While language models plausibly are trained with comparable amounts of FLOP to humans today here are some differences:
These might explain some of the strengths/weaknesses of language models
If this is your implementation:
https://github.com/amudide/switch_sae/blob/main/dictionary_learning/trainers/switch.py
It looks like you when you encode you do a dense encoder forward pass and then mask using the expert router.
I think this means that the FLOP scaling laws claim is misleading because (my impression is that) your current train code uses much more FLOP than the scaling law graphs, because it calculates every expert's activations for every input.
But I think the empirical claims about the learned features and the FLOP scaling laws still should hold up for implementations that actually do the conditional computations.
I also expect H100/B100-time scaling charts than FLOP charts to be more informative for future work because I now think memory-bandwidth has decent odds of being the main bottleneck for training time.
One barrier to SAE circuits is that it's currently hard to understand how attention out SAE latents are calculated. Even if you do IG attribution patching to try to understand which earlier latents are relevant to the attention out SAE latents, it doesn't tell you how these latents interact inside the attention layer at all.
TinyModel SAEs have these first entity and second entity latents.
E.g. if the story is 'Once upon a time Tim met his friend Sally.', Tim is the first entity and Sally is the second entity. The latents fire on all instances of first|second entity after the first introduction of that entity.
I think I at one point found an 'object owned by second entity' latent but have had trouble finding it again.
I wonder if LMs are generating these reusable 'pointers' and then doing computation with the pointers. For example to track that an object is owned by the first entity, you just need to calculate which entities are instances of the first entity, calculate when first entity is shown to own an object and write 'owned by first entity' to the object token, and then broadcast that forward to other instances of the object. Then, if you have the tokens Tim|'s
(and 's has calculated that the first entity is immediately before it), 's can, with a single attention head, look for objects owned by the first entity.
This means that the exact identity information of the object (e.g. ' hammer') and the exact identity information of the first entity (' Tim') don't need to be passed around in computations, you can just do much cheaper pointer calculations and grab the relevant identity information when necessary.
This suggests a more fine-grained story for what duplicate name heads are doing in IOI.
You know I was thinking ab this-- say that there are two children and they're orthogonal to the parent and each have probability 0.4 given the parent. If you imagine the space it looks like three clusters, two with probability 0.4, norm 1.4 and one with probability 0.2 and norm 1. They all have high cosine similarity with each other. From this frame, having the parent 'include' the children directions a bit doesn't seem that inappropriate. One SAE latent setup that seems pretty reasonable is to actually have one parent latent that's like "one of these three clusters is active" and three child latents pointing to each of the three clusters. The parent latent decoder in that setup would also include a bit of the child feature directions.
This is all sketchy though. It doesn't feel like we have a good answer to the question "How exactly do we want the SAEs to behave in various scenarios?"
This is cool! I wonder if it can be fixed. I imagine it could be improved some amount by nudging the prefix distribution, but it doesn't seem like that will solve it properly. Curious if this is a large issue in real LMs. It's frustrating that there aren't ground-truth features we have access to in language models.
I think how large of a problem this is can probably be inferred from a description of the feature distribution. It'd be nice to have a better sense of what that distribution is (assuming the paradigm is correct enough).
To generate the trees in sparselatents.com/tree_view, I use a variant of Masked Cosine Similarity (MCS), a metric introduced in Towards Monosemanticity. The original MCS is calculated like this: For any two latents A and B, first compute the cosine similarity between their activations, but only considering tokens where latent A is active. Then compute the same similarity, but only for tokens where latent B is active. The final MCS value is the larger of these two similarities.
Instead of taking the max, I do a directed MCS where I just consider the cosine similarity between A and B's activations on tokens where B is active. Then, I multiply this directed MCS score by max(B activations)/max(A activations) to ignore latents that don't fire very much. I'm not sure that this multiplication step is necessary.
I also use a higher threshold of 0.6.
Starting from a parent latent, say S/1/12, I find all latents in a larger-width SAE (say S/2) that pass the directed MCS threshold. Then, I re-apply the method to those S/2 latents to find children in S/3.
The result is often a non-tree DAG as some of the identified latents in S/3 have more than one parent in S/2. To simplify rendering, I assign these latents to the parent they have the highest score with. This obscures the true structure, but I wasn't sure of a clean way to automatically render these DAGs.
The trees should be thought of not as fully displaying the structure of the model, but instead of surfacing small sets of latents that I expect demonstrate feature absorption when viewed together.
The Matryoshka SAE trained on the toy model learn the true features on most runs, not all of them. Sometimes a small number of latents, modally one, seem to get stuck in a bad state.
I think historically UMA oracle token holder profiteers have misresolved some markets without Polymarket overriding.
I would guess profiteers would focus on markets with more liquidity. I would guess that the base rate so far has been much less than 3%, but maybe there are lots of resolved markets with lower trading volume ('Will Jesus Christ...' has $400K in volume). It does seem like it would be unusually bad for Polymarket if this particular market was misresolved.
It seems not impossible to me for many markets to be misresolved by UMA in one big attack, but I don't know how UMA and Polymarket work.