Very interesting!  Some thoughts:

Is there a clear motivation for choosing the MLP activations as the autoencoder target?  There are other choices of target that seem more intuitive to me (as I'll explain below), namely:

• the MLP's residual stream update (i.e. MLP activations times MLP output weights)
• the residual stream itself (after the MLP update is added), as in Cunningham et al

In principle, we could also imagine using the "logit versions" of each of these as the target: 

• the change in logits due to the residual stream update^[1]
• the logits themselves

(In practice, the "logit versions" might be prohibitively expensive because the vocab is larger than other dimensions in the problem. But it's worth thinking through what might happen if we did autoencode these quantities.)

At the outset, our goal is something like "understand what the MLP is doing."  But that could really mean one of 2 things:

1. understand the role that the function computed by the MLP sub-block plays in the function computed by the network as whole
2. understand the role that the function computed by the MLP neurons plays in the function computed by the network as whole

The feature decomposition in the paper provides a potentially satisfying answer for (1). If someone runs the network on a particular input, and asks you to explain what the MLP was doing during the forward pass, you can say something like: 

Here is a list of features that were activated by the input. Each of these features is active because of a particular, intuitive/"interpretable" property of the input.

Each of these features has an effect on the logits (its logit weights), which is intuitive/"interpretable" on the basis of the input properties that cause it to be active.

The net effect of the MLP on the network's output (i.e. the logits) is approximately^[2] a weighted sum over these effects, weighted by how active the features were. So if you understand the list of features, you understand the effect of the MLP on the output.

However, if this person now asks you to explain what MLP neuron A/neurons/472 was doing during the forward pass, you may not be able to provide a satisfying answer, even with the feature decomposition in hand.

The story above appealed to the interpetability of each feature's logit weights.  To explain individual neuron activations in the same manner, we'd need the dictionary weights to be similarly interpretable.  The paper doesn't directly address this question (I think?), but I expect that the matrix of dictionary weights is fairly dense^[3] and thus difficult to interpret, with each neuron being a long and complicated sum over many apparently unrelated features.  So, even if we understand all the features, we still don't understand how they combine to "cause" any particular neuron's activation.

Is this a bad thing?  I don't think so!

An MLP sub-block in a transformer only affects the function computed by the transformer through the update it adds to the residual stream. If we understand this update, then we fully understand "what the MLP is doing" as a component of that larger computation.  The activations are a sort of "epiphenomenon" or "implementation detail"; any information in the activations that is not in the update is inaccessible the rest of the network, and has no effect on the function it computes^[4].

From this perspective, the activations don't seem like the right target for a feature decomposition. The residual stream update seems more appropriate, since it's what the rest of the network can actually see^[5].

In the paper, the MLP that is decomposed into features is the last sub-block in the network.

Because this MLP is the last sub-block, the "residual stream update" is really just an update to the logits. There are no indirect paths going through later layers, only the direct path.

Note also that MLP activations are have a much more direct relationship with this logit update than they do with the inputs. If we ignore the nonlinear part of the layernorm, the logit update is just a (low-rank) linear transformation of the activations. The input, on the other hand, is related to the activations in a much more complex and distant manner, involving several nonlinearities and indeed most of the network.

With this in mind, consider a feature like  A/1/2357. Is it...

• ..."a base64-input detector, which causes logit increases for tokens like 'zc' and 'qn' because they are more likely next-tokens in base64 text"?
• ..."a direction in logit-update space pointing towards 'zc' and 'qn' (among other tokens), which typically has ~0 projection on the logit update, but has large projection in a rare set of input contexts corresponding to base64"?

The paper implicitly the former view: the features are fundamentally a sparse and interpretable decomposition of the inputs, which also have interpretable effects on the logits as a derived consequence of the relationship between inputs and correct language-modeling predictions.

(For instance, although the automated interpretability experiments involved both input and logit information^[6], the presentation of these results in the paper and the web app (e.g. the "Autointerp" and its score) focuses on the relationship between features and inputs, not features and outputs.)

Yet, the second view -- in which features are fundamentally directions in logit-update space --  seems closer to the way the autoencoder works mechanistically.

The features are a decomposition of activations, and activations in the final MLP are approximately equivalent to logit updates.  So, the features found by the autoencoder are

• directions in logit-update space (because logit-updates are, approximately^[7], what gets autoencoded),
• which usually have small projection onto the update (i.e. they are sparse, they can usually be replaced with 0 with minimal degradation), 
• but have large projection in certain rare sets of input contexts (i.e. they have predictive value for the autoencoder, they can't be replaced with 0 in every context)

To illustrate the value of this perspective, consider the token-in-context features. When viewed as detectors for specific kinds of inputs, these can seem mysterious or surprising:

But why do we see hundreds of different features for "the" (such as "the" in Physics, as distinct from "the" in mathematics)? We also observe this for other common words (e.g. "a", "of"), and for punctuation like periods. These features are not what we expected to find when we set out to investigate one-layer models!

An example of such a feature is A/1/1078, which Claude glosses as

The [feature] fires on the word "the", especially in materials science writing.

This is, indeed, a weird-sounding category to delineate in the space of inputs.

But now consider this feature as a direction in logit-update space, whose properties as a "detector" in input space derive from its logit weights -- it "detects" exactly those inputs on which the MLP wants to move the logits in this particular, rarely-deployed direction.

The question "when is this feature active?" has a simple, non-mysterious answer in terms of the logit updates it causes: "this feature is active when the MLP wants to increase the logit for the particular tokens ' magnetic', ' coupling', 'electron', ' scattering' (etc.)"

Which inputs correspond to logit updates in this direction?  One can imagine multiple scenarios in which this update would be appropriate.  But we go looking for inputs on which the update was actually deployed, our search will be weighted by

• the ease of learning a given input-output pattern (esp. b/c this network is so low-capacity), and
• how often a given input-output pattern occurs in the Pile.

The Pile contains all of Arxiv, so it contains a lot of materials science papers.  And these papers contain a lot of "materials science noun phrases":  phrases that start with "the," followed by a word like "magnetic" or "coupling," and possibly more words.

This is not necessarily the only input pattern "detected" by this feature^[8] -- because it is not necessarily the only case where this update direction is appropriate -- but it is an especially common one, so it appears at a glance to be "the thing the feature is 'detecting.' "  Further inspection of the activation might complicate this story, making the feature seem like a "detector" of an even weirder and more non-obvious category -- and thus even more mysterious from the "detector" perspective. Yet these traits are non-mysterious, and perhaps even predictable in advance, from the "direction in logit-update space" perspective.

That's a lot of words. What does it all imply? Does it matter?

I'm not sure.

The fact that other teams have gotten similar-looking results, while (1) interpreting inner layers from real, deep LMs and (2) interpreting the residual stream rather than the MLP activations, suggests that these results are not a quirk of the experimental setup in the paper.

But in deep networks, eventually the idea that "features are just logit directions" has to break down somewhere, because inner MLPs are not only working through the direct path. Maybe there is some principled way to get the autoencoder to split things up into "direct-path features" (with interpretable logit weights) and "indirect-path features" (with non-interpretable logit weights)? But IDK if that's even desirable.

1. ^{^}

   We could compute this exactly, or we could use a linear approximation that ignores the layer norm rescaling.  I'm not sure one choice is better motivated than the other, and the difference is presumably small.

2. ^{^}

   because of the (hopefully small) nonlinear effect of the layer norm

3. ^{^}

   There's a figure in the paper showing dictionary weights from one feature (A/1/3450) to all neurons. It has many large values, both positive and negative. I'm imagining that this case is typical, so that the matrix of dictionary vectors looks like a bunch of these dense vectors stacked together.
   
   It's possible that slicing this matrix along the other axis (i.e. weights from all features to a single neuron) might reveal more readily interpretable structure -- and I'm curious to know whether that's the case! -- but it seems a priori unlikely based on the evidence available in the paper.

4. ^{^}

   However, while the "implementation details" of the MLP don't affect the function computed during inference, they do affect the training dynamics. Cf. the distinctive training dynamics of deep linear networks, even though they are equivalent to single linear layers during inference.

5. ^{^}

   If the MLP is wider than the residual stream, as it is in real transformers, then the MLP output weights have a nontrivial null space, and thus some of the information in the activation vector gets discarded when the update is computed.
   
   A feature decomposition of the activations has to explain this "irrelevant" structure along with the "relevant" stuff that gets handed onwards.

6. ^{^}

   Claude was given logit information when asked to describe inputs on which a feature is active; also, in a separate experiment, it was asked to predict parts of the logit update.

7. ^{^}

   Caveat: L2 reconstruction loss on logits updates != L2 reconstruction loss on activations, and one might not even be a close approximation to the other.
   
   That said, I have a hunch they will give similar results in practice, based on a vague intuition that the training loss will tend encourage the neurons to have approximately equal "importance" in terms of average impacts on the logits.

8. ^{^}

   At a glance, it seems to also activate sometimes on tokens like " each" or " with" in similar contexts.

Sparse autoencoders have been one of the most important developments in mechanistic interpretability in the past year or so, and significantly shaped the research of the field (including my own work). I think this is in substantial part due to Towards Monosemanticity, between providing some rigorous preliminary evidence that the technique actually worked, a bunch of useful concepts like feature splitting, and practical advice for training these well. I think that understanding what concepts are represented in model activations is one of the most important problems in mech interp right now. Though highly imperfect, SAEs seem the best current bet we have here, and I expect whatever eventually works to look at least vaguely like an SAE.

I have various complaints and caveats about the paper (that I may elaborate on in a longer review in the discussion phase), and pessimisms about SAEs, but I think this work remains extremely impactful and significantly net positive on the field, and SAEs are a step in the right direction.

Curated. 

It's still unclear to me how well interpretability can scale and solve the core problems in superintelligence alignment, but this felt like a good/healthy incremental advance. I appreciated the exploration of feature splitting, beginnings of testing for universality, and discussion of the team's update against architectural approaches. I found this remark at the end interesting:

Finally, we note that in some of these expanded theories of superposition, finding the "correct number of features" may not be well-posed. In others, there is a true number of features, but getting it exactly right is less essential because we "fail gracefully", observing the "true features" at resolutions of different granularity as we increase the number of learned features in the autoencoder.

I don't think I've parsed the paper well enough to confidently endorse how well the paper justifies its claims, but it seemed to pass a bar that was worth paying attention to, for people tracking progress in the interpretability field.

One comment I'd note is that I'd have liked more information about how the feature interpretability worked in progress. The description is fairly vague. When reading this paragraph:

We see that features are substantially more interpretable than neurons. Very subjectively, we found features to be quite interpretable if their rubric value was above 8. The median neuron scored 0 on our rubric, indicating that our annotator could not even form a hypothesis of what the neuron could represent! Whereas the median feature interval scored a 12, indicating that the annotator had a confident, specific, consistent hypothesis that made sense in terms of the logit output weights.  

I certainly can buy that the features were a lot more interpretable than individual neurons, but I'm not sure, at the end of the day, how useful the interpretations of features were in absolute terms.

Paper walkthrough 

Superposition of features is only advantageous at a certain point in a network when it is followed by non-linear filtering, as explained in Toy Models of Superposition. Yet, this work places the sparse autoencoder at a point in the one-layer LLM which, up to the logits, is not followed by any non-linear operations. Given this, I would expect that there is no superposition among the activations fed to the sparse autoencoder, and that 512 (the size of the MLP output vector) is the maximum number of features the model can usefully represent.

If the above is true, then expansion factors to the sparse representation greater than 1 would not improve the quality or granularity of the 'true' feature representation. The additional features observed would not truly be present in the model's MLP activations, but would rather be an artifact of applying the sparse auto-encoder. Perhaps individual feature interpretability would still improve because the autoencoder could be driven to represent a rotation of the up-to 512 features to a privileged basis via the sparsity penalty. That all said, this work clearly reports various metrics, such as log-likelihood loss reduction, as being improved as the number of sparse feature coefficients expands well beyond 512, which I would think strongly contradicts my point above. Please help me understand what I am missing.

Side note: There is technically a non-linearity after the features, i.e. the softmax operation on the logits (...and layer norm, which I assume is not worth considering for this question). I haven't seen this discussed anywhere, but perhaps softmax is capable of filtering interference noise and driving superposition?

Quotation from Toy Models of Superposition:

"The Saxe results reveal that there are fundamentally two competing forces which control learning dynamics in the considered model. Firstly, the model can attain a better loss by representing more features (we've labeled this "feature benefit"). But it also gets a worse loss if it represents more than it can fit orthogonally due to "interference" between features. In fact, this makes it never worthwhile for the linear model to represent more features than it has dimensions."

Quotation from this work:

"We can easily analyze the effects features have on the logit outputs, because these are approximately linear in the feature activations."

UPDATE: After some more thought, it seems clear that softmax can provide the filtering needed for superposition to be beneficial given a sparse distribution of features. It's interesting that some parts of the LLM model have ReLUs for decoding features, other parts have softmax. I wonder if these two different non-linearities have distinct impacts on the geometries of the over-complete feature basis.