Thanks! I read and enjoyed the book based on this recommendation

Thanks for writing this up, I found it useful to have some of the maths spelled out! In particular, I think that the equation constraining l, the number of simultaneously active features, is likely crucial for constraining the number of features in superposition

We dig into this in post 3. The layers compose importantly with each other and don't seem to be doing the same thing in parallel, path patching the internal connections will break things, so I don't think it's like what you're describing

The illusion is most concerning when learning arbitrary directions in space, not when iterating over individual neurons OR SAE features. I don't have strong takes on whether the illusion is more likely with neurons than SAEs if you're eg iterating over sparse subsets, in some sense it's more likely that you get a dormant and a disconnected feature in your SAE than as neurons since they are more meaningful?

Interesting post, thanks for writing it!

I think that the QK section somewhat under-emphasises the importance of the softmax. My intuition is that models rarely care about as precise a task as counting the number of pairs of matching query-key features at each pair of token positions, and that instead softmax is more of an "argmax-like" function that finds a handful of important token positions (though I have not empirically tested this, and would love to be proven wrong!). This enables much cheaper and more efficient solutions, since you just need the correct answer to be the argmax-ish.

For example, ignoring floating point precision, you can implement a duplicate token head with $d_{head}=2$ and arbitrarily high $d_{vocab}$. If there are $n$ vocab elements, map the $m$th query and key to the point $\frac{m}{n}$ of the way round the unit circle. The dot product is maximised when they are equal.

If you further want the head to look at a resting position unless the duplicate token is there, you can increase $d_{h}ead=3$, and have a dedicated BOS dimension with a score of $1-ϵ$, so you only get a higher score for a perfect match. And then make the softmax temperature super low so it's an argmax.

These models were not trained with dropout. Nice idea though!

I'm not sure! My guess is that it's because some athlete names were two tokens and others were three tokens (or longer) and we left padded so all prompts were the same length (and masked the attention so it couldn't attend to the padding tokens). We definitely didn't need to do this, and could have just filtered for two token names, it's not an important detail.

I really like this paper! This is one of my favourite interpretability papers of 2022, and has substantially influenced my research. I voted at 9 in the annual review. Specific things I like about it:

• It really started the "narrow distribution" focused interpretability, just examining models on sentences of the form "John and Mary went to the store, John gave a bag to" -> " Mary". IMO this is a promising alternative focus to the "understand what model components mean on the full data distribution" mindset, and worth some real investment in. Model components often do many things in different contexts (are polysemantic), and narrow distributions allow us to ignore their other roles.
  • This is less ambitious and less useful than full distribution interp, but may be much easier, and still sufficient for useful applications of interp like debugging model failures (eg why does BingChat gaslight people) or creating adversarial examples.
• It really pushed forwards causal intervention based mech interp (ie activation patching), rather than "analysing weights based" mech interp. Causal interventions are inherently distribution dependent and in some sense less satisfying, but much more scalable, and an important tool in our toolkit. (eg they kinda just worked on Chinchilla 70B
  • Patching was not original to IOI, but IOI is the first time I saw someone actually try to use it to uncover a circuit
  • It was the first place I saw edge/path patching, which is a cool and important innovation on the technique. It's a lot easier to interpret a set of key nodes and how they connect up than just heads that matter in isolation.
• It's really useful to have an example of a concrete circuit when reasoning through mech interp! I often use IOI as a standard example when teaching or thinking through something
• When you go looking inside a model you see weird phenomena, which is valuable to know about in future - the role of the work is by giving existence proofs of these, so just a single example is sufficient
  • It was the first place I saw the phenomena of backup/self-repair, which I found highly unexpected
  • It was the first place I saw negative heads (which directly led to the copy suppression paper I supervised, one of my favourite interp papers of 2023!)
• It's led to a lot of follow-up works trying to uncover different circuits. I think this line of research is hitting diminishing returns, but I'd still love to eg have a zoo of at least 10 circuits in small to medium language models!
• This was the joint first mech interp work published at a top ML conference, which seems like solid field-building, with more than 100 citations in the past 14 months!

I personally didn't find the paper that easy to read, and tend to recommend people read other resources to understand the techniques used, and I'd guess it suffered somewhat from trying to conform to peer review. But idk, the above is just a lot of impressive things for a single paper!

Meta level I wrote this post in 1-3 hours, and am very satisfied with the returns per unit time! I don't think this is the best or most robust post I could have written, and I think some of these theories of impact are much more important than others. But I think that just collecting a ton of these in the same place was a valuable thing to do, and have heard from multiple people who appreciated this post's existence! More importantly, it was easy and fun, and I personally want to take this as inspiration to find more, easy-to-write-yet-valuable things to do.

Object level I think the key point I wanted to make with this post was "there's a bunch of ways that interp can be helpful", which I think basically stands. I go back and forth on how much it's valuable to think about theories of impact day to day, vs just trying to do good science and pluck impactful low-hanging fruit, but I think that either way it's valuable to have a bunch in mind rather than carefully back-chaining from a specific and fragile theory of change.

This post got some extensive criticism in Against Almost Every Theory of Impact of Interpretability, but I largely agree with Richard Ngo and Rohin Shah's responses.

Self-Review: After a while of being insecure about it, I'm now pretty fucking proud of this paper, and think it's one of the coolest pieces of research I've personally done. (I'm going to both review this post, and the subsequent paper). Though, as discussed below, I think people often overrate it.

Impact The main impact IMO is proving that mechanistic interpretability is actually possible, that we can take a trained neural network and reverse-engineer non-trivial and unexpected algorithms from it. In particular, I think by focusing on grokking I (semi-accidentally) did a great job of picking a problem that people cared about for non-interp reasons, where mech interp was unusually easy (as it was a small model, on a clean algorithmic task), and that I was able to find real insights about grokking as a direct result of doing the mechanistic interpretability. Real models are fucking complicated (and even this model has some details we didn't fully understand), but I feel great about the field having something that's genuinely detailed, rigorous and successfully reverse-engineered, and this seems an important proof of concept. IMO the other contributions are the specific algorithm I found, and the specific insights about how and why grokking happens. but in my opinion these are much less interesting.

Field-Building Another large amount of impact is that this was a major win for mech interp field-building. This is hard to measure, but some data:

• There are multiple papers I like that are substantially building on/informed by these results (A toy model of universality, the clock and the pizza, Feature emergence via margin maximization, Explaining grokking through circuit efficiency
  • It's got >100 citations in less than a year (a decent chunk of these are semi-fake citations from this being used as a standard citation for 'mech interp exists as a field', so I care more about the "how many papers would not exist without this" metric)
• It went pretty viral on Twitter (1,000 likes, 300,000 views)
• This was the joint first mech interp paper at a top ML conference (ICLR 23 spotlight) and seemed to get a lot of interest at the conference.
• Anecdotally, I moderately often see people discussing this paper, or who know of me from this paper
• At least one of my MATS scholars says he got into the field because of this work.

Is field-building good? It's plausible to me that, on the margin, less alignment effort should be going into mech interp, and more should go into other agendas. But I'm still excited about mech interp field building, think this is a solid and high-value thing, and that field-building is often positive sum - people often have strong personal fits to different areas, and many people are drawn to it from non-alignment motivations. And though there's concern over capabilities externalities, my guess is that good interp work is strongly net good.

Is it worth publishing in academic venues Submitting this to ICLR was my first serious experience with peer review. I'm not sure what updates I've made re whether this was worth it. I think some, but probably <50% of the field-building benefit came from this, and that going Twitter viral was much more important for ensuring people became aware of the work. I think it made the work more legitimate-seeming, more citable, more respectable, etc. On an object level, it resulted in the writing, ideas and experiments becoming much better and clearer (though led to some of the more interesting speculation being relegated to appendix E :'( ) though this was largely due to /u/lawrencec 's skills. I definitely find peer review/conforming to academic conventions very tedious and irritating, and am very grateful to Lawrence for doing almost all of the work.

Personal benefit It's hard to measure, but I think this turned out to be substantially good for my career, reputation and influence. It's often been what people know me for, and I think has helped me snowball into other career successes.

Ways it's overrated As noted, I do think there's ways people overrate the results/ideas here, and that there's too much interest in the object level results (the Fourier Multiplication algorithm, and understanding grokking). Some thoughts:

• The specific techniques I used to understand the model are super specific to modular addition + Fourier stuff, and not very useful on real models (though I hold out hope that it'll be relevant to how language models do addition!)
• People often think grokking is a key insight about how language models learn, I think this can be misleading. Grokking is a fragile and transitionary state you get when your hyper-parameters are just right (a bit more or less data makes it memorise or generalise immediately) and requires a ton of overtraining on the same data gain and again. I think grokking gives some hints that individual circuits may be learned in sudden phase transitions (the quantization model of neural scaling), but we need much more evidence from real models on these questions. And something like "true reasoning" is plausibly a mix of many circuits, each with their own phase transition, rather than a thing that'll be suddenly grokked.
• People often underestimate the difficulty jump in interpreting real models (even a 1L language model) compared to the modular addition model, and get too excited about how easy it'll be
  • People also get excited about more algorithmic interp work. I think this is largely played out, and focus on real models in my own work (and the work I supervise). I ultimately care about reverse-engineering AGI, and I think language models (even small ones) are decent proxies for this, while algorithmic problem models are not, unless you set up a really good one, that captures some property of real models that we care about. And I'm unconvinced there's much more marginal value in demonstrating that algorithmic mech interp is possible.