Approximating Real-Time Recurrent Learning with Random Kronecker Factors
This work addresses the problem of learning long-term dependencies in sequential data for machine learning practitioners by offering a more efficient alternative to RTRL, though it is incremental as it builds on existing RTRL approximations.
The paper tackles the computational inefficiency of Real-Time Recurrent Learning (RTRL) for recurrent neural networks by proposing the Kronecker Factored RTRL (KF-RTRL) algorithm, which approximates gradients with a Kronecker product decomposition, resulting in unbiased and memory-efficient online learning with reduced noise compared to prior methods like UORO, and it achieves performance close to TBPTT on tasks such as synthetic string memorization and Penn TreeBank.
Despite all the impressive advances of recurrent neural networks, sequential data is still in need of better modelling. Truncated backpropagation through time (TBPTT), the learning algorithm most widely used in practice, suffers from the truncation bias, which drastically limits its ability to learn long-term dependencies.The Real-Time Recurrent Learning algorithm (RTRL) addresses this issue, but its high computational requirements make it infeasible in practice. The Unbiased Online Recurrent Optimization algorithm (UORO) approximates RTRL with a smaller runtime and memory cost, but with the disadvantage of obtaining noisy gradients that also limit its practical applicability. In this paper we propose the Kronecker Factored RTRL (KF-RTRL) algorithm that uses a Kronecker product decomposition to approximate the gradients for a large class of RNNs. We show that KF-RTRL is an unbiased and memory efficient online learning algorithm. Our theoretical analysis shows that, under reasonable assumptions, the noise introduced by our algorithm is not only stable over time but also asymptotically much smaller than the one of the UORO algorithm. We also confirm these theoretical results experimentally. Further, we show empirically that the KF-RTRL algorithm captures long-term dependencies and almost matches the performance of TBPTT on real world tasks by training Recurrent Highway Networks on a synthetic string memorization task and on the Penn TreeBank task, respectively. These results indicate that RTRL based approaches might be a promising future alternative to TBPTT.