Long-term Forecasting using Tensor-Train RNNs

Rose Yu, Stephan Zheng, Anima Anandkumar, Yisong Yue

Abstract: We present Tensor-Train RNN (TT-RNN), a novel family of neural sequence architectures for multivariate forecasting in environments with nonlinear dynamics. Long-term forecasting in such systems is highly challenging, since there exist long-term temporal dependencies, higher-order correlations and sensitivity to error propagation. Our proposed tensor recurrent architecture addresses these issues by learning the nonlinear dynamics directly using higher order moments and high-order state transition functions. Furthermore, we decompose the higher-order structure using the tensor-train (TT) decomposition to reduce the number of parameters while preserving the model performance. We theoretically establish the approximation properties of Tensor-Train RNNs for general sequence inputs, and such guarantees are not available for usual RNNs. We also demonstrate significant long-term prediction improvements over general RNN and LSTM architectures on a range of simulated environments with nonlinear dynamics, as well on real-world climate and traffic data.

TL;DR: Accurate forecasting over very long time horizons using tensor-train RNNs

Keywords: RNNs, time series forecasting, nonlinear dynamics, tensor-train

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/long-term-forecasting-using-tensor-train-rnns/code)