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.
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.
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differen…
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.
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.
We present a method of discovering governing differential equations from data without the need to specify a priori the terms to appear in the equation. The input to our method is a dataset (or ensemble of datasets) corresponding to a particular solution (or ensemble of particular solutions) of a differential equation. …
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.
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.
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.
In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by…
We compute many new classes of effective divisors in Mg,n coming from the strata of abelian differentials and efficiently reproduce many known results obtained by alternate methods. Our method utilises maps between moduli spaces and the degeneration of abelian differentials.
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,…
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.
In this work we show that Evolution Strategies (ES) are a viable method for learning non-differentiable parameters of large supervised models. ES are black-box optimization algorithms that estimate distributions of model parameters; however they have only been used for relatively small problems so far. We show that it …
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.
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.
A major challenge for machine learning is increasing the availability of data while respecting the privacy of individuals. Here we combine the provable privacy guarantees of the differential privacy framework with the flexibility of Gaussian processes (GPs). We propose a method using GPs to provide differentially priva…
This paper deals with the computation of second or higher order greeks of financial securities. It combines two methods, Vibrato and automatic differentiation and compares with other methods. We show that this combined technique is faster than standard finite difference, more stable than automatic differentiation of se…
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…
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…
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.
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other Monte Carlo methods, incurs a significant computational cost as it requires explic…
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.
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.
We introduce Taylor expansions that do not require the differentiability. We also provide new solutions to partial differential equations. We apply our methods to finance.
Dagma-DCE improves causal discovery with interpretable measures and open-source code.
problem Arbitrary proxy measures of causal strength in non-parametric causal discovery.
method Uses weighted adjacency matrices based on an interpretable measure of causal strength.
result Achieves state-of-the-art performance in simulated datasets.
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.
Diffsurv extends differentiable sorting to handle censored time-to-event data.
problem Handling censored time-to-event data in survival analysis.
method Extending differentiable sorting methods to account for censored samples.
result Diffsurv outperforms established baselines in various risk prediction scenarios.
Examines scalar curvature results via covariant and contravariant methods.
problem Scalar curvature results in differential geometry.
method Covariant and contravariant methods.
result Fundamental results on scalar curvature established.
New methods prove existence of rotating shapes moving in space.
problem Existence of rotating shapes moving in space.
method Different methods to prove existence based on singular ordinary differential equation.
result Existence of rotationally symmetric translating solutions proven without partial differential equations.
Local Kan conditions enable differentiation of simplicial manifolds.
problem Differentiating simplicial manifolds into Lie algebroids.
method Expanding a technique for higher Lie groupoids to simplicial manifolds.
result Derivation of a method to differentiate simplicial manifolds into higher Lie algebroids.
Proposes efficient, modular method for implicit differentiation.
problem Implicit differentiation of optimization problems.
method Automatic implicit differentiation using autodiff and implicit function theorem.
result Automatic differentiation of optimization problems is made easier and more modular.
Develops a new method for statistical optimal allocation problems.
problem Statistical optimal allocation problems with constraints.
method Functional differentiability approach and Hadamard differentiability of value functions.
result Validates margin assumption for fast convergence rate of plug-in methods.
Probabilistic method combines space and time uncertainties in PDEs.
problem Separate treatment of space and time in PDE solvers obscures interactions and error quantification.
method Gaussian process interpretation of finite difference methods interacting with probabilistic ODE solvers.
result Joint quantification of space- and time-uncertainty possible without sacrificing ODE solver performance.
A method makes particle filters differentiable without altering their forward pass.
problem Compatibility issues between particle filters and automatic differentiation.
method Introduces a correction to particle weights using the stop-gradient operator.
result Automatic differentiation produces good estimators for gradients and second-order derivatives.
Review of privacy-preserving linear models for high-dimensional data.
problem Overfitting and data memorization in high-dimensional linear models.
method Comprehensive comparison of optimization techniques for differentially private high-dimensional linear models.
result Coordinate-optimized algorithms perform best in empirical tests.
Researchers develop methods to calibrate ABMs using Bayesian techniques.
problem Challenges in calibrating ABMs due to likelihood intractability and non-differentiability.
method Generalised variational inference for differentiable ABMs.
result Accurate Bayesian parameter inferences for differentiable ABMs demonstrated.
Optimal privacy-preserving ranking from noisy comparisons.
problem Protecting individual privacy in ranking from noisy comparisons.
method Differentially private ranking algorithms under edge and individual differential privacy.
result Achieved minimax optimal rates of convergence under privacy constraints.