abstract asserts superiority after 'extensive evaluation' but the provided details do not allow verification of effect sizes or controls for path-dependent biases.
  3. [Axioms discussion] Axioms section: Completeness (sum of attributions equals f(x) − f(baseline)) must be verified numerically for the SVD path, as any deviation from a valid IG curve could make attributions incomplete or path-dependent in uncontrolled ways. The paper should include a proof sketch or empirical check that the ordering from largest to smallest singular values preserves this property.
minor comments (2)
  1. [Abstract] Abstract: Briefly list the specific datasets and at least one quantitative metric to support the performance claim, improving readability for readers scanning the paper.
  2. [Method] Notation: Define the parameterization of the SVD path (e.g., how components are scaled with t) with an equation early in the method section to avoid ambiguity in later derivations.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive comments on our manuscript. We address each of the major comments point by point below, providing clarifications and indicating revisions where necessary to strengthen the presentation of Spectral Integrated Gradients.

read point-by-point responses

  1. Referee: [§3] §3 (Path Construction): The SVD-based path must be explicitly shown to be a continuous, differentiable curve parameterized by a single scalar t ∈ [0,1] from baseline (zero components) to full input. It is unclear whether the progressive activation of singular components (largest to smallest) forms a monotonic trajectory that satisfies the fundamental theorem of calculus underlying the IG proof, or if it introduces piecewise behavior or interpolation artifacts.

    Authors: We appreciate the referee's emphasis on rigorously defining the integration path. In the original manuscript, Section 3 describes the construction via SVD and progressive activation, but we acknowledge that the explicit parameterization as a function of t could be stated more formally. In the revised manuscript, we will add the definition of the path γ(t) for t ∈ [0,1] as a continuous curve in the spectral domain that monotonically activates components from largest to smallest singular value. This construction ensures differentiability and satisfies the conditions for the path integral underlying Integrated Gradients, with a derivation showing that the fundamental theorem of calculus holds without introducing piecewise artifacts or uncontrolled interpolation. revision: yes

  2. Referee: [§4 or §5] §4 or §5 (Evaluation): The claim of improved quantitative performance and reduced noise requires concrete metrics (e.g., insertion/deletion scores, faithfulness metrics), statistical tests, dataset names/sizes, and direct comparisons to baselines such as standard IG and other path variants. The abstract asserts superiority after 'extensive evaluation' but the provided details do not allow verification of effect sizes or controls for path-dependent biases.

    Authors: We agree that additional concrete details on the evaluation protocol would improve verifiability. The manuscript reports results across multiple image classification datasets with quantitative comparisons to standard Integrated Gradients and other path-based methods, including metrics such as insertion and deletion scores. To address the concern directly, we will revise the evaluation section to include an expanded summary table with dataset sizes, specific metric values, and controls for path-dependent effects, allowing clearer assessment of the reported improvements. revision: yes

  3. Referee: [Axioms discussion] Axioms section: Completeness (sum of attributions equals f(x) − f(baseline)) must be verified numerically for the SVD path, as any deviation from a valid IG curve could make attributions incomplete or path-dependent in uncontrolled ways. The paper should include a proof sketch or empirical check that the ordering from largest to smallest singular values preserves this property.

    Authors: We thank the referee for this observation on axiomatic guarantees. For any continuous path connecting the baseline to the input, completeness follows directly from the fundamental theorem of calculus applied to the gradient integral, independent of the particular ordering of singular components. The SVD ordering shapes the trajectory but preserves path validity. In the revised manuscript, we will add a short proof sketch to the axioms discussion and include numerical verification in the experiments section confirming that attribution sums match f(x) − f(baseline) within floating-point precision. revision: yes

Circularity Check

0 steps flagged

No circularity: SIG path is independently defined and evaluated empirically

full rationale

The paper defines Spectral Integrated Gradients by constructing an integration path via SVD decomposition of the baseline-to-input difference and ordering singular components from largest to smallest. This construction is presented as a direct proposal to achieve coarse-to-fine progression, independent of any evaluation outcomes or fitted parameters. The claimed improvements in attribution quality are supported solely by empirical results across image classification datasets, not by any reduction of the method to its own inputs or self-referential definitions. No self-citations, uniqueness theorems, or ansatzes from prior author work are invoked in the provided text to justify the central path choice. The derivation chain remains self-contained against external benchmarks, with the path definition standing apart from the quantitative performance claims.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The method relies on standard linear-algebra SVD and the existing IG axiomatic framework.

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