Neural Regenerative Stochastic Differential Equation: Dropout Scheme for Neural Differential Equations

Jonghun Lee, YongKyung Oh, Sungil Kim, Dongyoung Lim

Keywords: neural differential equations, neural stochastic differential equations, dropout, regularization, renewal process

Abstract: Neural Differential Equations (NDEs) are an excellent tool for modeling continuous-time (stochastic) dynamics, effectively handling challenges such as irregular observations, missing values, and noise. Despite their advantages, there is a lack of regularization techniques in the NDE framework, particularly those like dropout, which have been successfully implemented in other discrete neural networks, making them susceptible to overfitting. To address this research gap, we introduce Neural Regenerative Stochastic Differential Equation (NRSDE), based on alternating renewal processes, as a universally applicable regularization technique for NDEs. Our study reveals that NRSDE can effectively represent a continuous approximation of neural networks that randomly deactivate some neurons during training, similar to dropout, thereby enhancing the robustness and generalization capabilities of NDEs. Through extensive experiments, we demonstrate that NRSDE outperforms existing regularization methods for NDEs and can be applied to all existing NDE models, significantly improving their performance across various deep learning tasks, including time series classification and image classification.

Primary Area: learning on time series and dynamical systems

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Submission Number: 3014