Monotonic differentiable sorting networks improve upon previous methods.
problem Non-monotonicity in differentiable sorting networks.
method Relaxation of conditional swap operations using sigmoid functions to ensure monotonicity.
result Monotonic differentiable sorting networks improve upon previous methods.
Talks about new methods in differential geometry.
problem None explicitly stated in the abstract.
method Stresses the neighbor relation as a basic notion.
result Not explicitly stated in the abstract.
New method efficiently computes gradients for stochastic differential equations.
problem Computing gradients for stochastic differential equations efficiently.
method Generalized adjoint sensitivity method to stochastic differential equations.
result Time-efficient and memory-efficient computation of gradients with high-order solvers.
Solves a differential equation problem using Cartan's method.
problem Equivalence of second order ordinary differential equations under point transformations.
method E. Cartan's method of equivalence
result Solves the point equivalence problem for second order ODEs.
Paper develops differentially private methods for estimating precision matrices.
problem Estimating precision matrices from sensitive data while maintaining privacy.
method Differential privacy framework, ridge estimator, graphical lasso estimator, ADMM algorithm.
result The proposed methods provide utility in estimating precision matrices from private data.
Improved privacy and utility in machine learning with adaptive differential privacy.
problem Enhancing privacy in machine learning models while maintaining utility.
method Adaptive differentially private (ADP) learning method that optimally adapts noise to stepsize.
result ADP method significantly improves utility compared to standard differentially private methods.
Differentiable programming aids in solving differential equations and their sensitivities.
problem Computing gradients of numerical solutions of differential equations.
method Review of existing techniques and mathematical foundations.
result Established a coherent framework for combining differential equations with data-driven approaches.
A new differentiable resampling method for Monte Carlo simulations.
problem Improving the efficiency and differentiability of resampling in Monte Carlo simulations.
method Proposes a diffusion model surrogate for resampling, proving consistency and outperforming existing methods.
result The proposed method outperforms state-of-the-art differentiable resampling methods on various benchmarks.
New method speeds up ABC for differential equation parameter estimation.
problem Significant computational cost in ABC for differential equations.
method Uses derivatives of Gaussian processes to smooth observations.
result Significantly reduced execution time with comparable parameter estimates.
New effective divisors found in moduli spaces from abelian differentials.
problem Computing effective divisors in moduli spaces Mg,n. method Utilizing maps between moduli spaces and the degeneration of abelian differentials.
result Many new classes of effective divisors computed and reproduced known results.
Discover governing equations from data without specifying terms.
problem Discovering differential equations from data without predefined terms.
method Data-driven approach using genetic programming and automatic differentiation.
result Calibrated differential equations from various solutions of a differential equation.
New method reduces errors in pricing and sensitivities for discontinuous payoffs.
problem Errors in pricing and sensitivities for discontinuous payoffs in digital and barrier options.
method Alternative methods for estimating sensitivities, including likelihood ratio and hybrid methods.
result New methods substantially reduce test errors in prices and sensitivities.
Two new differentially private optimization algorithms derived from accelerated methods.
problem Improving privacy in optimization algorithms while maintaining convergence rates.
method Polyak's heavy ball method and Nesterov's accelerated gradient method with differential privacy.
result The proposed algorithms outperform existing differentially private optimization methods.
ES for non-differentiable parameters scales to large models.
problem Learning non-differentiable parameters in large models.
method Hybrid approach combining ES for non-differentiable and gradient-based methods for differentiable parameters.
result Hybrid approach is competitive and allows training sparse models from the start.
Combines differential privacy and Gaussian processes for private regression.
problem Combining privacy and flexibility in machine learning models.
method Proposes a method using Gaussian processes to provide differentially private regression, improving privacy by crafting the noise covariance structure.
result Achieves the greatest accuracy while providing privacy guarantees.
Unified framework for Gaussian process methods in differential equations.
problem Fragmented approaches to Gaussian process methods in differential equations.
method Unified Bayesian perspective integrating differential equation constraints.
result Consolidation of existing methods and foundation for future research.
Develops a mathematical model for automatic differentiation in machine learning.
problem Current automatic differentiation lacks a simple mathematical model for machine learning.
method Articulates relationships between program differentiation and nonsmooth functions, provides a class of functions and nonsmooth calculus.
result Shows how nonsmooth calculus applies to stochastic approximation methods and evidence of artificial critical points.
Differentially private random block coordinate descent improves utility in machine learning.
problem Lack of privacy in classical CD methods when handling sensitive information.
method Proposes a differentially private random block coordinate descent method using sketch matrices and importance sampling.
result Demonstrates improved convergence rates and utility guarantees compared to non-private methods.
Paper solves equivalence problems for fifth-order differential operators using Cartan's method.
problem Equivalence problem for fifth-order differential operators under fiber-preserving transformations.
method Cartan's method of equivalence applied to solve two versions of the equivalence problem.
result Sufficient and necessary conditions for fiber-preserving transformations between fifth-order differential operators.
Stabilized neural differential equations enforce constraints on dynamical systems.
problem Ensuring dynamical systems preserve known constraints like conservation laws.
method SNDEs with a stabilization term to enforce manifold constraints.
result SNDEs outperform existing methods and broaden constraint types.
DEQGAN uses GANs to solve differential equations without supervision.
problem Solving differential equations with neural networks.
method Generative Adversarial Networks (GANs) to learn the loss function.
result DEQGAN achieves lower mean squared errors and competitive solution accuracy compared to traditional methods.
New method learns differential equations from data with hidden variables.
problem Learning differential equations from data with hidden variables.
method Sparse linear regression optimization problem with higher order time derivatives and dictionary of functions.
result High quality short-term forecasts with orders of magnitude faster than competing methods.
Neural DEs improve single image super-resolution.
problem Challenging tasks in image super-resolution.
method Applied Neural Differential Equations to image super-resolution, using variational methods and backpropagation.
result Differential models match state-of-the-art performance.
Lectures introduce differential geometry for holomorphic vector bundles on Riemann surfaces.
problem Analyzing holomorphic vector bundles on Riemann surfaces.
method Differential-geometric techniques.
result Introduction of geometric methods for studying these bundles.
Paper introduces a new method for solving complex stochastic equations.
problem Solving forward-backward stochastic differential equations with jumps.
method Linear basis function regression technique.
result The proposed method is convergent and effective as shown by numerical experiments.
Method finds invariants of surfaces using differential operators.
problem Finding invariants of surfaces under motion groups.
method Existence of commuting system of invariant partial differential operators and finite system of invariants.
result Any invariant of the surface is a function of these invariants and their derivatives.
Differentiable pipeline replaces non-differentiable CAE components for shape optimization.
problem Gradient-based optimization is limited by non-differentiable components in CAE workflows.
method Surrogate models replace non-differentiable pipeline components, enabling gradient-based optimization.
result Gradient-based shape optimization possible without differentiable solvers.
Method finds explicit solutions to certain PDEs.
problem Finding solutions to specific types of PDEs.
method Exploiting solvable structures to find explicit solutions.
result Effectiveness demonstrated on several examples.
A new deep learning method using differential flows and Gaussian processes.
problem Improving deep learning performance through more flexible transformations.
method Differential flows and Gaussian processes to learn stochastic differential equations.
result Exceeds performance of deep Gaussian processes and neural networks.
Differentiable methods fail due to spectral issues in Jacobians.
problem Chaos-based failures in differentiable programming.
method Trace failures to the spectrum of Jacobians.
result Criteria for avoiding spectral failure in optimization.
Paper combines Vibrato and automatic differentiation for efficient financial option sensitivities.
problem Efficient computation of high-order derivatives for financial option sensitivities.
method Combines Vibrato and automatic differentiation methods.
result Combined method is faster and more stable than standard finite difference methods.
We formulate a method of computing invariant 1-forms and structure equations of symmetry pseudo-groups of differential equations based on Cartan's method of equivalence and the moving coframe method introduced by Fels and Olver. Our apparoach does not require a preliminary computation of infinitesimal defining systems,…
Method finds differential equations for integrable billiard tables.
problem Finding differential equations for integrable billiard tables.
method Introducing a method to find differential equations for functions defining tables.
result Illustrated method in three billiard systems.
Geometric methods solve differential equations by analyzing space dimensions.
problem Interplay between geometry and partial differential equations.
method Calculating space dimensions associated with differential equations' zeros.
result Classical algebraic geometry results are central to analysis.
Differentiable PF via entropy-regularized OT for better inference.
problem Non-differentiability of traditional PF resampling methods.
method Entropy-regularized optimal transport for differentiable resampling.
result Convergent differentiable PF method with improved gradient estimates.
Paper improves differential privacy in sparse Gaussian process models.
problem Ensuring privacy in machine learning with sparse Gaussian processes.
method Combining differential privacy with sparse Gaussian processes, addressing low data density and high dimensions.
result Sparse approximation and modified Laplace approximation provide robust differential privacy in outlier areas and at higher dimensions.
This is the lecture 4 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The Cartan reduction method is a technique in Differential Geometry for determining whet…
This is the lecture 3 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The Cartan reduction method is a technique in Differential Geometry for determining whet…
This is the lecture 1 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The Cartan reduction method is a technique in Differential Geometry for determining whet…
This is the lecture 2 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The Cartan reduction method is a technique in Differential Geometry for determining whet…
Novel method identifies structural differences between networks using structural equation models.
problem Identifying structural differences between networks characterized by structural equation models.
method Reparameterization and algorithm design with calibration and construction stages to identify differential structures.
result Our method outperformed independently constructed networks on synthetic data and demonstrated applicability on a real data set.
Differentiable clustering method using perturbed spanning forests.
problem Efficient clustering in trainable pipelines with noisy data.
method Stochastic perturbations of minimum-weight spanning forests.
result Method performs well even in challenging settings.
New method solves PDEs for any initial condition without retraining.
problem Solving PDEs for different initial conditions requires retraining neural solvers.
method Formulate solution as conditional probability distribution.
result Approximates PDE solution for arbitrary initial conditions.
Graph neural networks are extended to continuous-depth models using differential equations.
problem Improving graph neural networks for static and dynamic graph data.
method Formalizing GNNs as GDEs, blending discrete structures with differential equations.
result GDEs offer computational advantages in static settings and improved performance in dynamic settings.
Differentiable causal discovery methods perform robustly under model violations.
problem Causal discovery algorithms struggle with real-world data due to unverifiable causal assumptions.
method Benchmarked differentiable causal discovery methods under eight model assumption violations.
result Differentiable causal discovery methods exhibit robust performance under Structural Hamming Distance and Structural Intervention Distance metrics.
Many methods for reducing and simplifying differential equations are known. They provide various generalizations of the original symmetry approach of Sophus Lie. Plenty of relations between them have been noticed and in this note a unifying approach will be discussed. It is rather close to the classical differential co…
Pymanopt simplifies manifold optimization with Python and automatic differentiation.
problem Complex optimization problems on manifolds with tedious derivative calculations.
method Python toolbox, automated differentiation for derivatives.
result Saves users time and reduces errors in manifold optimization.
Paper solves a class of differential equations with specific solutions.
problem Identifying solutions to a class of nonlinear ODEs.
method Solves using a proposed side condition involving a third-order linear ODE.
result New closed and integral-form solutions for the Tzitzeica curve equation.