  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
sensitivity to the initialization variations. Our architecture consistently
outperforms state-of-the-art models in multivariate time series, including
TimeLLM, GPT2TS, PatchTST, DLinear, TimeNet, and the baseline Transformer, with
an error reduction of up to -59\% in various fields such as ETTh, ETTm, and air
quality, demonstrating that an ensemble of butterfly learning can improve the
adequacy and certainty of event prediction, despite of the traveling time to
the unknown future.
