Gradient-free training of recurrent neural networks
This addresses the training difficulties in recurrent neural networks for time-dependent problems, offering a potentially more stable and efficient alternative to backpropagation through time.
The authors tackled the problem of training recurrent neural networks without using gradient-based methods, which often suffer from exploding or vanishing gradients, by introducing a gradient-free approach based on random feature networks and Koopman operator theory. They reported improved training time and forecasting accuracy in experiments on time series, chaotic systems, control problems, and weather data compared to gradient-based methods.
Recurrent neural networks are a successful neural architecture for many time-dependent problems, including time series analysis, forecasting, and modeling of dynamical systems. Training such networks with backpropagation through time is a notoriously difficult problem because their loss gradients tend to explode or vanish. In this contribution, we introduce a computational approach to construct all weights and biases of a recurrent neural network without using gradient-based methods. The approach is based on a combination of random feature networks and Koopman operator theory for dynamical systems. The hidden parameters of a single recurrent block are sampled at random, while the outer weights are constructed using extended dynamic mode decomposition. This approach alleviates all problems with backpropagation commonly related to recurrent networks. The connection to Koopman operator theory also allows us to start using results in this area to analyze recurrent neural networks. In computational experiments on time series, forecasting for chaotic dynamical systems, and control problems, as well as on weather data, we observe that the training time and forecasting accuracy of the recurrent neural networks we construct are improved when compared to commonly used gradient-based methods.