This repository contains the code used for the experiments in the paper Linearity of Relation Decoding in Transformer LMs.

How an LM decodes a relation such as (Miles Davis, plays the instrument, trumpet) involves a sequence of non-linear computations spanning multiple layers. But, in this work we show that for a subset of relations this highly non-linear decoding procedure can be approximated by a simple linear transformation ($\textbf{LRE}$) on the subject representation $\mathbf{s}$ at some intermediate layer.

Please check lre.baulab.info for more information.

All code is tested on MacOS Ventura (>= 13.1) and Ubuntu 20.04 using Python >= 3.10. It uses a lot of newer Python features, so the Python version is a strict requirement.

To run the code, create a virtual environment with the tool of your choice, e.g. conda:

conda create --name relations python=3.10

Then, after entering the environment, install the project dependencies:

python -m pip install invoke
invoke install

demo/demo.ipynb shows how to get $LRE$ approximation for a certain relation. This notebook also explains the setup of our evaluation metrics $faithfulness$ and $causality$.

demo/attribute_lens.ipynb demonstrates Attribute Lens, which is motivated by the idea that a hidden state $\mathbf{h}$ may contain pieces of information beyond the prediction of the immediate next token. And, an $\text{LRE}$ can be used to extract a certain attribute from $\mathbf{h}$ without relevant textual context. In the figure below $\text{LRE}$ approximating the relation country-capital is applied on hidden state $\mathbf{h}$ after different layers in different token positions.

@article{hernandez2023linearity,
    title={Linearity of Relation Decoding in Transformer Language Models}, 
    author={Evan Hernandez and Arnab Sen Sharma and Tal Haklay and Kevin Meng and Martin Wattenberg and Jacob Andreas and Yonatan Belinkov and David Bau},
    year={2023},
    eprint={2308.09124},
    archivePrefix={arXiv},
    primaryClass={cs.CL}
}