  We present Higher-Order Tensor RNN (HOT-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 recurrent
architecture addresses these issues by learning the nonlinear dynamics directly
using higher-order moments and higher-order state transition functions.
Furthermore, we decompose the higher-order structure using the tensor-train
decomposition to reduce the number of parameters while preserving the model
performance. We theoretically establish the approximation guarantees and the
variance bound for HOT-RNN for general sequence inputs. We also demonstrate 5%
~ 12% improvements for long-term prediction over general RNN and LSTM
architectures on a range of simulated environments with nonlinear dynamics, as
well on real-world time series data.
