Transformers for dynamical systems learn transfer operators in-context
arXiv:2602.18679v1 Announce Type: new Abstract: Large-scale foundation models for scientific machine learning adapt to physical settings unseen during training, such as zero-shot transfer between turbulent scales. This phenomenon, in-context learning, challenges conventional understanding of learning and adaptation in physical systems. Here, we study in-context learning of dynamical systems in a minimal setting: we train a small two-layer, single-head transformer to forecast one dynamical system, and then evaluate its ability to forecast a different dynamical system without retraining. We discover an early tradeoff in training between in-distribution and out-of-distribution performance, which manifests as a secondary double descent phenomenon. We discover that attention-based models apply a transfer-operator forecasting strategy in-context. They (1) lift low-dimensional time series using delay embedding, to detect the system's higher-dimensional dynamical manifold, and (2) identify an
arXiv:2602.18679v1 Announce Type: new Abstract: Large-scale foundation models for scientific machine learning adapt to physical settings unseen during training, such as zero-shot transfer between turbulent scales. This phenomenon, in-context learning, challenges conventional understanding of learning and adaptation in physical systems. Here, we study in-context learning of dynamical systems in a minimal setting: we train a small two-layer, single-head transformer to forecast one dynamical system, and then evaluate its ability to forecast a different dynamical system without retraining. We discover an early tradeoff in training between in-distribution and out-of-distribution performance, which manifests as a secondary double descent phenomenon. We discover that attention-based models apply a transfer-operator forecasting strategy in-context. They (1) lift low-dimensional time series using delay embedding, to detect the system's higher-dimensional dynamical manifold, and (2) identify and forecast long-lived invariant sets that characterize the global flow on this manifold. Our results clarify the mechanism enabling large pretrained models to forecast unseen physical systems at test without retraining, and they illustrate the unique ability of attention-based models to leverage global attractor information in service of short-term forecasts.
Executive Summary
The article explores the ability of transformer models to learn transfer operators in-context, enabling them to forecast unseen physical systems without retraining. The authors discover a secondary double descent phenomenon and an attention-based forecasting strategy that lifts low-dimensional time series and identifies long-lived invariant sets. This research clarifies the mechanism behind large pretrained models' ability to forecast unseen physical systems and highlights the unique ability of attention-based models to leverage global attractor information. The findings have significant implications for scientific machine learning and the development of more robust and adaptable models.
Key Points
- ▸ Transformer models can learn transfer operators in-context, enabling zero-shot transfer between turbulent scales.
- ▸ The authors discover a secondary double descent phenomenon in training, manifesting as a tradeoff between in-distribution and out-of-distribution performance.
- ▸ Attention-based models apply a transfer-operator forecasting strategy in-context, lifting low-dimensional time series and identifying long-lived invariant sets.
Merits
Strength
The research provides a comprehensive understanding of the mechanism behind large pretrained models' ability to forecast unseen physical systems, shedding light on the role of transfer operators and attention-based models.
Strength
The study demonstrates the unique ability of attention-based models to leverage global attractor information in service of short-term forecasts, highlighting their potential for scientific machine learning applications.
Demerits
Limitation
The research is limited to a minimal setting, using a small two-layer, single-head transformer, and therefore may not generalize to more complex models or real-world applications.
Limitation
The study focuses on a specific type of model (transformer) and may not be applicable to other types of models or architectures.
Expert Commentary
The article provides a comprehensive analysis of the mechanism behind transformer models' ability to forecast unseen physical systems, shedding light on the role of transfer operators and attention-based models. The study's findings have significant implications for the development of more robust and adaptable models in scientific machine learning and highlight the potential for attention-based models to leverage global attractor information in service of short-term forecasts. However, the research is limited to a minimal setting and may not generalize to more complex models or real-world applications. Nevertheless, the study provides a valuable contribution to the field of scientific machine learning and has the potential to inform policy decisions in fields such as climate modeling and weather forecasting.
Recommendations
- ✓ Future research should investigate the generalizability of the study's findings to more complex models and real-world applications.
- ✓ The development of more robust and adaptable models in scientific machine learning should be prioritized, leveraging the insights gained from this study and other related research.
