Authors: Firuz Kamalov, Fadi Thabtah, R. Sivaraj, Neda Abdelhamid
Organizations: Department of Computational Sciences, Canadian University Dubai, UAE · Abu Dhabi School of Management, Abu Dhabi, UAE · Department of Mathematics, Dr. B.R. Ambedkar National Institute of Technology, India
We introduce path-sampled integrated gradients (PS-IG), a framework that generalizes feature attribution by computing the expected value over baselines sampled along the linear interpolation path. We prove that PS-IG is mathematically equivalent to path-weighted integrated gradients, provided the weighting function matches the cumulative distribution function of the sampling density. This equivalence allows the stochastic expectation to be evaluated via a deterministic Riemann sum, improving the error convergence rate from O(m−1/2) to O(m−1) for smooth models. Furthermore, we demonstrate analytically that PS-IG functions as a variance-reducing filter against gradient noise - strictly lowering attribution variance by a factor of 1/3 under uniform sampling - while preserving key axiomatic properties such as linearity and implementation invariance.
Figures & tables
Function
Var(IG)
Var(PS-IG)
Ratio
Linear ( x1+x2+x3 )
0.00992
0.00333
0.3356
Quadratic ( x12+x1x2+x32 )
0.01003
0.00335
0.3337
Sigmoidal ( σ(10(xˉ−0.5)) )
0.00982
0.00333
0.3394
Table 1: Empirical variance of attribution scores under stochastic gradient noise. PS-IG consistently reduces variance by a factor of ≈1/3 compared to standard IG.
Figure 1: Convergence rate comparison between the deterministic PS-IG estimator and Monte Carlo sampling on a log-log scale.
Gradient-Based Attribution uses model derivatives to estimate which inputs, features, parameters, or training examples influence predictions and behaviors.
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/.
Soyeon Kim, Seongwoo Lim, Kyowoon Lee +1
Korea Advanced Institute of Science and Technology Seongnam, Gyeonggi-do, Republic of Korea · INEEJI Corp. Seongnam, Gyeonggi-do, Republic of Korea
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 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/.
Soyeon Kim, Seongwoo Lim, Kyowoon Lee +1
Kim Jaechul Graduate School of AI, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea · INEEJI, Seongnam, Korea · KAIST InnoCORE LLM, KAIST, Daejeon, Korea
Path-based attribution methods such as Integrated Gradients (IG) are widely adopted for their strong axiomatic properties and effectiveness in attributing model predictions to input features by integrating gradients along a path from a baseline to the input. However, the choice of the attribution path largely affects the quality of explanations, and existing approaches rely on fixed or hand-crafted paths that often produce noisy or distorted attributions. To address this limitation, we propose Diffusion Integrated Gradients (DiffIG), a novel method that reformulates path generation as a conditional generative modeling problem. DiffIG first trains a diffusion model to learn a distribution over paths generated from a Stick-Breaking Process, then employs guided sampling to embed user guidance during the sampling procedure. We demonstrate that DiffIG quantitatively matches or outperforms existing path-based methods, achieving perceptually aligned explanations. This work introduces a new generative perspective for flexible, inference-time controllable Explainable Artificial Intelligence (XAI) methods.
Soyeon Kim, Kyowoon Lee, Jaesik Choi
1KAIST, Korea · 3INEEJI Corp., Korea · 2Ajou University, Korea