arXiv Machine Learning

Transformers as Cross-Task Learners: Shared Structure Drives Sample Efficiency in In-Context Learning

Transformers can learn broad families of tasks during pretraining and adapt to unseen tasks from a short prompt, but a rigorous understanding of this capability is limited. This paper studies how shared cross‑task structure influences the sample complexity of in‑context learning (ICL) by characterizing task‑space complexity through covering numbers, yielding a set of anchor functions that localize unseen tasks and predict responses. The authors construct a Transformer with Softmax attention to approximate this procedure and derive an error bound that separates the effects of pretraining tasks and prompt length, showing that once enough tasks are available the dependence on prompt length becomes dimension‑free.

arXiv AI
Sep 21

Understanding In-context Learning of Addition via Activation Subspaces

The paper investigates how transformer language models perform few‑shot learning for a simple addition task, showing that the ability is concentrated in a handful of attention heads. Using dimensionality reduction, the authors identify low‑dimensional subspaces—three heads with six‑dimensional spaces in Llama‑3‑8B‑Instruct—where specific dimensions encode the units digit via trigonometric patterns and magnitude via low‑frequency components. They also derive a mathematical identity linking aggregator and extractor subspaces, enabling tracking of information flow from examples to the final prediction.

By Xinyan Hu, Kayo Yin, Michael I. Jordan, Jacob Steinhardt, Lijie Chen