On the Promise of the Stochastic Generalized Gauss-Newton Method for Training DNNs

by   Matilde Gargiani, et al.

Following early work on Hessian-free methods for deep learning, we study a stochastic generalized Gauss-Newton method (SGN) for training DNNs. SGN is a second-order optimization method, with efficient iterations, that we demonstrate to often require substantially fewer iterations than standard SGD to converge. As the name suggests, SGN uses a Gauss-Newton approximation for the Hessian matrix, and, in order to compute an approximate search direction, relies on the conjugate gradient method combined with forward and reverse automatic differentiation. Despite the success of SGD and its first-order variants, and despite Hessian-free methods based on the Gauss-Newton Hessian approximation having been already theoretically proposed as practical methods for training DNNs, we believe that SGN has a lot of undiscovered and yet not fully displayed potential in big mini-batch scenarios. For this setting, we demonstrate that SGN does not only substantially improve over SGD in terms of the number of iterations, but also in terms of runtime. This is made possible by an efficient, easy-to-use and flexible implementation of SGN we propose in the Theano deep learning platform, which, unlike Tensorflow and Pytorch, supports forward and reverse automatic differentiation. This enables researchers to further study and improve this promising optimization technique and hopefully reconsider stochastic second-order methods as competitive optimization techniques for training DNNs; we also hope that the promise of SGN may lead to forward and reverse automatic differentiation being added to Tensorflow or Pytorch. Our results also show that in big mini-batch scenarios SGN is more robust than SGD with respect to its hyperparameters (we never had to tune its step-size for our benchmarks!), which eases the expensive process of hyperparameter tuning that is instead crucial for the performance of first-order methods.


page 1

page 2

page 3

page 4


Small steps and giant leaps: Minimal Newton solvers for Deep Learning

We propose a fast second-order method that can be used as a drop-in repl...

Second-order Neural Network Training Using Complex-step Directional Derivative

While the superior performance of second-order optimization methods such...

Local SGD Accelerates Convergence by Exploiting Second Order Information of the Loss Function

With multiple iterations of updates, local statistical gradient descent ...

Fast and Furious Convergence: Stochastic Second Order Methods under Interpolation

We consider stochastic second order methods for minimizing strongly-conv...

Training Neural Networks with Stochastic Hessian-Free Optimization

Hessian-free (HF) optimization has been successfully used for training d...

ViViT: Curvature access through the generalized Gauss-Newton's low-rank structure

Curvature in form of the Hessian or its generalized Gauss-Newton (GGN) a...

Batched Second-Order Adjoint Sensitivity for Reduced Space Methods

This paper presents an efficient method for extracting the second-order ...

Please sign up or login with your details

Forgot password? Click here to reset