Explains geometric structures of information manifolds.
problem Understanding information geometry.
method Differential geometry concepts.
result Fundamental theorem of information geometry.
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48 results for “differential information”
Graph neural controlled differential equations learn graph dynamics from vertex observations.
problem Predicting future states of dynamical systems on graphs with limited vertex data.
method Incorporates graph topology information into NCDE to predict graph dynamics.
result Informed NCDE requires fewer parameters and lower MAE compared to previous methods.
Integral Transforms in a Physics-Informed (Quantum) Neural Network setting: Applications & Use-Casesquant-ph
This work integrates differentiation and integration in Physics-Informed Neural Networks.
problem Solving integro-differential equations and computing integral transforms.
method Augmenting Physics-Informed Neural Networks with automatic integration.
result Solving complex integral transforms and integro-differential equations.
Physics-informed neural networks solve PDEs using neural networks.
problem Solving nonlinear partial differential equations (PDEs) with neural networks.
method Physics-informed neural networks trained to solve PDEs while respecting physical laws.
result Physics-informed neural networks can infer solutions to PDEs and create differentiable surrogate models.
Paper discusses the Fisher metric and differentiability in statistical models.
problem Understanding the relationship between Fisher metric and differentiability in statistical models.
method Comparison of different concepts and models in Information Geometry, mathematical statistics, and measure theory.
result Discussion of various models and their differentiability properties.
This paper develops, in a Brownian information setting, an approach for analyzing the preference for information, a question that motivates the stochastic differential utility (SDU) due to Duffie and Epstein [Econometrica 60 (1992) 353-394]. For a class of backward stochastic differential equations (BSDEs) including th…
The paper improves ODE solvers by integrating diverse information types.
problem Improving accuracy and physical meaningfulness of ODE solutions.
method Leveraging probabilistic solvers to include second-order information and physical conservation laws.
result Solutions become more accurate and physically meaningful with additional information.
Data processing inequalities link Fisher information to local differential privacy constraints.
problem Understanding how Fisher information scales with local differential privacy constraints.
method Developed data processing inequalities for Fisher information under local differential privacy.
result Implications for private estimation with optimal bounds and error rates.
We introduce a fully probabilistic framework of consumer product choice based on quality assessment. It allows us to capture many aspects of marketing such as partial information asymmetry, quality differentiation, and product placement in a supermarket.
Develops DP-SCD for stochastic coordinate descent, making it differentially private.
problem Privacy leak in auxiliary information during stochastic coordinate descent training.
method Develops DP-SCD, leveraging independent noise addition and decoupling/parallelizing coordinate updates.
result Demonstrates competitive performance against DP-SGD with less tuning.
New framework explains neural network bias in solving differential equations.
problem Understanding and controlling the bias in PINNs for differential equations.
method Deriving an integro-differential equation from PINNs and GPR equivalence.
result PINN predictions are influenced by a kernel term reflecting architecture choices.
Proposes HOPF framework for CC using higher-order propagation.
problem Collective Classification struggles with node information morphing across multiple hops.
method Iterative inference mechanism with differentiable kernels for multi-hop neighborhood information.
result NIP models preserve node information and provide more robust performance.
Physics-informed neural networks solve physics problems using neural nets.
problem Discovering nonlinear PDEs from data.
method Two classes of algorithms: continuous time and discrete time models.
result Demonstrated effectiveness on various physics problems.
This study compares different thermodynamic structure-informed neural networks for solving differential equations.
problem Improving the accuracy and physical consistency of neural network solutions to differential equations.
method Comprehensive evaluation of various thermodynamic formulations in physics-informed neural networks.
result Newtonian-residual-based PINNs fail to reliably recover physical quantities, while structure-preserving formulations enhance accuracy and robustness.
Unified bounds for neural networks incorporating physical laws.
problem Limitations in existing generalization analyses for PINNs and VPINNs.
method Unified framework using Taylor expansion and Koopman-based analysis.
result High-rank networks can generalize well even with differential operators.
Study of curves and surfaces from single-direction projections.
problem Obtaining complete shape information from a single view.
method Theoretical study of differential geometric information from multiple orthogonal projections.
result Formulae for recovering certain information on curves or surfaces from their projections.
New method uses PINNs to efficiently compute Gerber-Shiu functions.
problem Calculating the Gerber-Shiu function efficiently.
method Physics-informed neural networks (PINNs) embedded with differential equations.
result Demonstrates good performance in approximating Gerber-Shiu functions.
New algorithms ensure privacy in online learning with optimal regret bounds.
problem Privacy in online learning with optimal regret bounds.
method Differentially private algorithms for online linear optimization in full information and bandit settings.
result Optimal regret bounds of $O(\sqrt{T})+ ilde{O}\left(\frac{1}{\epsilon}
ight)$ in full information and $ ilde{O}\left(\frac{1}{\epsilon}\sqrt{T}
ight)$ in bandit settings.
We approximate differential entropy for efficient Bayesian experimental design.
problem Efficiently estimating expected information gain in large-scale inference problems.
method Approximate differential entropy using Monte Carlo or quasi-Monte Carlo surrogates.
result Our approach achieves comparable or better convergence rates than state-of-the-art methods.
PIELM uses deep learning to solve PDEs quickly and accurately.
problem Solving partial differential equations (PDEs) efficiently and accurately.
method Physics Informed Extreme Learning Machine (PIELM) for solving PDEs.
result PIELM matches or exceeds the accuracy of Physics Informed Neural Networks (PINNs) on various problems.
ξ-torch simplifies physics-informed learning by providing differentiable functionals.
problem Training physics-informed deep neural networks requires differentiable physical simulations.
method ξ-torch offers a library of differentiable functionals for scientific simulations.
result Improves numerical stability and reduces memory requirements for higher order derivatives.
Solves a game between brokers and informed traders using stochastic differential equations.
problem Optimizing wealth in a game between brokers and informed traders with private signals.
method Closed-form solutions to a mean-field game using forward-backward SDEs.
result Optimal trading strategies for both brokers and informed traders are found.
Paper discovers differential equations from data using neural networks and Bayesian methods.
problem Discovering differential equations from datasets using machine learning.
method Integrates neural network-based surrogates with Sparse Bayesian Learning (SBL).
result Proposes a robust model discovery algorithm and a Physics Informed Normalizing Flow (PINF).
Study on convergence rates of degenerate SDEs using Fisher information and generalized Bochner's formula.
problem Analysis of dynamical behaviors of degenerate stochastic differential equations.
method Use of Fisher information as Lyapunov functional, generalized Gamma calculus, and generalized Bochner's formula.
result Derivation of convergence rate conditions and examples in specific sub-Riemannian structures.
This paper bounds min-entropy leakage for Blowfish privacy using graph symmetries.
problem Bounding min-entropy leakage for Blowfish privacy mechanisms.
method Organizing analysis over symmetrical partitions corresponding to orbits of graph automorphism groups.
result Demonstrates a construction meeting the bound with asymptotic equality, showing tightness.
Proposes a privacy-preserving recommendation system using matrix factorization and differential privacy.
problem Privacy leakage in recommendation systems when anonymizing user data is not sufficient.
method Uses matrix factorization and differential privacy via the Gaussian mechanism.
result Demonstrates excellent utility for privacy-preserving recommendation systems.
Paper proposes a method to verify PINN fidelity using Fisher information from dynamical systems.
problem Quantifying PINN fidelity beyond simple trajectory prediction.
method Employing Fisher information for differentiable dynamical systems to compare PINN's learned equations with analytical models.
result PINN fidelity is verified by matching Fisher information landscapes of learned equations and analytical models.
Study on potential functions for tensors of rank four in differential geometry.
problem Applying potential functions to tensors of rank four.
method Analyzing the inverse problem and intrinsic perspective.
result Negative result: Potential functions cannot be applied to tensors of rank four.
Physics-informed DeepONets solve PDEs without paired data, predicting solutions quickly.
problem Lack of paired input-output data for solving PDEs.
method Physics-informed DeepONets use automatic differentiation to enforce physical laws as soft penalty constraints.
result Physics-informed DeepONets can solve PDEs without paired data, predicting solutions up to 3 orders of magnitude faster.
Paper reveals free information from differential privacy mechanisms improving query accuracy.
problem Improving query accuracy with differential privacy mechanisms.
method Analysis of Noisy Max and Sparse Vector mechanisms.
result Noisy Max releases the noisy gap between the approximate maximizer and runner-up.
DE-QT detects optimal Q-learning stopping points.
problem Information loss in Q-learning during prolonged training.
method Introducing DE-QT to detect entropy changes in Q-tables.
result DE-QT identifies the best stopping point for Q-learning.
Differential privacy for simple linear regression protects small datasets from individual data leaks.
problem Protecting sensitive personal information in small datasets from individual data leaks.
method Differential privacy algorithms for simple linear regression tailored for small datasets (tens to hundreds of datapoints).
result Robust estimators like Theil-Sen perform well on small datasets, but standard algorithms improve as dataset size increases.
Physics-informed neural networks approximate diffusion process pdfs efficiently.
problem Approximating the probability density function of diffusion processes.
method Physics-informed neural networks solving Fokker-Planck or integro-differential equations.
result Neural network solutions approximate target solutions for various types of differential equations.
Proposes PI-VAE for solving SDEs with limited measurements.
problem Solving SDEs with limited measurements of system parameters.
method Physics-informed Variational Autoencoder (PI-VAE) integrating VAE and governing equations.
result Satisfactory accuracy and efficiency compared to PI-WGAN.
PIKS combines physics principles with kernel methods for universal consistency.
problem Lack of learning theory for physics-informed machine learning.
method Physics-Informed Kernel methodS (PIKS) for linear differential constraints.
result PIKS achieves universal consistency for linear differential constraints with Gaussian or Matérn kernels.
Study optimal portfolio strategy under uncertain market conditions.
problem Optimizing portfolio under partial information and drift uncertainty.
method Developed optimal strategy using BSDE and particle representation.
result An efficient numerical scheme approximates the optimal portfolio.
This research enhances ML models using gradient information from neural networks.
problem Improving the accuracy of machine learning models.
method Leveraging gradients extracted from neural networks to improve model performance.
result Gradient information can effectively enhance machine learning models with existing datasets.
Analysis of model updates reveals sensitive data leaks.
problem Information leakage during model updates.
method Differential analysis of language model snapshots.
result New metrics (differential score, differential rank) reveal sensitive data leaks.
Diffeology explores -forms and bundles with more information than traditional differential forms.
problem Understanding -forms and bundles in diffeological spaces.
method Developed theory of diffeological vector pseudo-bundles, including limits and colimits, and various operations.
result Sections of bundles of -forms contain more information than differential forms.
Improved differentially private drug sensitivity prediction using compact representations.
problem Challenges in differentially private machine learning with genomic data.
method Representation learning using variational autoencoders, PCA, and random projection.
result Variational autoencoders provide the most accurate predictions for differentially private drug sensitivity prediction.
As increasing amounts of sensitive personal information is aggregated into data repositories, it has become important to develop mechanisms for processing the data without revealing information about individual data instances. The differential privacy model provides a framework for the development and theoretical analy…
Density destructors simplify complex PDFs to maximize entropy, linking to information theory.
problem Complex multivariate PDFs are hard to analyze.
method Invertible transforms that progressively remove structure from PDFs.
result Density destructors can improve estimates of information theoretic quantities.
Differential privacy protects data privacy by adding noise to data.
problem Leakage of sensitive data through common methods like encryption and endpoint protection.
method Randomized response technique to add noise to data collection.
result Differential privacy ensures strong privacy with better utility.
Differentially private policy evaluation improves reinforcement learning efficiency.
problem Sample inefficiency in reinforcement learning.
method Differentially private actor-critic model initialization.
result Improves sample efficiency in control problems.
Proposes a new method to optimize graph neural network architectures on heterogeneous information networks.
problem Weaknesses in instability and inflexibility of existing graph neural architecture search methods.
method Partial Message Meta Multigraph search (PMMM) using a differentiable framework to search for a meaningful meta multigraph.
result Significantly more stable and effective than state-of-the-art heterogeneous GNNs.
Repulsive ensembles improve uncertainty estimates in PINNs for differential equations.
problem Improving uncertainty estimates in PINNs for differential equations.
method Employing repulsive ensembles (RE-PINN) with a repulsive term in the loss function.
result Repulsive ensembles produce more accurate uncertainty estimates and higher sample diversity.
Study uses Amari functors to investigate metric structures in gauge theories.
problem Investigating whether a gauge structure in a vector bundle is metric.
method Introduces generalized Amari functors and differential equations to analyze gauge structures.
result Links new index functions to the main concerns of metric structures in gauge theories.
The paper proposes differentially private sliced inverse regression algorithms for high-dimensional data.
problem Privacy concerns in high-dimensional data analysis.
method Differentially private sliced inverse regression algorithms designed for privacy preservation.
result Achieves minimax lower bounds up to logarithmic factors.