Neural Jump ODEs improve online filtering and classification with robust performance.
problem Online filtering and classification in settings with irregular and partial observations.
method Modeling conditional expectation using Neural Jump ODEs, with theoretical convergence guarantees.
result Demonstrated superior performance over classical methods, especially in complex scenarios.
Neural Jump ODE improves continuous-time prediction and filtering of irregularly sampled time series.
problem Theoretical guarantees for continuous-time prediction and filtering of irregularly observed time series.
method Introducing Neural Jump ODE (NJ-ODE) that models conditional expectation between observations with neural ODEs and jumps.
result Theoretical guarantees for the L2-optimal prediction are provided, showing convergence of model output to optimal prediction. Paper improves neural ODEs for forecasting non-Markovian processes.
problem Forecasting irregularly observed time series with incomplete data.
method Path-dependent Neural Jump ODEs with signature transform.
result Path-dependent NJ-ODE outperforms original framework in non-Markovian data.
Neural Jump ODEs model Itô processes without adversarial training.
problem Generating samples from Itô processes with irregular data.
method Neural Jump ODEs framework for drift and diffusion approximation.
result NJODEs can recover true parameters of Itô processes in the limit.
Enhanced model predicts chaotic systems with improved long-term accuracy.
problem Learning chaotic systems and long-term predictions from incomplete data.
method Path-dependent Neural Jump ODE (PD-NJ-ODE) model for online prediction.
result The model matches true chaotic system dynamics closely and improves long-term predictions.
Cubic spline smoothing improves interpolation between irregularly sampled data.
problem Interpolation discontinuity in recurrent neural networks for irregularly sampled sequences.
method Cubic spline smoothing compensation module trained end-to-end with ODE-RNN.
result Improves interpolation between irregularly sampled data points.
Extends PD-NJ-ODE to noisy observations and dependent observation times.
problem Predicting continuous-time stochastic processes with irregular and noisy observations.
method Extends PD-NJ-ODE to handle conditional independence and noisy observations.
result Theoretical guarantees and empirical examples for handling noisy observations and dependent observation times.
New neural method for inferring Markov jump processes.
problem Inference in Markov jump processes is challenging.
method Variational inference using neural ODEs and backpropagation.
result Trains neural representations of data to approximate process rates.
Extends nonlinear filtering to predictable jump times.
problem Filtering with jumps in both signal and observation, especially when jump times are known.
method Derive Kushner-Stratonovich and Zakai equations for predictable discontinuities.
result Extends classical nonlinear filtering results to a setting with predictable discontinuities.
Investigates optimal portfolio selection with regime-switching-induced stock price shocks.
problem Mean-variance portfolio selection with regime-switching and stock price jumps.
method Modeling regime-switching and stock price jumps, deriving optimal portfolio strategy and efficient frontier using ODEs.
result Added complexity due to regime-switching-induced stock price shocks, leading to nonlinear ODEs.
Paper solves MV portfolio selection in jump-diffusion models with no-shorting constraint.
problem Mean-variance portfolio selection in jump-diffusion model with no-shorting constraint.
method Reduces problem to LQ control and finding a maximal point of a function, constructs viscosity solution.
result Explicit viscosity solution to Hamilton-Jacobi-Bellman equation, optimal controls derived.
This work provides a semi-analytic approximation method for decoupled forwardbackward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDEs driven by the random Poisson measures with σ-finite compensators as well as the standard Brownian motions around the small-variance limit …
This study shows why training Neural ODEs is hard and proposes a new method.
problem Training Neural ODEs is challenging, especially in practice.
method Proposed a new stabilization method and provided an analytical convergence analysis.
result Insights and techniques for researchers starting work on Neural ODEs.
CTM improves diffusion model sampling quality with efficient ODE traversal.
problem Lack of natural trade-off between sample quality and speed in consistency models.
method CTM trains a neural network to output scores and traverse ODE trajectories efficiently.
result CTM achieves state-of-the-art FIDs and improves sample quality with increased computational budget.
A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximisation problem in this setting. We provide an ODE for the optimal value function, wh…
We show that Neural Ordinary Differential Equations (ODEs) learn representations that preserve the topology of the input space and prove that this implies the existence of functions Neural ODEs cannot represent. To address these limitations, we introduce Augmented Neural ODEs which, in addition to being more expressive…
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.
This paper explores normalization in neural ODEs, achieving high accuracy in CIFAR-10.
problem Understanding the role of normalization in neural ODEs.
method Investigated different normalization techniques and their impact on neural ODEs performance.
result Achieved 93% accuracy in CIFAR-10 classification task.
Faster training of neural ODEs using Gauß-Legendre quadrature.
problem Training neural ODEs is slow due to solving ODEs numerically.
method Use Gauß-Legendre quadrature to solve integrals faster than ODE-based methods.
result Faster training of neural ODEs, especially for large models.
Enhanced Neural ODEs outperform traditional models in image classification and video prediction.
problem Efficiently modeling time-varying dynamics in neural networks.
method Proposed a novel family of non-autonomous Neural ODEs with time-varying weights.
result Outperformed previous Neural ODE variants in speed and representational capacity.
Improved neural-ODE for faster convergence and stability.
problem Stability, consistency, and convergence issues in neural-ODE solvers.
method Proposed a first-order Nesterov's accelerated gradient (NAG) based ODE-solver.
result Efficacy demonstrated in three tasks: supervised classification, density estimation, and time-series modelling.
New method sparsifies hybrid neural ODEs for better performance and stability.
problem Excessive latent states and interactions from mechanistic models lead to training inefficiency and over-fitting.
method Automatic state selection and structure optimization combining domain-informed graph modifications with data-driven regularization.
result Improved predictive performance and robustness with desired sparsity.
Generalization bounds derived for neural ODEs and deep residual networks.
problem Understanding the generalization capability of neural ODEs and deep residual networks.
method Lipschitz-based argument and analogy with deep residual networks.
result A generalization bound involving the magnitude of weight matrix differences.
New method trains neural ODEs faster with fewer layers.
problem Training neural ODEs on large datasets is computationally expensive.
method Combines optimal transport and stability regularizations.
result Significant reductions in training time with no performance loss.
New ODE solvers improve training efficiency and accuracy.
problem Training Neural ODEs requires efficient and accurate gradient calculation.
method Presented algebraically reversible ODE solvers that are time and memory efficient, calculate exact gradients, and are numerically stable.
result Reversible solvers strictly improve upon previous architectures in efficiency and accuracy.
Neural ODEs' performance varies with numerical method, requiring adaptive step size control.
problem Neural ODEs' performance depends on the numerical method used during training.
method Proposes an adaptive step size control algorithm to ensure a valid ODE without increasing computational cost.
result Valid Neural ODEs require careful numerical method selection and step size adaptation.
A new interpolation method speeds up neural ODE training.
problem Efficiently approximating gradients in neural ODEs.
method Interpolation-based technique to approximate gradients.
result Our method trains neural ODEs faster than the reverse dynamic method.
Improves generative models by adding jump-diffusion noise.
problem Limited performance of diffusion models in generating samples from unknown distributions.
method Generalizes diffusion processes to include jump-diffusion noise, deriving closed-form generalized score functions.
result Jump-diffusion models outperform Gaussian models in specific parameter regimes.
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.
Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their robustness is still yet unclear. In this work, we fill this important gap by expl…
Stochastic neural ODEs outperform deterministic ones on image classification tasks.
problem Improving generalization in continuous-time models like neural ODEs.
method Empirical study of stochastically regularized neural ODEs using SDEs.
result Data augmentation negates the benefits of stochastic regularization, making neural ODEs and SDEs nearly equivalent.
A simple regularization technique speeds up training of Neural ODEs.
problem Training Neural ODEs is computationally expensive.
method Randomly sampling the end time of the ODE during training.
result Significantly decreases training time and improves performance.
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.
HomoODE connects DEQs and Neural ODEs via homotopy continuation, improving accuracy and memory efficiency.
problem Connecting DEQs and Neural ODEs for better model performance and efficiency.
method Established a connection between DEQs and Neural ODEs using homotopy continuation, proposing HomoODE.
result HomoODE outperforms existing implicit models in accuracy and memory consumption.
It has been observed that residual networks can be viewed as the explicit Euler discretization of an Ordinary Differential Equation (ODE). This observation motivated the introduction of so-called Neural ODEs, which allow more general discretization schemes with adaptive time stepping. Here, we propose ANODEV2, which is…
We present Ordinary Differential Equation Variational Auto-Encoder (ODE2VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE2VAE can simultaneously learn the embedding of high dimensional trajectories and infer arbitrarily complex conti…
The paper investigates how activation functions impact the training of Neural ODEs, leading to global convergence.
problem Challenges in training Neural ODEs, particularly gradient computation accuracy and convergence analysis.
method Investigates the impact of activation functions on the training dynamics of Neural ODEs.
result Establishes global convergence of Neural ODEs under gradient descent in overparameterized regimes.
Symmetry-regularized Neural ODEs improve model stability and interpretability.
problem Improving the stability and physical interpretability of Neural ODEs.
method Integrating Lie symmetries and conservation laws into the loss function.
result Symmetry-regularized Neural ODEs enhance model stability and interpretability.
Neural ODEs and i-ResNet are recently proposed methods for enforcing invertibility of residual neural models. Having a generic technique for constructing invertible models can open new avenues for advances in learning systems, but so far the question of whether Neural ODEs and i-ResNets can model any continuous inverti…
Deep residual networks implicitly converge to neural ODEs.
problem Link between discrete and continuous deep learning models.
method Establishing implicit regularization for residual networks towards neural ODEs.
result Deep residual networks initialized as discretizations of neural ODEs converge to such ODEs during training.
Researchers dissect Neural ODEs to understand their dynamics.
problem Understanding the inner workings of Neural ODEs.
method Developing continuous-depth formulation to clarify design choices.
result Clarified the influence of design choices on Neural ODE dynamics.
Neural ODEs provide a framework for studying the training dynamics of neural networks.
problem Training dynamics of neural networks
method Dynamical mean field theory
result Derive learning curves in the high-dimensional limit
A new method for estimating uncertainties in neural ODEs without numerical integration.
problem Accurate estimation of predictive uncertainties in neural ODEs.
method Distributional Gradient Matching (DGM) algorithm that jointly trains a smoother and a dynamics model.
result Significantly more accurate predictions compared to traditional methods.
Balanced Neural ODEs combine VAEs and Neural ODEs for efficient time series modeling.
problem Efficiently modeling systems with time-varying inputs and varying complexity.
method Combines VAEs for dimensionality reduction and Neural ODEs for dynamics, using variational parameters to adaptively learn.
result Balanced Neural ODEs (B-NODE) efficiently approximate Koopman operator without predefined dimensionality.
New paradigm for Neural ODEs stabilizes training and improves model performance.
problem Gradient vanishing-explosion problem in training deep neural networks.
method ODEtoODE: Nested system of flows with orthogonal group constraints.
result Strong convergence results and improved downstream models in reinforcement learning and supervised learning.
Neural ODEs control graph dynamics with low energy feedback.
problem Controlling complex dynamical systems on graphs.
method Neural Ordinary Differential Equation Control (NODEC) framework.
result NODEC learns low-energy control signals for graph dynamical systems.
Hypersolvers enable fast continuous-depth models for practical applications.
problem Infinite-depth models like Neural ODEs are computationally infeasible for large problems.
method Introducing hypersolvers, neural networks that solve ODEs efficiently with theoretical guarantees.
result Hypersolvers achieve comparable inference time to traditional discrete networks, making continuous-depth models practical.
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.