Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks
This work addresses training inefficiencies and overfitting for deep learning practitioners, representing an incremental improvement by integrating existing techniques.
The paper tackles the issues of pathological curvature and overfitting in deep neural networks by combining adaptive preconditioners with Stochastic Gradient Langevin Dynamics (SGLD), achieving state-of-the-art performance on Logistic Regression, Feedforward Neural Nets, and Convolutional Neural Nets.
Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for Stochastic Gradient Descent (SGD). These methods improve convergence by adapting to the local geometry of parameter space. A second issue is overfitting, which is typically addressed by early stopping. However, recent work has demonstrated that Bayesian model averaging mitigates this problem. The posterior can be sampled by using Stochastic Gradient Langevin Dynamics (SGLD). However, the rapidly changing curvature renders default SGLD methods inefficient. Here, we propose combining adaptive preconditioners with SGLD. In support of this idea, we give theoretical properties on asymptotic convergence and predictive risk. We also provide empirical results for Logistic Regression, Feedforward Neural Nets, and Convolutional Neural Nets, demonstrating that our preconditioned SGLD method gives state-of-the-art performance on these models.