However, we find that in our trained models the learned encoder weights are not the transpose of the decoder weights and are cleverly offset to increase representational capacity. Specifically, we find that similar features which have closely related dictionary vectors have encoder weights that are offset so that they prevent crosstalk between the noisy feature inputs and confusion between the distinct features.
That post also includes a summary of Neel Nanda’s replication of the experiments, and they provided an additional interpretation of this that I think is interesting.
One question from this work is whether the encoder and decoder should be tied. I find that, empirically, the decoder and encoder weights for each feature are moderately different, with median cosine similiarty of only 0.5, which is empirical evidence they’re doing different things and should not be tied. Conceptually, the encoder and decoder are doing different things: the encoder is detecting, finding the optimal direction to project onto to detect the feature, minimising interference with other similar features, while the decoder is trying to represent the feature, and tries to approximate the “true” feature direction regardless of any interference.
Thank you for sharing this! I clearly didn’t read the original “Towards Monsemanticity” closely enough! It seems like the main argument is that when the weights are untied, the encoder and decoder learn different vectors, thus this is evidence that the encoder and decoder should be untied. But this is consistent with the feature absorption work—we see the encoder and decoder learning different things, but that’s not because the SAE is learning better representations but instead because the SAE is finding degenerate solutions which increase sparsity.
Are there are any known patterns of feature firings where untying the encoder and decoder results in the SAE finding the correct or better representations, but where tying the encoder and decoder does not?
I don’t know of specific examples, but this is the image I have in my head when thinking about why untied weights are more free than tied weights:
I think more generally this is why I think studying SAEs in the TMS setup can be a bit challenging, because there’s often too much symmetry and not enough complexity for untied weights to be useful, meaning just forcing your weights to be tied can fix a lot of problems! (We include it in ARENA mostly for illustration of key concepts, not because it gets you many super informative results). But I’m keen for more work like this trying to understand feature absorption better in more tractible cases
Originally they were tied (because it makes intuitive sense), but I believe Anthropic was the first to suggest untying them, and found that this helped it differentiate similar features:
That post also includes a summary of Neel Nanda’s replication of the experiments, and they provided an additional interpretation of this that I think is interesting.
Thank you for sharing this! I clearly didn’t read the original “Towards Monsemanticity” closely enough! It seems like the main argument is that when the weights are untied, the encoder and decoder learn different vectors, thus this is evidence that the encoder and decoder should be untied. But this is consistent with the feature absorption work—we see the encoder and decoder learning different things, but that’s not because the SAE is learning better representations but instead because the SAE is finding degenerate solutions which increase sparsity.
Are there are any known patterns of feature firings where untying the encoder and decoder results in the SAE finding the correct or better representations, but where tying the encoder and decoder does not?
I don’t know of specific examples, but this is the image I have in my head when thinking about why untied weights are more free than tied weights:
I think more generally this is why I think studying SAEs in the TMS setup can be a bit challenging, because there’s often too much symmetry and not enough complexity for untied weights to be useful, meaning just forcing your weights to be tied can fix a lot of problems! (We include it in ARENA mostly for illustration of key concepts, not because it gets you many super informative results). But I’m keen for more work like this trying to understand feature absorption better in more tractible cases