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.

In our case, it boils down to: ' The smoothing effect induced by the average helps to reduce the visual noise, and hence improves the explanations. For the experiment, m and are the same as SmoothGrad. We start by deriving the closed form of Saliency (SA) and naturally Gradient-Input (GI): ' The case of V arGrad is specific, as the gradient of a linear system being constant, its variance is null. W We recall that for Gradient Input, Integrated Gradients, Occlusion, ' It was quickly realized that they unified properties of various domains such as graph theory, linear algebra or geometry. Later, in the '60s, a connection was made At each step, the insertion metric selects the concepts of maximum score given a cardinality constraint.

Neural Information Processing Systems http://nips.cc/

That is, thestrong (s( )= k k1) andweakinstantiations (s( )= sum( )) coincideforone-layerneural networks.

AIinfinance: Challenges, techniques, andopportunities.ACMComputing Surveys (CSUR), 55(3):1-38, 2022.

Early detection of cancer plays a key role in improving survival rates, but identifying reliable biomarkers from RNA-seq data is still a major challenge. The data are high-dimensional, and conventional statistical methods often fail to capture the complex relationships between genes. In this study, we introduce RGE-GCN (Recursive Gene Elimination with Graph Convolutional Networks), a framework that combines feature selection and classification in a single pipeline. Our approach builds a graph from gene expression profiles, uses a Graph Convolutional Network to classify cancer versus normal samples, and applies Integrated Gradients to highlight the most informative genes. By recursively removing less relevant genes, the model converges to a compact set of biomarkers that are both interpretable and predictive. We evaluated RGE-GCN on synthetic data as well as real-world RNA-seq cohorts of lung, kidney, and cervical cancers. Across all datasets, the method consistently achieved higher accuracy and F1-scores than standard tools such as DESeq2, edgeR, and limma-voom. Importantly, the selected genes aligned with well-known cancer pathways including PI3K-AKT, MAPK, SUMOylation, and immune regulation. These results suggest that RGE-GCN shows promise as a generalizable approach for RNA-seq based early cancer detection and biomarker discovery (https://rce-gcn.streamlit.app/ ).