How Few-Shot Examples Add Up: A Causal Decomposition of Function Vectors in In-Context Learning

In-context learning (ICL) excels at new tasks from minimal examples, yet we still lack a mechanistic explanation of how few-shot prompts shape a model’s function vector (FV)--a causal activation direction that drives task behavior on the ICL query. Across tasks and models, an $n$-shot FV is well-approximated by a linear combination of example-level sub-FVs, suggesting additive and composable contributions from individual demonstrations. Beyond additivity, we show that models contextualize individual examples' representations based on prior examples to adaptively reweight which demonstrations dominate the FV: attention shifts toward examples that are more informative and less ambiguous under the context. Finally, a causal decomposition separates Query–Key routing from Value updates, finding that contextualization’s most consistent contributions to FV quality arise from Query–Key alignment--particularly in ambiguous settings--while Value-mediated effects are more heterogeneous. Together, these results unify additive superposition with context-dependent attention reweighting into a mechanistic, testable account of how few-shot prompts implement tasks.

Large language models can often learn what to do from just a few examples in the prompt, without being retrained. But it is still unclear how the model combines those examples internally, especially when some examples are more helpful than others. We study this process by looking inside the model while it performs simple few-shot tasks. We find that each example contributes a small “task signal,” and the model’s overall understanding of the task is approximately built by adding these signals together. However, the model does not treat all examples equally. When some examples clearly reveal the intended task, and others are ambiguous, the model learns to focus more on the clearer examples. These findings help explain why a few well-chosen examples can strongly guide a language model, and why unclear or misleading examples may have less influence than expected.