Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning

Recently-developed time series foundation models for scientific machine learning exhibit emergent abilities to predict physical systems. These abilities include zero-shot forecasting, in which a model forecasts future states of a system given only a short trajectory as context. Here, we show that foundation models applied to physical systems can give accurate predictions, but that they fail to develop meaningful representations of the underlying physics. Instead, foundation models often forecast by context parroting, a simple zero-shot forecasting strategy that copies directly from the context. As a result, a naive direct context parroting model scores higher than state-of-the-art time-series foundation models on predicting a diverse range of dynamical systems, at a tiny fraction of the computational cost. We draw a parallel between context parroting and induction heads, which explains why large language models trained on text can be repurposed for time series forecasting. Our dynamical systems perspective also ties the scaling between forecast accuracy and context length to the fractal dimension of the attractor, providing insight into the previously observed in-context neural scaling laws. Context parroting thus serves as a simple but tough-to-beat baseline for future time-series foundation models and can help identify in-context learning strategies beyond parroting.