Improving Infinitely Deep Bayesian Neural Networks with Nesterov's Accelerated Gradient Method

TL;DR

This paper introduces a Nesterov-accelerated gradient method for Bayesian neural networks based on stochastic differential equations, significantly reducing computational cost and improving convergence and accuracy.

Contribution

The paper proposes integrating Nesterov acceleration into SDE-based Bayesian neural networks with an NFE-dependent residual connection, enhancing efficiency and performance.

Findings

Reduces the number of function evaluations during training and testing.

Achieves higher predictive accuracy compared to traditional SDE-BNNs.

Demonstrates effectiveness on image classification and sequence modeling tasks.

Abstract

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.