Neural differential equations combine deep learning and differential equations for modeling complex systems.
problem Modeling complex systems with high capacity and efficiency.
method Combining neural networks and differential equations, focusing on neural ordinary, controlled, and stochastic differential equations.
result NDEs offer high-capacity function approximation, strong priors, and handle irregular data efficiently.
DiffEqFlux.jl integrates neural networks with differential equations.
problem Combining machine learning and differential equations for modeling complex systems.
method Fusing neural networks and differential equations using DiffEqFlux.jl.
result Demonstrates the integration of differential equations into neural networks and vice versa.
Neural Laplace models diverse DEs in the Laplace domain for better dynamics.
problem Inadequate ODEs for long-range dependencies and discontinuities.
method Unified framework in Laplace domain, using stereographic map for smoothness.
result Superior performance in diverse DEs, including complex history dependency and abrupt changes.
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.
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).
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.
NeuPDE uses neural networks to model time-dependent data using differential equations.
problem Modeling time-dependent data from dynamic datasets.
method Neural network approach with both shallow multilayer perceptrons and nonlinear differential terms.
result Demonstrated on various dynamical systems, NeuPDE outperforms other methods.
Differential equations explain neural network dynamics.
problem Understanding neural networks using differential equations.
method Analyzing properties of differential equations as machine learning models.
result Neural networks can be modeled by differential equations.
PNDEs project neural dynamics onto constraint manifolds, improving accuracy and stability.
problem Learning dynamics from data without violating known constraints.
method Projecting the learned vector field onto the tangent space of the constraint manifold.
result PNDEs outperform existing methods in learning constrained dynamical systems.
Efficient neural networks compute various differential operators cheaply.
problem Efficient computation of higher time complexity differential operators.
method Restricted neural network architectures with diagonal and hollow Jacobian matrices, allowing efficient extraction of dimension-wise derivatives.
result Demonstrated efficient computation of differential operators for various applications.
Neural GDEs improve graph prediction by blending discrete structures and differential equations.
problem Dynamic graph prediction challenges in irregularly sampled data.
method Continuous-depth graph neural networks (GNNs) with Neural GDEs.
result Neural GDEs enhance performance across various applications.
Neural controlled DEs model irregular time series by adjusting based on observations.
problem Modeling irregularly sampled multivariate time series with memory-efficient adjoint-based backpropagation.
method Neural controlled differential equations (CDEs) that adjust based on subsequent observations.
result Achieves state-of-the-art performance on various datasets.
Proposes a method to train neural networks that solve differential equations faster.
problem Training neural networks that solve differential equations becomes computationally expensive.
method Introduces a differentiable surrogate for numerical solver time cost using higher-order derivatives.
result Trains models that are faster to solve while maintaining nearly the same accuracy.
Neural networks model financial data with Lévy processes.
problem Forecasting chaotic financial time series with big jumps.
method Lévy-induced stochastic differential equation network approximated by neural networks.
result The method improves prediction accuracy using non-Gaussian Lévy processes.
MSLs use parallelizable root-finding for efficient ODE and PDE solutions.
problem Efficiently solving initial value problems for ODEs and PDEs.
method Leveraging time-parallel methods, MSLs use parallelizable root-finding algorithms.
result MSLs offer significant speedups in NFEs and inference time.
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.
Efficient echo state network with explicit memory performs well on benchmark tasks.
problem Training differentiable neural computers is difficult and time-consuming.
method Echo state network with an explicit memory.
result Echo state network can recognize all regular languages, including those contractive networks cannot.
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.
VSDN models sporadic time series with neural SDEs.
problem Modeling irregular and sparse time series data.
method Variational Bayesian method and neural SDEs.
result VSDNs outperform state-of-the-art models in prediction and interpolation.
New model predicts neural network performance from early training epochs, incorporating architecture impact.
problem Predicting neural network performance from early training epochs, neglecting architecture impact.
method Architecture-aware graph ordinary differential equation model.
result Model outperforms state-of-the-art methods for MLP and CNN learning curves.
This paper uses ODE to improve RNN models for time series data.
problem Improving RNN models for irregularly sampled time series data.
method Extending RNNs with Neural Ordinary Differential Equations (ODEs).
result New ODE-based RNN models reduce training and evaluation time.
Bayesian Neural Nets improve model stability and fit.
problem Improving model stability and fit in time series prediction.
method Assign Bayesian Neural Nets to drift and diffusion terms of SDE, infer posterior using SGLD.
result Significantly improved stability and better model fit on benchmarks.
Proposes Neural SDE for better model robustness and generalization.
problem Missing regularization mechanisms in Neural ODE networks.
method Integrates various regularization mechanisms via stochastic noise injection.
result Improves robustness and generalization compared to Neural ODE.
We develop a scalable method for Bayesian neural networks with stochastic differential equations.
problem Uncertainty quantification in deep neural networks.
method Gradient-based stochastic variational inference in continuous-depth Bayesian neural networks.
result Gradient estimator with zero variance as the approximation improves.
This research explores neural SDEs as deep latent Gaussian models in the diffusion limit.
problem Deep latent Gaussian models with time-inhomogeneous Markov chains and Gaussian perturbations.
method Develops variational inference for neural SDEs using stochastic automatic differentiation in Wiener space.
result The limiting latent object is an Itô diffusion process governed by neural nets.
Neural painters learn to generate brushstrokes from a non-deterministic painting program.
problem Training an agent to generate realistic brushstrokes from a non-differentiable painting program.
method A differentiable neural painter model trained on brushstrokes, optimizing for human-like strokes and intrinsic style transfer.
result Direct optimization of brushstrokes can visualize ImageNet categories and generate ideal paintings.
Neural networks can approximate complex stochastic equations well.
problem Approximating general stochastic differential equations.
method Identified neural network classes approximating continuous functions.
result Neural stochastic differential equations can approximate general stochastic differential equations arbitrarily well.
Neural SDEs model continuous sequences using neural networks.
problem Modeling continuous-time dynamics in sequence data.
method Interprets time-series as samples from a continuous dynamical system, parameterized by Neural SDE.
result Demonstrates superior performance in diverse sequence modeling tasks.
Neural networks improve predictions of complex network dynamics.
problem Improving neural network predictions for complex network dynamics.
method Extended neural network models to complex systems, ensuring they conform to dynamical model assumptions and using a statistical significance test.
result Achieved advanced generalization of neural network predictions for complex systems.
Proposes a method to improve neural architectures reproducibly.
problem Lack of reproducibility in Neural Architecture Transformer (NAT).
method Differentiable Neural Architecture Transformation (DNAT).
result DNAT outperforms NAT and is applicable to various models and datasets.
A new method to simplify deep neural networks by removing unnecessary parts.
problem Overly complex deep neural networks require significant resource investment for size reduction.
method A fully differentiable sparsification method that optimizes a regularized objective function with stochastic gradient descent.
result The method can learn both the sparsified structure and weights of a network in an end-to-end manner.
Efficient neural models for complex multi-hop reasoning tasks.
problem Complex multi-hop reasoning tasks in large knowledge bases.
method Differentiable neural models using symbolic knowledge bases, with a new operation for multi-hop template construction.
result Simple neural models achieve competitive performance on multi-hop reasoning tasks.
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.
Privacy-preserving continual learning for hospitals.
problem Forgetting old data when updating neural networks for privacy.
method Differentially private variational inference and generative models.
result Estimates likelihood of old data given current model.
Improves discrete latent representations using differentiable approximation bridges.
problem Improving discrete latent representations in neural networks.
method Training with a differentiable approximation bridge (DAB) neural network.
result Improves state-of-the-art performance in various domains.
DeepHoyer introduces differentiable, scale-invariant sparsity measures for neural networks.
problem Efficiently sparsifying neural networks with scale-invariant sparsity measures.
method Developed DeepHoyer, a set of differentiable, scale-invariant sparsity-inducing regularizers based on the Hoyer measure.
result DeepHoyer produces sparser neural networks than previous methods, maintaining similar accuracy.
Neural networks trained with Q-learning converge to optimal control.
problem Optimal control of reinforcement learning with neural networks.
method Analysis of a limit differential equation derived from Q-learning.
result The limit differential equation has a unique stationary solution that is optimal.
Neural jump model improves option pricing accuracy.
problem Jump risk in option pricing.
method Neural jump stochastic differential equation model with Gumbel-Softmax gradient learning.
result Neural jump components significantly improve option pricing accuracy.
This paper extends geometric study of neural networks to non-differentiable layers and random walks.
problem Understanding the geometric properties of neural networks, especially those with non-differentiable activation functions.
method Singular Riemannian geometry approach to convolutional, residual, and recursive neural networks.
result Illustrated geometric findings with numerical experiments on image classification and thermodynamic problems.
Study uses machine learning to predict predator-prey dynamics without prior knowledge.
problem Predicting predator-prey interactions without prior knowledge of the system.
method Applied Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the Lotka-Volterra model.
result UDEs outperform Neural ODEs in predicting predator-prey dynamics, especially in noisy data.
Neural sorting network improves sorting accuracy for complex inputs.
problem Sorting complex inputs like multi-digit images.
method Differentiable swap function and permutation-equivariant Transformer network.
result Our method outperforms baseline methods on various sorting benchmarks.
Deep ResNets exhibit distinct scaling properties with depth, challenging neural ODE models.
problem Understanding the scaling properties of deep ResNets and their relation to neural ODEs.
method Detailed numerical experiments on weights trained by stochastic gradient descent.
result Deep ResNets can exhibit different scaling regimes, including stochastic differential equations or neither, challenging the neural ODE model.
Pruning neural networks adds differential privacy noise, preserving data utility.
problem Achieving differential privacy in neural networks without sacrificing data utility.
method Proving equivalence between pruning and adding differential privacy noise to hidden-layer activations.
result Pruning can be a more effective alternative to adding differential privacy noise for neural networks.
Extends Neural ODEs to model discrete changes in continuous systems.
problem Lack of explicit termination time in existing Neural ODE formulations.
method Introduces neural event functions to implicitly define termination criteria.
result Models discrete changes in continuous systems without prior knowledge.
PINNs solve differential geometry problems in complex shapes.
problem Solving differential geometry problems in complex shapes.
method Training neural networks with loss functions inspired by differential conditions.
result PINNs are effective for differential geometry problems.
Normalization layers improve the accuracy of Differentially Private training of deep neural networks.
problem Reduced accuracy in deep neural networks with Differentially Private training.
method Proposed a novel method for integrating batch normalization with Differentially Private Stochastic Gradient Descent (DPSGD) without additional privacy loss.
result Training deeper networks with better utility-privacy trade-off is possible.
Paper develops a consistent algorithm for learning graph structure from continuous-time stochastic differential equations.
problem Learning structure from continuous-time stochastic differential equations.
method Score-based structure learning using Neural Ordinary Differential Equations with adaptive regularization.
result The method consistently recovers directed graphs of local independencies in systems of stochastic differential equations.
A lifelong learning architecture improves reinforcement learning policies using simulations and a DNC model.
problem Improving reinforcement learning policies in dynamic environments.
method Iterative training of a Reinforcement Learning agent and a DNC model in conjunction.
result DNC models can continually learn from pixels alone to simulate new tasks.