arXiv research

RIG extends IG to Riemannian manifolds for explainable AI.

Combines Integrated Gradients and PatternAttribution into PGIG, outperforming alternatives.

Gradient and Laplacian estimates for complex Monge-Ampère equations found.

Proposes a new method to interpret EEG classification models without needing a baseline.

Gradient flow preserves speed for integral Menger curvature curves.

The challenge of assigning importance to individual neurons in a network is of interest when interpreting deep learning models. In recent work, Dhamdhere et al. proposed Total Conductance, a "natural refinement of Integrated Gradients" for attributing importance to internal neurons. Unfortunately, the authors found tha…

The paper provides gradient estimates for solutions on manifolds with integral Ricci bounds.

Proposes Geodesic Integrated Gradients (GIG) for more accurate feature attributions in deep networks.

The paper studies a gradient system on a beta statistical manifold, proving integrability and deriving explicit expressions.

We observe that stable integral simplicial volume of closed manifolds gives an upper bound for the rank gradient of the corresponding fundamental groups.

The paper proves gradient estimates for a weighted p-Laplacian equation on Riemannian manifolds.

Paper tackles fooling deep networks with minimal perturbations.

The paper derives new gradient estimates for nonlinear elliptic equations under integral Ricci curvature bounds.

Sharp gradient estimate for harmonic functions on Kähler manifolds.

PS-IG improves feature attribution by reducing noise and variance.

Improved saliency maps for deep neural networks with reduced noise.

HF-opt uses Hamiltonian dynamics to optimize functions, achieving accelerated rates with randomized integration time.

Estimates gradients of solutions on closed surfaces.

GIG improves IG to explain diverse ML functions.

Regularizes persistent homology gradients for neural network integration.

Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of th…

New method improves policy gradient performance in continuous control tasks.

Study on gradient h-almost Yamabe solitons with scalar curvature estimation.

Graph manifolds are manifolds that decompose along tori into pieces with a tame $S^1$-structure. In this paper, we prove that the simplicial volume of graph manifolds (which is known to be zero) can be approximated by integral simplicial volumes of their finite coverings. This gives a uniform proof of the vanishing of …

A vector field on a Riemannian manifold is called geodesic if its integral curves are reparametrized geodesics. We classify compact Kähler manifolds admitting nontrivial real-holomorphic geodesic gradient vector fields that satisfy an additional integrability condition. They are all biholomorphic to bundles of complex …

The paper studies integral formulas for a specific type of soliton.

In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact gradient shrinking Ricci solitons, under the conditions that the Ricci curvatur…

Examples of Morse functions with integrable gradient flows on some classical Riemannian manifolds are considered. In particular, we show that a generic height function on the symmetric embeddings of classical Lie groups and certain symmetric spaces is a perfect Morse function, i.e. has as many critical points as the ho…

We study integral and pointwise bounds on the curvature of gradient shrinking Ricci solitons. As applications we discuss gap and compactness results for gradient shrinkers.

This paper extends explainability methods to non-Gaussian Gaussian Processes.

The gradient shrinking $ρ$-Einstein soliton is a triple $(M^n,g,f)$ such that $R_{ij}+f_{ij}=(ρR+λ) g_{ij},$ where $(M^n,g)$ is a Riemannian manifold, $λ>0, ρ\in\mathbb{R}\setminus\{0\}$ and $f$ is the potential function on $M^n$. In this paper, using algebraic curvature estimates and the Yamabe-Sobolev inequality, w…

Proposes a new method for better explaining neural network decisions.

The paper proves various inequalities on gradient shrinking Ricci solitons.

Simplified uHMC with time integration improves accuracy and efficiency.

Study on gradient steady Kähler Ricci solitons with specific curvature properties.

Greedy PIG adapts integrated gradients for better feature attribution.

Study shows Sasaki solitons with harmonic Weyl tensor are spheres.

The article characterizes gradient ρ-Einstein solitons under specific conditions.

The paper examines Ricci solitons with convex potential and finds them flat and split.

Enhanced visual feature attribution via adaptive baseline weighting.

A new method for estimating uncertainties in neural ODEs without numerical integration.

Study on test risk dynamics in learning theory with stochastic gradient flow.

We classify compact Kähler surfaces with nonconstant Killing potentials such that all integral curves of their gradients are reparametrized geodesics.

New method preserves convergence rates in gradient-based optimization.

The paper establishes Harnack inequalities for solutions of nonlinear parabolic equations on manifolds with integral Ricci curvature bounds.

Study on Ricci-Bourguignon solitons and almost solitons, generalizing previous results.

The paper studies metrics on Lie groups SO(2) and SO(3) and their integrability.

A new flow on null manifolds yields gradient estimates.