Improving Infinitely Deep Bayesian Neural Networks with Nesterov's Accelerated Gradient Method
This work addresses computational inefficiencies in continuous-depth Bayesian neural networks, which is an incremental improvement for researchers and practitioners in machine learning.
The paper tackles the high computational cost and convergence instability of SDE-based Bayesian neural networks by proposing a Nesterov-accelerated gradient method with residual skip connections, resulting in reduced function evaluations and improved predictive accuracy across tasks like image classification and sequence modeling.
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.