As a representative continuous-depth neural network approach, stochastic differential equation (SDE)-based Bayesian neural networks (BNNs) have attracted considerable attention due to their solid theoretical foundations and strong potential for real-world applications. However, their reliance on numerical SDE solvers inevitably incurs a large number of function evaluations (NFEs), resulting in high computational cost and occasional convergence instability. To address these challenges, we propose a Nesterov-accelerated gradient (NAG) enhanced SDE-BNN model. By integrating NAG into the SDE-BNN framework along with an NFE-dependent residual skip connection, our method accelerates convergence and substantially reduces NFEs during both training and testing. Extensive empirical results show that our model consistently outperforms conventional SDE-BNNs across various tasks, including image classification and sequence modeling, achieving lower NFEs and improved predictive accuracy.

Neural Information Processing Systems http://nips.cc/

LSTMs are designed to help alleviate the issue of vanishing and exploding gradients commonly associatedwithtrainingRNNs[5].

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Weintroducethe"continuized"Nesterovacceleration,aclosevariantofNesterov acceleration whose variables are indexed by a continuous time parameter.

Neural ordinary differential equations describe howvalues change intime.