Changes by Butterflies: Farsighted Forecasting with Group Reservoir
  Transformer
Md Kowsher Jia Xu
In Chaos, a minor divergence between two initial conditions exhibits
exponential amplification over time, leading to far-away outcomes, known as the
butterfly effect. Thus, the distant future is full of uncertainty and hard to
forecast. We introduce Group Reservoir Transformer to predict long-term events
more accurately and robustly by overcoming two challenges in Chaos: (1) the
extensive historical sequences and (2) the sensitivity to initial conditions. A
reservoir is attached to a Transformer to efficiently handle arbitrarily long
historical lengths, with an extension of a group of reservoirs to reduce the
uncertainty due to the initialization variations. Our architecture consistently
outperforms state-of-the-art DNN models in multivariate time series, including
NLinear, Pyformer, Informer, Autoformer, and the baseline Transformer, with an
error reduction of up to -89.43\% in various fields such as ETTh, ETTm, and air
quality, demonstrating that an ensemble of butterfly learning, the prediction
can be improved to a more adequate and certain one, despite of the traveling
time to the unknown future.