Yu Bai

Yu Bai, Fan Chen, Huan Wang et al.

Neural sequence models based on the transformer architecture have demonstrated remarkable \emph{in-context learning} (ICL) abilities, where they can perform new tasks when prompted with training and test examples, without any parameter update to the model. This work first provides a comprehensive statistical theory for transformers to perform ICL. Concretely, we show that transformers can implement a broad class of standard machine learning algorithms in context, such as least squares, ridge regression, Lasso, learning generalized linear models, and gradient descent on two-layer neural networks, with near-optimal predictive power on various in-context data distributions. Using an efficient implementation of in-context gradient descent as the underlying mechanism, our transformer constructions admit mild size bounds, and can be learned with polynomially many pretraining sequences. Building on these ``base'' ICL algorithms, intriguingly, we show that transformers can implement more complex ICL procedures involving \emph{in-context algorithm selection}, akin to what a statistician can do in real life -- A \emph{single} transformer can adaptively select different base ICL algorithms -- or even perform qualitatively different tasks -- on different input sequences, without any explicit prompting of the right algorithm or task. We both establish this in theory by explicit constructions, and also observe this phenomenon experimentally. In theory, we construct two general mechanisms for algorithm selection with concrete examples: pre-ICL testing, and post-ICL validation. As an example, we use the post-ICL validation mechanism to construct a transformer that can perform nearly Bayes-optimal ICL on a challenging task -- noisy linear models with mixed noise levels. Experimentally, we demonstrate the strong in-context algorithm selection capabilities of standard transformer architectures.

Tianyu Guo, Wei Hu, Song Mei et al.

While large language models based on the transformer architecture have demonstrated remarkable in-context learning (ICL) capabilities, understandings of such capabilities are still in an early stage, where existing theory and mechanistic understanding focus mostly on simple scenarios such as learning simple function classes. This paper takes initial steps on understanding ICL in more complex scenarios, by studying learning with representations. Concretely, we construct synthetic in-context learning problems with a compositional structure, where the label depends on the input through a possibly complex but fixed representation function, composed with a linear function that differs in each instance. By construction, the optimal ICL algorithm first transforms the inputs by the representation function, and then performs linear ICL on top of the transformed dataset. We show theoretically the existence of transformers that approximately implement such algorithms with mild depth and size. Empirically, we find trained transformers consistently achieve near-optimal ICL performance in this setting, and exhibit the desired dissection where lower layers transforms the dataset and upper layers perform linear ICL. Through extensive probing and a new pasting experiment, we further reveal several mechanisms within the trained transformers, such as concrete copying behaviors on both the inputs and the representations, linear ICL capability of the upper layers alone, and a post-ICL representation selection mechanism in a harder mixture setting. These observed mechanisms align well with our theory and may shed light on how transformers perform ICL in more realistic scenarios.