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Do you have any updates on this? I'm interested in this.
I've trained some sparse MLPs with 20K neurons on a 4L TinyStories model with ReLU activations and no layernorm and I took a look at them after reading this post. For varying integer , I applied an L1 penalty of on the average of the activations per token, which seems pretty close to doing an L1 of on the sum of the activations per token. Your L1 of with 12K neurons is sort of like in my setup. After reading your post, I checked out the cosine similarity between encoder/decoder of original mlp neurons and sparse mlp neurons for varying values of (make sure to scroll down once you click one of the links!):
S=3
https://plotly-figs.s3.amazonaws.com/sparse_mlp_L1_2exp3
S=4
https://plotly-figs.s3.amazonaws.com/sparse_mlp_L1_2exp4
S=5
https://plotly-figs.s3.amazonaws.com/sparse_mlp_L1_2exp5
S=6
https://plotly-figs.s3.amazonaws.com/sparse_mlp_L1_2exp6
I think the behavior you're pointing at is clearly there at lower L1s on layers other than layer 0 (? what's up with that?) and sort of decreases with higher L1 values, to the point that the behavior is there a bit at S=5 and almost not there at S=6. I think the non-dead sparse neurons are almost all interpretable at S=5 and S=6.
Original val loss of model: 1.128 ~= 1.13.
Zero ablation of MLP loss values per layer: [3.72, 1.84, 1.56, 2.07].
S=6 loss recovered per layer
Layer 0: 1-(1.24-1.13)/(3.72-1.13): 96% of loss recovered
Layer 1: 1-(1.18-1.13)/(1.84-1.13): 93% of loss recovered
Layer 2: 1-(1.21-1.13)/(1.56-1.13): 81% of loss recovered
Layer 3: 1-(1.26-1.13)/(2.07-1.13): 86% of loss recovered
Compare to 79% of loss-recovered from Anthropic's A/1 autoencoder with 4K features and a pretty different setup.
(Also, I was going to focus on S=5 MLPs for layers 1 and 2, but now I think I might instead stick with S=6. This is a little tricky because I wouldn't be surprised if tiny-stories MLP neurons are interpretable at higher rates than other models.)
Basically I think sparse MLPs aren't a dead end and that you probably just want a higher L1.
This link is a broken
This is great.
[word] and [word]
can be thought of as "the previous token is ' and'."
It might just be one of a family of linear features or ?? aspect of some other representation ?? corresponding to what the previous token is, to be used for at least induction head.
Maybe the reason you found ' and' first is because ' and' is an especially frequent word. If you train on the normal document distribution, you'll find the most frequent features first.
Consistency models are trained from scratch in the paper in addition to distilled from diffusion models. I think it'll probably just work with text-conditioned generation, but unclear to me w/o much thought how to do the equivalent of classifier-free guidance.
I think this post is great and I'm really happy that it's published.
I really appreciate this work!
I wonder if the reason MLPs are more polysemantic isn't because there are fewer MLPs than heads but because the MLP matrices are larger--
Suppose the model is storing information as sparse [rays or directions]. Then SVD on large matrices like the token embeddings can misunderstand the model in different ways:
- Many of the sparse rays/directions won't be picked up by SVD. If there are 10,000 rays/directions used by the model and the model dimension is 768, SVD can only pick 768 directions.
- If the model natively stores information as rays, then SVD is looking for the wrong thing: directions instead of rays. If you think of SVD as a greedy search for the most important directions, the error might increase as the importance of the direction decreases.
- Because the model is storing things sparsely, it can squeeze in far more meaningful directions than the model dimension. But these directions can't be perfectly orthogonal, they have to interfere with each other at least a bit. This noise could make SVD with large matrices worse and also means that the assumptions involved in SVD are wrong.
As evidence for the above story, I notice that the earliest PCA directions on the token embeddings are interpretable, but they quickly become less interpretable?
Maybe because the QK/OV matrices have low rank they specialize in a small number of the sparse directions (possibly greater than their rank) and have less interference noise. These could contribute to interpretability of SVD directions.
You might expect in this world that the QK/OV SVD directions would be more interpretable than the MLP matrices which would in turn be more interpretable than the token embedding SVD.
I wonder if multiple heads having the same activation pattern in a context is related to the limited rank per head; once the VO subspace of each head is saturated with meaningful directions/features maybe the model uses multiple heads to write out features that can't be placed in the subspace of any one head.