In our paper, we formalize the linear representation hypothesis of large language models, and define a causal inner product that respects the semantic structure of language.

We confirm our theory with LLaMA-2 representations and this repo provides the code for the experiments.

In word_pairs, each [___ - ___].txt has counterfactual pairs of words for each concept. We use them to estimate the unembedding representations.

In paired_contexts, each __-__.jsonl has context samples from Wikipedia in different languages. We use them for the measurement experiment (3_measurement.ipynb).

You need to install Python packages transformers, torch, numpy, seaborn, matplotlib, json, and tqdm to run the codes. Also, you need some GPUs to implement the code efficiently.

Make a directory matrices and run store_matrices.py first before you run other jupyter notebooks.

• 1_subspace.ipynb: We compare the projection of differences between counterfactual pairs (vs random pairs) onto their corresponding concept direction
• 2_heatmap.ipynb: We compare the orthogonality between the unembedding representations for causally separable concepts based on the causal inner product (vs Euclidean and random inner product)
• 3_measurement.ipynb: We confirm that the concept direction acts as a linear probe
• 4_intervention.ipynb: We confirm that the embedding representation changes the target concept, without changing off-target concepts.
• 5_sanity_check.ipynb: We verify that the causal inner product we find satisfies the uncorrelatedness condition in Assumption 3.3.