Enhances foliation results for non-C2 codimension one foliations.
problem Classical foliation results for non-C2 foliations. method Flow box decompositions and enhancements of classical results.
result Extensions of foliation results to non-C2 foliations. Algorithm decides if pseudo-Anosov flows have perfect fits.
problem Determining if pseudo-Anosov flows have specific asymptotic properties.
method Algorithm based on box decompositions and universal cover analysis.
result Algorithmic decision on pseudo-Anosov flows' perfect fit status.
New method uses random decompositions for high-dimensional Bayesian optimization.
problem Learning accurate decompositions for high-dimensional black-box functions.
method Data-independent random tree-based decomposition sampling.
result Random decomposition upper-confidence bound algorithm (RDUCB) yields significant empirical gains.
Decomposes flat nonlinear discrete-time systems into simpler components.
problem Flatness of nonlinear discrete-time systems.
method Coordinate transformations and feedback, using flow-box and Frobenius theorems.
result Flatness of a discrete-time system can be checked algorithmically.
Generalizes Hoeffding's decomposition for dependent inputs under mild conditions.
problem Performing global sensitivity analysis on black-box models with dependent inputs.
method Proposes a novel framework based on probability theory, functional analysis, and combinatorics to handle dependencies.
result Any square-integrable, real-valued function of random elements with mild dependence assumptions can be uniquely additively decomposed.
Paper proposes a new black-box adversarial attack using normalizing flows.
problem Adversarial vulnerability of deep neural networks.
method Proposes a novel black-box adversarial attack using normalizing flows.
result Demonstrates competitive performance against well-known black-box adversarial attack methods.
Paper advances black-box VI using flows and Monte-Carlo methods.
problem Improving automatic posterior inference in black-box VI.
method Combines normalizing flows, Monte-Carlo methods, and optimization considerations.
result Significant improvement in state-of-the-art variational inference.
Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.
problem Challenges in sensitivity analysis of black-box computer experiments with complex, nonlinear functional outputs.
method Functional-output orthogonal additive Gaussian process (FOAGP) with conditional orthogonality constraint.
result Demonstrates effectiveness in orthogonal effect decomposition and variance decomposition through simulations and real-world application.
A generalization of the Flow-box Theorem is given. The assumption of continuous differentiability of the vector field is relaxed to a local Lipschitz condition. The theorem holds in any Banach space.
CDFD analyzes circularity and directionality in weighted directed networks.
problem Analyzing circularity and directionality in weighted directed networks.
method CDFD framework separates flow into circular and acyclic components.
result CDFD yields a normalized circularity index capturing flow in cycles and directionality.
Analyzes vector fields in polytope decompositions, proving curve finiteness.
problem Analyzing vector fields in polytope decompositions.
method Proves integral curves are chopped into finitely many pieces by polytope decompositions.
result Finiteness of edge flips in discrete Yamabe flow.
TreeHFD algorithm explains tree ensemble models through hierarchical orthogonality.
problem Difficulty in explaining black-box tree ensemble models.
method TreeHFD algorithm using hierarchical orthogonality constraints.
result TreeHFD estimates Hoeffding decomposition from data samples.
In this paper, we introduce and study various kinds of decomposition complexity. First, we give a characterization of residually finite groups having finite decomposition complexity (FDC). Secondly, we introduce equi-variant straight FDC (sFDC), and prove that a group having equi-variant sFDC if and only if its box spa…
The paper connects matrix decompositions to Riemannian geometry and optimal transport.
problem Understanding matrix decompositions through geometric perspectives.
method Riemannian geometry, optimal transport, and information geometry.
result New geometric interpretations and gradient flows for matrix decompositions.
Proves mean curvature flow from conical singularities to shrinkers.
problem Proving mean curvature flow from conical singularities to shrinkers.
method Ważewski box argument
result Existence of embedded closed hypersurface with mean curvature flow.
The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.
problem Understanding the training dynamics of gradient flow on tensor decomposition.
method Empirical observation and mathematical proof of gradient flow dynamics for orthogonally decomposable tensors.
result Gradient flow dynamics for orthogonally decomposable tensors follows a tensor deflation process, recovering all tensor components.
This paper shows equivalence between SVGD and BBVI using kernel gradient flows.
problem Bayesian inference methods and their equivalence.
method Formalizes equivalence between SVGD and BBVI using kernel gradient flows.
result BBVI corresponds precisely to SVGD when using the neural tangent kernel.
AdvFlow generates imperceptible adversarial images using normalizing flows.
problem Adversarial attacks on deep learning classifiers.
method Normalizing flows to model adversarial examples.
result Generated adversaries closely follow clean data distribution, making them harder to detect.
The paper solves curvature problems on infinite hyperbolic surfaces.
problem Prescribed curvature flow on hyperbolic surfaces with infinite topological type.
method Introduced a prescribed curvature flow adapted to infinite cellular decompositions.
result Established well-posedness of the flow and proved convergence under certain conditions.
Method reformulates constrained optimization as latent space inference.
problem Optimizing black-box functions with hard constraints.
method Posterior inference in latent space using flow-based models and diffusion models.
result Method achieves superior performance across various tasks.
Paper uses black-box inference to estimate non-linear latent force models.
problem Estimating posterior state and forcing term in non-linear systems with unknown forcing terms.
method Black-box variational inference with local inverse autoregressive flows.
result Demonstrates effectiveness of approximation on known posterior systems and non-linear dynamics.
This paper uses combinatorial Ricci flow to tackle Thurston's triangulation conjecture.
problem Thurston's triangulation conjecture for hyperbolic 3-manifolds.
method Combinatorial Ricci flow approach to prove convergence and geometric decompositions.
result Combinatorial Ricci flow converges if and only if the triangulation is geometric.
Grey-box model combines GP with motion data to analyze skiing forces.
problem Analyzing forces in cross-country skiing races.
method Combines motion model formulae with Gaussian process regression.
result Grey-box approach reduces predictive uncertainty by 30-40%.
Excises interesting subsets from symplectic manifolds.
problem Excision of interesting closed subsets from symplectic manifolds.
method Time-independent incomplete Hamiltonian flows.
result Generalizes a result about excision of a ray.
New flows on convex real projective structures on surfaces.
problem Deforming convex real projective structures on surfaces.
method Introducing internal bulging and eruption flows on the deformation space C(S).
result Eruption flows and generalized twist flows give a half-dimensional family of commuting flows.
Study controls curvature in Ricci flows using necks.
problem Controlling curvature in Ricci flows.
method Introducing necks of maximal symmetry and decomposing curvature into uniform bounds.
result Established L1-bounds on Riemann curvature tensor. An efficient algorithm calculates exact EHVI values for multi-objective optimization problems.
problem Efficient computation of EHVI values for multi-objective optimization problems.
method Partitioning the integration volume into axis-parallel slices and using a new hyperbox decomposition technique.
result Theoretical time complexity improved to Θ(nlogn), asymptotically optimal. New method for interpreting complex ML models.
problem Interpreting complex black-box ML models.
method Functional decomposition of black-box predictions into simpler subfunctions.
result Main effects provide insights into feature contributions and interactions.
Graphical normalizing flows use Bayesian networks to improve normalizing flows' interpretability and performance.
problem Improving the interpretability and performance of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models, proposing graphical normalizing flows with either prescribed or learnable graph structures.
result Graphical conditioners lead to competitive white box density estimators.
End-to-end training of neural networks with black-box functions.
problem Training neural networks for tasks that require precise, non-differentiable functions.
method Approximate black-box functions with differentiable neural networks and integrate them into neural network training.
result Neural network trained to compute inputs for black-box functions, generalizing better and learning more efficiently.
Paper shows how SFA fits into FBM framework for time series separation.
problem Identifying time series decomposition in flow-based models.
method Combining SFA and FBM to make time series decomposition identifiable.
result Time series decomposition becomes identifiable using SFA and FBM.
Decomposes flows with jumps into simpler components.
problem Understanding dynamics of flows with discontinuities.
method Extension of Itô-Ventzel-Kunita formula for stochastic flows with jumps.
result Explicit equations for each component of the decomposition.
A new method to explain black box models using Shapley values.
problem Quantifying the impact of individual input variables in black box functions.
method Cohort Shapley measure based on cooperative game theory, using similarity cohorts.
result Introduces a new squared cohort Shapley value for variable importance.
Develops methods to analyze feature-outcome associations in subpopulations.
problem Challenges in understanding feature-outcome associations in high-dimensional data.
method Geometric decomposition framework using gradient flow and co-monotonicity decomposition.
result Identifies context-dependent patterns and improves statistical power and interpretability.
Gradient flow solves optimal mass transport for covariance matrices.
problem Optimal mass transport for covariance matrices.
method Gradient flow on fiber bundle structure.
result Global convergence to polar decomposition.
Efficiently explains model outputs using HSIC, a dependence measure.
problem Efficiently explain model outputs for various architectures.
method HSIC, RKHS, Reproducing Kernel Hilbert Spaces, black-box attribution.
result Up to 8 times faster than previous methods while maintaining fidelity.
The study connects geodesic flows on Riemann surfaces to random walks on their dual graphs.
problem Understanding ergodicity of geodesic flows on infinite Riemann surfaces.
method Analyzing random walks on the dual graph of pants decompositions.
result Equivalence between ergodicity of geodesic flows and recurrence of random walks.
Unified framework for MCMC and machine learning problems.
problem Intersection of MCMC and machine learning problems.
method Unified framework integrating various MCMC and machine learning techniques.
result Translation and generalization of theory and methods.
Continuous time analysis of bubble formation in harmonic maps.
problem Understanding bubble formation in harmonic map heat flow.
method Continuous time approach to analyze bubbling sequences.
result Solutions approach multi-bubble configurations in continuous time.
FlowVAT improves variational inference for multi-modal distributions.
problem Mode-seeking behavior and collapse in variational inference for complex posteriors.
method Conditional tempering approach for normalizing flow variational inference.
result FlowVAT outperforms traditional and adaptive annealing methods in multi-modal distributions, finding more modes and achieving better ELBO values.
In recent work, we have proven uniform decay bounds for solutions of the wave equation □gφ=0 on a Schwarzschild exterior, in particular, the uniform pointwise estimate ∣φ∣≤Cv+−1, which holds throughout the domain of outer communications, where v is an advanced Eddington-Finkelstein coordinate, $v_+=\ma…
Graph neural networks are explained through energy gradient flow and framelet decomposition.
problem Understanding and improving graph neural networks.
method Viewing framelet-based models as gradient flows of energy, proposing a generalized energy via framelet decomposition.
result The proposed model leads to more flexible dynamics, enhancing graph neural networks.
Paper introduces new importance metrics for machine learning models, linking them to CATE.
problem Interpreting black-box models' importance metrics due to data dependence and non-parametric nature.
method Introduces MVIM and CVIM, proposing permutation-based estimation and bias-variance decomposition.
result MVIM and CVIM have a quadratic relationship with CATE, addressing bias in correlated predictors.
The paper analyzes sensitivities of cash flows using PDEs and Hansen-Scheinkman decomposition.
problem Large-time sensitivities of cash flows in quantitative finance.
method PDE representation of pricing operator with Hansen-Scheinkman decomposition.
result Detailed convergence rates of sensitivities are provided.
TVR optimizes black-box simulators by targeting variance reduction over control and noise parameters.
problem Optimizing black-box simulators with uncertain parameters.
method Targeted Variance Reduction (TVR) method that optimizes (x,θ) jointly. result Improved robust optimization performance over state-of-the-art methods.
Neural Decomposition breaks down VAE latent structure for better interpretability.
problem Limited interpretability of VAE latent representations.
method Adapted functional ANOVA to VAEs, applying constraints for identifiability.
result Decomposes data variation into latent and fixed input effects.
Unified framework for analyzing gradient flows of measures with exponential decay of entropy.
problem Analyzing exponential decay of entropy functionals in gradient flows of measures.
method Characterization of global exponential decay behaviors using Hellinger-Kantorovich geometry, shape-mass decomposition, and Polyak-Łojasiewicz-type inequalities.
result Unified theoretical framework for gradient flows with complete analysis of exponential decay behaviors.
We exhibit a concentration-collapse decomposition of singularities of fourth order curvature flows, including the L2 curvature flow and Calabi flow, in dimensions n≤4. The proof requires the development of several new a priori estimates. First, we develop a smoothing result for initial metrics with small ener…