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Function Vectors in Large Language Models

Paper · 2023 · Eric Todd, Millicent L. Li, Arnab Sen Sharma et al.

Summary

The paper asks whether autoregressive transformer LMs internally store an abstract representation of the task shown in in-context learning (ICL) prompts. The authors apply causal mediation analysis. They patch mean attention-head activations from clean ICL prompts into prompts with shuffled labels and measure how much each head restores the correct answer. A small set of heads, located mostly in early-middle layers, carries the task signal. Summing their outputs yields a "function vector" (FV). When an FV is added to a hidden state, the model performs the task on new inputs, including zero-shot prompts and natural text that look nothing like the original demonstrations. The method was evaluated on a curated suite of more than 40 ICL tasks and on models from 6B to 70B parameters. FVs encode part of the task's output vocabulary, but that vocabulary alone cannot rebuild them. FVs can also be added together, with partial success, to trigger composite tasks. The work shows that compact, causally effective representations of functions can be pulled out of LLMs. This matters for interpretability and for steering model behavior.

Key points

  • A simple baseline already transfers the task: adding the averaged last-token activation of antonym prompts at layer 12 of GPT-J gives 24.3% zero-shot antonym accuracy. FVs built from the selected heads perform better.
  • In GPT-J, the 10 heads with the highest average indirect effect form the FV. These heads mostly attend to the output tokens of the demonstrations.
  • Decoding FVs into vocabulary space shows they do not simply boost generic output words. They raise answers specific to each query. For example, with "South Africa" as input, the Country-Capital FV boosts "Pret(oria)" by +4.7 log-prob, while generic capitals such as London rise only about +1.
  • FVs can still promote correct answers that top-1 accuracy misses. For "wolf", the French translation "loup" is boosted even though the final output is wrong.
  • Code and data are released at functions.baulab.info.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓Northeastern UniversityBoston · United States68 works · 7,316 citations🎓Northeastern UniversityShenyang · China53 works · 2,205 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 18,614 worksArtificial Intelligence · 17,965 worksArts and Humanities · 17,450 worksLanguage and Linguistics · 17,296 works

🧭 Topics 1Research subjects and languages the work is about.Language models & pretraining · 3,894 works

Cite

Cite as Eric Todd, Millicent L. Li, Arnab Sen Sharma, Aaron Mueller, Byron C. Wallace and David Bau. 2023. Function Vectors in Large Language Models. arXiv:2310.15213.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2310.15213 · arXiv 2310.15213

@misc{todd2023function,
  title = {{Function Vectors in Large Language Models}},
  author = {Eric Todd, Millicent L. Li, Arnab Sen Sharma, Aaron Mueller, Byron C. Wallace and David Bau},
  year = {2023},
  doi = {10.48550/arxiv.2310.15213},
  eprint = {2310.15213},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2310.15213}
}

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