Related papers: Symmetry-Preserving Paths in Integrated Gradients
Attribution methods are primarily designed to study input component contributions to individual model predictions. However, some research applications require a summary of attribution patterns across the entire dataset to facilitate the…
Integrated Gradients (IG) is a widely used algorithm for attributing the outputs of a deep neural network to its input features. Due to the absence of closed-form integrals for deep learning models, inaccurate Riemann Sum approximations are…
Integrated Gradients (IG) as well as its variants are well-known techniques for interpreting the decisions of deep neural networks. While IG-based approaches attain state-of-the-art performance, they often integrate noise into their…
Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing…
Discrete gradient methods are geometric integration techniques that can preserve the dissipative structure of gradient flows. Due to the monotonic decay of the function values, they are well suited for general convex and nonconvex…
Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…
The explication of Convolutional Neural Networks (CNN) through xAI techniques often poses challenges in interpretation. The inherent complexity of input features, notably pixels extracted from images, engenders complex correlations.…
The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD)…
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
We introduce Generalized Integrated Gradients (GIG), a formal extension of the Integrated Gradients (IG) (Sundararajan et al., 2017) method for attributing credit to the input variables of a predictive model. GIG improves IG by explaining a…
We introduce Riemannian Integrated Gradients (RIG); an extension of Integrated Gradients (IG) to Riemannian manifolds. We demonstrate that RIG restricts to IG when the Riemannian manifold is Euclidean space. We show that feature attribution…
Deep learning has become the standard approach for most machine learning tasks. While its impact is undeniable, interpreting the predictions of deep learning models from a human perspective remains a challenge. In contrast to model…
Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between…
An appealing property of the natural gradient is that it is invariant to arbitrary differentiable reparameterizations of the model. However, this invariance property requires infinitesimal steps and is lost in practical implementations with…
We analyze the convergence of the Conjugate Gradient (CG) method in exact arithmetic, when the coefficient matrix $A$ is symmetric positive semidefinite and the system is consistent. To do so, we diagonalize $A$ and decompose the algorithm…
In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…