Training multilayer perceptrons with the extended Kalman algorithm
Advances in neural information processing systems 1
Fast exact multiplication by the Hessian
Neural Computation
Dynamics and algorithms for stochastic search
Dynamics and algorithms for stochastic search
Fast curvature matrix-vector products for second-order gradient descent
Neural Computation
Automatic Learning Rate Maximization in Large Adaptive Machines
Advances in Neural Information Processing Systems 5, [NIPS Conference]
Conjugate Directions for Stochastic Gradient Descent
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Hi-index | 0.00 |
We consider the problem of developing rapid, stable, and scalable stochastic gradient descent algorithms for optimisation of very large nonlinear systems. Based on earlier work by Orr et al. on adaptive momentum--an efficient yet extremely unstable stochastic gradient descent algorithm--we develop a stabilised adaptive momentum algorithm that is suitable for noisy nonlinear optimisation problems. The stability is improved by introducing a forgetting factor 0 驴 驴 驴 1 that smoothes the trajectory and enables adaptation in non-stationary environments. The scalability of the new algorithm follows from the fact that at each iteration the multiplication by the curvature matrix can be achieved in O (n) steps using automatic differentiation tools. We illustrate the behaviour of the new algorithm on two examples: a linear neuron with squared loss and highly correlated inputs, and a multilayer perceptron applied to the four regions benchmark task.