Manifold-Aligned Guided Integrated Gradients for Reliable Feature Attribution

Abstract: Feature attribution is central to diagnosing and trusting deep neural networks, and Integrated Gradients (IG) is widely used due to its axiomatic properties. However, IG can yield unreliable explanations when the integration path between a baseline and the input passes through regions with noisy gradients. While Guided Integrated Gradients reduces this sensitivity by adaptively updating low-gradient-magnitude features, input-space guidance still produces intermediate inputs that deviate from the data manifold. To address this limitation, we propose \emph{Manifold-Aligned Guided Integrated Gradients} (MA-GIG), which constructs attribution paths in the latent space of a pre-trained variational autoencoder. By decoding intermediate latent states, MA-GIG biases the path toward the learned generative manifold and reduces exposure to implausible input-space regions. Through qualitative and quantitative evaluations, we demonstrate that MA-GIG produces faithful explanations by aggregating gradients on path features proximal to the input. Consequently, our method reduces off-manifold noise and outperforms prior path-based attribution methods across multiple datasets and classifiers. Our code is available at https://github.com/leekwoon/ma-gig/.

• The paper introduces MA-GIG, a method that constructs gradient attribution paths in a VAE latent space to reduce off-manifold noise.
• It uses geometry-aware latent updates that project onto the data manifold’s tangent space for improved attribution fidelity.
• Empirical results on datasets like ImageNet and Oxford confirm that MA-GIG yields tighter, more interpretable attribution maps.

Manifold-Aligned Guided Integrated Gradients (MA-GIG) for Reliable Feature Attribution

Introduction and Motivation

Feature attribution is fundamental for interpreting and diagnosing deep neural representations, offering transparency required in safety-critical applications. While path-based methods like Integrated Gradients (IG) (2605.02167) guarantee desirable axiomatic properties, their fidelity depends heavily on the geometry of the integration path between the baseline and input. Classic IG leverages a straight-line path in input space—this traverses regions of $\mathbb{R}^n$ unsupported by the data manifold, inducing unreliable gradients and noisy attributions. Guided IG (GIG) (2605.02167) attempts to circumvent high-gradient regions adaptively but, remaining in pixel space, it is inherently limited: sparse axis-aligned updates rarely coincide with the true manifold tangent space, leading to significant off-manifold drift over the path integration.

To resolve these limitations, "Manifold-Aligned Guided Integrated Gradients for Reliable Feature Attribution" (2605.02167) proposes MA-GIG, which constructs the attribution path in the latent space of a VAE. Gradients are aggregated over a decoded path that remains closely aligned to the high-density regions of the learned data manifold, suppressing spurious off-support noise and providing more robust, perceptually faithful attributions.

Identification and Formalization of Manifold Deviation

GIG operates via adaptive feature selection: at each step, features with the smallest gradient magnitudes are greedily updated toward the input. However, unless the tangent space at the current point is axis-aligned (an event of measure zero for natural images), these pixel-wise updates will, to leading order, move the point off-manifold. The authors formalize this using the notion of manifold reach and project local update vectors onto the local tangent space, demonstrating (Proposition: Off-Manifold Drift) that the orthogonal component accumulates $O(1/q)$-sized deviation over $K$ steps, so that path samples diverge significantly from $\mathcal{M}$, traversing regions where both classifier behavior and $\nabla_x f$ are semantically meaningless.

Method: Latent-Space Path Construction

The key algorithmic innovation in MA-GIG is to transpose the greedy update rule into the latent space $\mathcal{Z}$ of a pre-trained VAE, treating the decoder $$D: \mathcal{Z} \to \mathcal{M} \subset \mathbb{R}^n$$ as a parametrization of the data manifold. The baseline and the input are projected into latent space, and sparse updates in $\mathcal{Z}$ are decoded into $\mathcal{X}$. Critically, while latent updates are axis-aligned in $\mathcal{Z}$, the columns of the Jacobian $O(1/q)$0—the natural tangent directions—are typically highly correlated in pixel space, ensuring that decoded steps follow the tangent bundle of the learned manifold. This alignment substantially reduces off-manifold deviation, both theoretically (under perfect autoencoder assumptions) and empirically.

Figure 1: Overview of MA-GIG showing the manifold-constrained latent path (green) avoiding high-frequency, off-manifold pixel-space regions traversed by classical GIG.

The concrete MA-GIG path construction proceeds as follows:

1. Encode $O(1/q)$1 into $O(1/q)$2 via $O(1/q)$3;
2. Initialize $O(1/q)$4 and for $O(1/q)$5 steps:
   • Decode $O(1/q)$6;
   • Compute latent-space gradients via backpropagation through $O(1/q)$7;
   • Select a fraction $O(1/q)$8 of latent dimensions with smallest $O(1/q)$9;
   • Update only these dimensions toward $K$0;
3. Decode all $K$1 steps to obtain path samples and perform Riemann-sum path integration in pixel space.

Empirical Results

Attribution Map Quality

MA-GIG consistently suppresses noise and background distraction compared to both classic and adaptive path methods. Across diverse datasets (ImageNet, Oxford-IIIT Pet, Oxford 102 Flower) and backbones (ResNet18, VGG16, InceptionV1), MA-GIG demonstrates that the majority of attribution mass concentrates on class-distinctive object regions, while background and inappropriate artifacts prevalent in alternatives are eliminated.

Figure 2: MA-GIG yields tighter, less noisy attribution maps than path-based and manifold-informed baselines across InceptionV1, ResNet18, and VGG16 on multiple benchmarks.

Manifold Alignment and Path Plausibility

LPIPS perceptual metrics between path samples and the input indicate that input-space guided methods (including GIG and IG variants) yield higher perceptual deviations—indicative of semantically implausible and visually incoherent transitions. In contrast, MA-GIG maintains perceptual proximity throughout the path, supporting the hypothesis that latent-space guidance induces more plausible interpolations.

Figure 3: LPIPS path analysis on ImageNet (ResNet18). MA-GIG sustains lower perceptual deviation to the input across the full path, implying path realism.

Quantitative Faithfulness

Faithfulness measured by DiffID, Insertion, and Deletion metrics demonstrates that MA-GIG outperforms all evaluated baselines—gradient-based, path-based, and manifold-informed—across multiple classifiers and datasets. Notably, improvements are robust to variations in the feature selection fraction $K$2 and the choice of VAE prior, with the best domain-aligned VAEs providing the highest DiffID/insertion scores.

Path Analysis and Gradient Aggregation

Analysis of intermediate path samples and their gradient magnitudes shows that, unlike baselines which accumulate substantial attributions in off-manifold or semantically irrelevant states, MA-GIG drives meaningful attributions to path regions proximate to the target input where object semantics are actually present. This is evidenced by aggregation of most feature importance near the end of the integration path, just as salient features become reconstructed.

Figure 4: Evolution of path features and gradients along MA-GIG and competing methods. MA-GIG defers important high-gradient latent dimensions until object semantics are reliably reconstructed and avoids attributing noise from unstructured intermediate states.

Geometric and Theoretical Implications

By reframing path-based attribution as a geometric problem of manifold consistency, MA-GIG resolves a central trade-off: completeness and sensitivity (axiomatic properties) do not guarantee meaningful attributions unless gradients are evaluated on points consistent with the true data distribution. Guiding attribution paths in generative model latent space formally ensures (under standard regularity) that each update lies in the tangent bundle of the data manifold, tightly bounding off-manifold error. The practical relevance extends beyond attributions: this paradigm can inform future robust explainability and counterfactual generation systems, especially as generative priors are increasingly integrated into the ML analysis pipeline.

Limitations and Future Directions

MA-GIG inherits the limitations of its generative prior. Attribution quality degrades if the decoder's reconstructions are poor, if the target distribution is semantically misaligned with the VAE training set, or if the latent representation lacks expressivity for the current domain. The approach is not mask-optimization or final-layer localization; path-based methods have intrinsic limitations for insertion AUC when compared against alternatives explicitly optimizing for deletion games or region-wise explanation highlighting (e.g., Grad-CAM).

Future work should address (a) principled combination of manifold-aligned paths with multi-path or stochastic smoothing methods (e.g., SmoothGrad), (b) diagnostics and adaptation for decoder prior alignment, and (c) integrating path-based constraints with mask optimization for attribution that is both axiomatized and semantically faithful.

Conclusion

MA-GIG introduces a theoretically principled and empirically validated solution to the manifold deviation problem plaguing path-based gradient attributions. By constructing integration paths in the latent space of generative models, decoded through to plausible data samples, it substantially enhances reliability, interpretability, and diagnostic value of feature attributions in modern neural networks. The framework offers a geometric perspective for future research in trustworthy model explanations, robust interpretability, and generative-model-informed attribution methodologies.