RIG extends IG to Riemannian manifolds for explainable AI.
problem Lack of explainability in AI models.
method Extension of Integrated Gradients to Riemannian manifolds.
result RIG restricts to IG in Euclidean space.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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48 results for “Integrated gradients”
Combines Integrated Gradients and PatternAttribution into PGIG, outperforming alternatives.
problem Improving neural network explainability methods.
method Combines Integrated Gradients and PatternAttribution into Pattern-Guided Integrated Gradients (PGIG).
result PGIG outperforms other explainability methods in a large-scale image degradation experiment.
Gradient and Laplacian estimates for complex Monge-Ampère equations found.
problem Estimating solutions to complex Monge-Ampère equations with singularities.
method Integral method applied to obtain gradient and Laplacian estimates.
result Gradient and Laplacian estimates for the solution to the singular complex Monge-Ampère equation.
Gradient flow preserves speed for integral Menger curvature curves.
problem Optimizing curves with integral Menger curvature constraints.
method Projected Sobolev gradient flow in Hilbert space.
result Long-time existence and -bounds for the flow.
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.
problem Global regularity estimates for solutions of on Riemannian manifolds.
method Proves -gradient estimates under integral Ricci bounds and constructs a counterexample.
result Optimal constant lower bounds on Ricci curvature are shown in the pointwise sense.
Integrated gradients are widely employed to evaluate the contribution of input features in classification models because it satisfies the axioms for attribution of prediction. This method, however, requires an appropriate baseline for reliable determination of the contributions. We propose a compensated integrated grad…
Proposes Geodesic Integrated Gradients (GIG) for more accurate feature attributions in deep networks.
problem Flawed attributions using straight paths from Integrated Gradients (IG).
method Introduces a model-induced Riemannian metric and computes attributions along geodesics.
result GIG produces more faithful attributions than IG on benchmarks.
The paper studies a gradient system on a beta statistical manifold, proving integrability and deriving explicit expressions.
problem Investigating the geometry and integrability of a gradient system on a bivariate beta statistical manifold.
method Proving the system is Hamiltonian and admitting a Lax pair representation, deriving explicit expressions using Stirling's approximation, and identifying the Hamiltonian function.
result The gradient flow is linearizable in dual affine coordinates, and the system is completely integrable.
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.
problem Gradient estimates for a weighted p-Laplacian equation on Riemannian manifolds.
method Assumes a Sobolev inequality and integral Ricci bounds, proving local gradient estimates and Liouville type results.
result Proves local gradient estimates and Liouville type results on manifolds with lower bounds of Ricci curvature.
The paper derives new gradient estimates for nonlinear elliptic equations under integral Ricci curvature bounds.
problem Gradient estimates for nonlinear elliptic equations under integral Ricci curvature bounds.
method Moser's iteration method applied to positive solutions.
result New local and global gradient estimates for positive solutions are derived.
PS-IG improves feature attribution by reducing noise and variance.
problem Improving feature attribution in machine learning models.
method Path-sampled integrated gradients (PS-IG) computes expected value over sampled baselines.
result PS-IG reduces attribution variance by a factor of 1/3 under uniform sampling.
Improved saliency maps for deep neural networks with reduced noise.
problem Noisy explanations in Integrated Gradients for deep neural networks.
method SmoothTaylor, adaptive noising, and SmoothGrad techniques.
result SmoothTaylor and adaptive noising generate better quality saliency maps.
Hamiltonian Descent Algorithms for Optimization: Accelerated Rates via Randomized Integration Timemath.OC
HF-opt uses Hamiltonian dynamics to optimize functions, achieving accelerated rates with randomized integration time.
problem Optimizing functions efficiently and accelerating convergence rates.
method Randomized Hamiltonian flow (RHF) with accelerated convergence rates.
result RHGD achieves accelerated convergence rates similar to Nesterov's AGD.
Estimates gradients of solutions on closed surfaces.
problem Gradient estimates for solutions on closed surfaces.
method Considered a new metric with bounded integral curvature, derived gradient estimates for , and used these to obtain gradient estimates for .
result Gradient estimates for solutions on closed surfaces are established.
Regularizes persistent homology gradients for neural network integration.
problem Ill-posed inverse problem in computing gradients of persistent homology.
method Regularization through a grouping term to define gradients for larger entities.
result Ensures gradients are defined with respect to larger entities, not individual points.
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…
Study on gradient h-almost Yamabe solitons with scalar curvature estimation.
problem Exploring triviality and scalar curvature estimation of gradient h-almost Yamabe solitons.
method Established sufficient conditions for triviality and scalar curvature estimation under integral inequalities involving the scalar curvature and soliton function.
result Extended and refined former works on almost and h-almost Yamabe solitons, characterizing their geometric structures.
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 …
Graph manifolds are manifolds that decompose along tori into pieces with a tame -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 …
The paper studies integral formulas for a specific type of soliton.
problem Integral formulas for compact gradient h-almost Ricci-Bourguignon solitons.
method Investigation of integral formulas and proving properties of solitons.
result Compact, non-trivial h-almost Ricci-Bourguignon solitons are isometric to a Euclidean sphere under certain conditions.
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…
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.
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…
This paper extends explainability methods to non-Gaussian Gaussian Processes.
problem Making non-Gaussian GP models transparent and explainable.
method Proposes Integrated Gradient-based explainability for non-Gaussian GP models.
result Offers both analytical and approximate solutions for non-Gaussian GP models.
The gradient shrinking -Einstein soliton is a triple such that where is a Riemannian manifold, and is the potential function on . In this paper, using algebraic curvature estimates and the Yamabe-Sobolev inequality, w…
Proposes a new method for better explaining neural network decisions.
problem Challenges in explaining neural network decisions due to base-point choice.
method Introduces tangentially aligned integrated gradients to maximize explanation tangential alignment.
result Optimal base-point maximizes explanation tangential alignment, leading to more accurate interpretations.
The paper proves various inequalities on gradient shrinking Ricci solitons.
problem Understanding geometric inequalities on gradient shrinking Ricci solitons.
method Proving multiple inequalities equivalent on complete gradient shrinking Ricci solitons.
result Various inequalities (Sobolev, logarithmic Sobolev, Schrödinger, etc.) are equivalent on gradient shrinking Ricci solitons.
Simplified uHMC with time integration improves accuracy and efficiency.
problem Improving the efficiency and accuracy of Hamiltonian Monte Carlo algorithms.
method Randomized time integrator for uHMC with stratified Monte Carlo.
result Achieves more accurate approximations with fewer gradient evaluations.
Study shows Sasaki solitons with harmonic Weyl tensor are spheres.
problem Characterizing gradient shrinking Sasaki-Ricci solitons.
method Integral curvature estimates and quotient analysis.
result Gradient shrinking Sasaki-Ricci solitons with harmonic Weyl tensor are finite quotients of spheres.
Greedy PIG adapts integrated gradients for better feature attribution.
problem Interpreting deep learning model predictions.
method Unified discrete optimization framework for feature attribution and selection.
result Greedy PIG improves feature attribution on various tasks.
The article characterizes gradient ρ-Einstein solitons under specific conditions.
problem Characterizing gradient ρ-Einstein solitons with certain properties.
method Analyzing solitons with vector fields of bounded norm, finite weighted Dirichlet integral, and specific Ricci curvature restrictions.
result Non-trivial complete gradient ρ-Einstein solitons with finite weighted Dirichlet integral and certain Ricci curvature restrictions are of constant scalar curvature and steady.
Enhanced visual feature attribution via adaptive baseline weighting.
problem IG's sensitivity to baseline images leads to noisy or unstable explanations.
method Weighted Integrated Gradients (WG) evaluates and weights baselines for improved reliability.
result WG improves over Expected Gradients (EG) by up to 36% across various models.
A new method for estimating uncertainties in neural ODEs without numerical integration.
problem Accurate estimation of predictive uncertainties in neural ODEs.
method Distributional Gradient Matching (DGM) algorithm that jointly trains a smoother and a dynamics model.
result Significantly more accurate predictions compared to traditional methods.
Study on test risk dynamics in learning theory with stochastic gradient flow.
problem Understanding test risk in stochastic gradient flow dynamics.
method Path integral formulation for small learning rates, explicit computation for weak features.
result Explicit corrections due to stochastic term in dynamics, good agreement with simulations.
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 broader variety of functions that arise from practical applications of ML in do…
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.
problem How to discretize gradient-based optimization systems while preserving stability and convergence rates.
method Geometric framework for dissipative symplectic integration.
result Dissipative symplectic integrators preserve rates of convergence up to a controlled error.
The paper establishes Harnack inequalities for solutions of nonlinear parabolic equations on manifolds with integral Ricci curvature bounds.
problem Analyzing solutions of nonlinear parabolic equations on manifolds with specific curvature constraints.
method Establishing space-time gradient estimates and integrating them to find Harnack inequalities.
result Harnack inequalities for positive solutions of nonlinear parabolic equations under integral Ricci curvature bounds.
The paper studies metrics on Lie groups SO(2) and SO(3) and their integrability.
problem Integrability of gradient systems on Lie groups via Fisher metrics.
method Analysis of Souriau-Fisher metrics and 2-cocycles on Lie groups SO(2) and SO(3).
result Cocycles can locally modify Fisher metrics on Lie group orbits.
Derives new optimization methods using variational integrators.
problem Optimization methods in machine learning.
method Variational integrators and principles of Hamilton and Lagrange-d'Alembert.
result Derives two families of optimization methods, including Nesterov's accelerated gradient method.
Integrates momentum into RNNs to improve training.
problem Vanishing gradient in RNNs during training.
method Established connection between RNN dynamics and GD, integrated momentum.
result MomentumRNNs alleviate vanishing gradient issue and improve convergence.
Paper proposes adaptive parameter selection for KGD algorithms.
problem Improving parameter selection for kernel-based gradient descent.
method Integrates bias-variance analysis with splitting method, introduces empirical effective dimension.
result Adaptive parameter selection strategy achieves optimal generalization error bound.
We study gradient-based optimization methods obtained by directly discretizing a second-order ordinary differential equation (ODE) related to the continuous limit of Nesterov's accelerated gradient method. When the function is smooth enough, we show that acceleration can be achieved by a stable discretization of this O…
Adapts IG for better feature attributions and robustness.
problem Reliability concerns in feature attributions for deep learning models.
method Adaptation of path-based feature attribution to Riemannian geometry of data manifolds.
result IG along geodesics generates more intuitive and robust explanations.
We prove some results for the solitons of the Ricci-Bourguignon flow, generalizing corresponding results for Ricci solitons. Taking motivation from Ricci almost solitons, we then introduce the notion of Ricci-Bourguignon solitons and prove some results about them which generalize previous results for Ricci alm…
Comparing Baseline Shapley and Integrated Gradients for Local Explanation: Some Additional Insightscs.LG
Paper compares two local explanation methods for machine learning models.
problem Comparing two local explanation methods for machine learning models.
method Integrated Gradients and Baseline Shapley methods.
result Additional insights on comparative behavior for tabular data and neural networks.