Stochasticity in Neural ODEs: An Empirical Study

• URL: http://arxiv.org/abs/2002.09779v2
• Date: Fri, 26 Jun 2020 17:02:20 GMT
• Title: Stochasticity in Neural ODEs: An Empirical Study
• Authors: Viktor Oganesyan, Alexandra Volokhova, Dmitry Vetrov
• Abstract summary: Regularization of neural networks (e.g. dropout) is a widespread technique in deep learning that allows for better generalization. We show that data augmentation during the training improves the performance of both deterministic and versions of the same model. However, the improvements obtained by the data augmentation completely eliminate the empirical regularization gains, making the performance of neural ODE and neural SDE negligible.
• Score: 68.8204255655161
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE), usually rely on a completely deterministic feed-forward operation. This work provides an empirical study of stochastically regularized neural ODE on several image-classification tasks (CIFAR-10, CIFAR-100, TinyImageNet). Building upon the formalism of stochastic differential equations (SDEs), we demonstrate that neural SDE is able to outperform its deterministic counterpart. Further, we show that data augmentation during the training improves the performance of both deterministic and stochastic versions of the same model. However, the improvements obtained by the data augmentation completely eliminate the empirical gains of the stochastic regularization, making the difference in the performance of neural ODE and neural SDE negligible.

Related papers

• CGNSDE: Conditional Gaussian Neural Stochastic Differential Equation for Modeling Complex Systems and Data Assimilation [1.4322470793889193]
  A new knowledge-based and machine learning hybrid modeling approach, called conditional neural differential equation (CGNSDE), is developed. In contrast to the standard neural network predictive models, the CGNSDE is designed to effectively tackle both forward prediction tasks and inverse state estimation problems.
  arXiv  Detail & Related papers  (2024-04-10T05:32:03Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• Neural Generalized Ordinary Differential Equations with Layer-varying Parameters [1.3691539554014036]
  We show that the layer-varying Neural-GODE is more flexible and general than the standard Neural-ODE. The Neural-GODE enjoys the computational and memory benefits while performing comparably to ResNets in prediction accuracy.
  arXiv  Detail & Related papers  (2022-09-21T20:02:28Z)
• EINNs: Epidemiologically-Informed Neural Networks [75.34199997857341]
  We introduce a new class of physics-informed neural networks-EINN-crafted for epidemic forecasting. We investigate how to leverage both the theoretical flexibility provided by mechanistic models as well as the data-driven expressability afforded by AI models.
  arXiv  Detail & Related papers  (2022-02-21T18:59:03Z)
• Neural Stochastic Partial Differential Equations [1.2183405753834562]
  We introduce the Neural SPDE model providing an extension to two important classes of physics-inspired neural architectures. On the one hand, it extends all the popular neural -- ordinary, controlled, rough -- differential equation models in that it is capable of processing incoming information. On the other hand, it extends Neural Operators -- recent generalizations of neural networks modelling mappings between functional spaces -- in that it can be used to learn complex SPDE solution operators.
  arXiv  Detail & Related papers  (2021-10-19T20:35:37Z)
• Sparse Flows: Pruning Continuous-depth Models [107.98191032466544]
  We show that pruning improves generalization for neural ODEs in generative modeling. We also show that pruning finds minimal and efficient neural ODE representations with up to 98% less parameters compared to the original network, without loss of accuracy.
  arXiv  Detail & Related papers  (2021-06-24T01:40:17Z)
• Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models [38.17499046781131]
  We propose a novel approach towards estimating uncertain neural ODEs, avoiding the numerical integration bottleneck. Our algorithm - distributional gradient matching (DGM) - jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.
  arXiv  Detail & Related papers  (2021-06-22T08:40:51Z)
• Neural ODE Processes [64.10282200111983]
  We introduce Neural ODE Processes (NDPs), a new class of processes determined by a distribution over Neural ODEs. We show that our model can successfully capture the dynamics of low-dimensional systems from just a few data-points.
  arXiv  Detail & Related papers  (2021-03-23T09:32:06Z)
• Meta-Solver for Neural Ordinary Differential Equations [77.8918415523446]
  We investigate how the variability in solvers' space can improve neural ODEs performance. We show that the right choice of solver parameterization can significantly affect neural ODEs models in terms of robustness to adversarial attacks.
  arXiv  Detail & Related papers  (2021-03-15T17:26:34Z)
• Bayesian Neural Ordinary Differential Equations [0.9422623204346027]
  We demonstrate the successful integration of Neural ODEs with Bayesian inference frameworks. We achieve a posterior sample accuracy of 98.5% on the test ensemble of 10,000 images. This gives a scientific machine learning tool for probabilistic estimation of uncertainties.
  arXiv  Detail & Related papers  (2020-12-14T04:05:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.