I really like the investigation into properties of SAE features, especially the angle of testing whether SAE features have particular properties than other (random) directions don’t have!
Random directions as a baseline: Based on my experience here I expect random directions to be a weak baseline. For example the covariance matrix of model activations (or SAE features) is very non-uniform. I’d second @Hoagy’s suggestion of linear combination of SAE features, or direction towards other model activations as I used here.
Ablation vs functional FT-LLC: I found the comparison between your LLC measure (weights before the feature), and the ablation effect (effect of this feature on the output) interesting, and I liked that you give some theories, both very interesting! Do you think @jake_mendel’s error correction theory is related to these in any way?
I really like the investigation into properties of SAE features, especially the angle of testing whether SAE features have particular properties than other (random) directions don’t have!
Random directions as a baseline: Based on my experience here I expect random directions to be a weak baseline. For example the covariance matrix of model activations (or SAE features) is very non-uniform. I’d second @Hoagy’s suggestion of linear combination of SAE features, or direction towards other model activations as I used here.
Ablation vs functional FT-LLC: I found the comparison between your LLC measure (weights before the feature), and the ablation effect (effect of this feature on the output) interesting, and I liked that you give some theories, both very interesting! Do you think @jake_mendel’s error correction theory is related to these in any way?