yeah that makes sense I think

with later small networks taking the outputs of earlier small networks as their inputs.

what's the distinction between two small networks connected in series with the first taking the output of the previous one as input and one big network? what defines the boundaries of the networks here? 

I kind of agree that Dennett is right about this, but I think it's important to notice that the idea he's attacking - that all representation is explicit representation - is an old and popular one in philosophy of mind that was, at one point, seen as natural and inevitable by many people working in the field, and one which I think still seems somewhat natural and obvious to many people who maybe haven't thought about the counterarguments much (e.g I think you can see echos of this view in a post like this one, or the idea that there will be some 'intelligence algorithm' which will be a relatively short python program). The idea that a thought is always or mostly something like a sentence in 'mentalese' is, I think, still an attractive one to many people of a logical sort of bent, as is the idea that formalised reasoning captures the 'core' of cognition.

I guess you are thinking about holes with the p-type semiconductor?

I don't think I agree (perhaps obviously) that it's better to think about the issues in the post in terms of physics analogies than in terms of the philosophy of mind and language. If you are thinking about how a mental representation represents some linguistic concept, then Dennett and Wittgenstein (and others!) are addressing the same problem as you! in a way that virtual particles are really not

I think atom would be a pretty good choice as well but I think the actual choice of terminology is less important than the making the distinction. I used latent here because that's what we used in our paper

‘Feature’ is overloaded terminology

In the interpretability literature, it’s common to overload ‘feature’ to mean three separate things:

1. Some distinctive, relevant attribute of the input data. For example, being in English is a feature of this text.

2. A general activity pattern across units which a network uses to represent some feature in the first sense. So we might say that a network represents the feature (1) that the text is in English with a linear feature (2) in layer 32.

3. The elements of some process for discovering features, like an SAE. An SAE learns a dictionary of activation vectors, which we hope correspond to the features (2) that the network actually uses. It is common to simply refer to the elements of the SAE dictionary as ‘features’ as well. For example, we might say something like ‘the network represents features of the input with linear features in its representation space, which are recovered well by feature 3242 in our SAE.

This seems bad; at best it’s a bit sloppy and confusing, at worst it’s begging the question about the interpretability or usefulness of SAE features. It seems important to carefully distinguish between them in case these don’t coincide. We think that it’s probably worth making a bit of an effort to carefully distinguish between all of these different concepts by giving them different names. A terminology that we prefer is to reserve ‘feature’ for the conceptual senses of the word (1 and 2) and use alternative terminology for case 3, like ‘SAE latent’ instead of ‘SAE feature’. So we might say, for example, that a model uses a linear representation for a Golden Gate Bridge feature, which is recovered well by an SAE latent. We have tried to follow this terminology in our recent Gemma Scope report. We think that this added precision is helpful in thinking about feature representations, and SAEs more clearly. To illustrate what we mean with an example, we might ask whether a network has a feature for numbers - i.e, whether it has any kind of localized representation of numbers at all. We can then ask what the format of this feature representation is ; for example, how many dimensions does it use, where is it located in the model, does it have any kind of geometric structure, etc. We could then separately ask whether it is discovered by a feature discovery algorithm; i.e is there a latent in a particular SAE that describes it well? We think it’s important to recognise that these are all distinct questions, and use a terminology that is able to distinguish between them.

We (the deepmind language model interpretability team) started using this terminology in the GemmaScope report, but we didn’t really justify the decision much there and I thought it was worth making the argument separately.

I'm not that confident about the statistical query dimension (I assume that's what you mean by SQ dimension?) But I don't think it's applicable; SQ dimension is about the difficulty of a task (e.g binary parity), wheras explicit vs tacit representations are properties of an implementation, so it's kind of apples to oranges.

To take the chess example again, one way to rank moves is to explicitly compute some kind of rule or heuristic from the board state, and another is to do some kind of parallel search, and yet another is to use a neural network or something similar. The first one is explicit, the second is (maybe?) more tacit, and the last is unclear. I think stronger variations of the LRH kind of assume that the neural network must be 'secretly' explicit, but I'm not really sure this is neccesary.

But I don't think any of this is really affected by the SQ dimension because it's the same task in all three cases (and we could possibly come up with examples which had identical performance?)

but maybe i'm not quite understanding what you mean

yeah, I think this paper is great!

i'm glad you liked it.

I definitely agree that the LRH and the interpretability of the linear features are seperate hypotheses; that was what I was trying to get at by having monosemanticity as a seperate assumption to the LRH. I think that these are logically independent; there could be some explicit representation such that everything corresponds to an interpretable feature, but that format is more complicated than linear (i.e monosemanticity is true but LRH is false) or, as you say, the network could in some sense be mostly manipulating features but these features could be very hard to understand (LRH true, monosemanticity false) or they could just both be the wrong frame. I definitely think it would be good if we spent a bit more effort in clarifying these distinctions; I hope this essay made some progress in that direction but I don't think it's the last word on the subject.

I agree coming up with experiments which would test the LRH in isolation is difficult. But maybe this should be more of a research priority; we ought to be able to formulate a version of the strong LRH which makes strong empirical predictions. I think something along the lines of https://arxiv.org/abs/2403.19647 is maybe going in the write direction here. In a shameless self-plug, I hope that LMI's recent work on open sourcing a massive SAE suite (Gemma Scope) will let people test out this sort of thing.

Having said that, one reason I'm a bit pessimistic is that stronger versions of the LRH do seem to predict there is some set of 'ground truth' features that a wide-enough or well tuned enough SAE ought to converge to (perhaps there should be some 'phase change' in the scaling graphs as you sweep the hyperparameters), but AFAIK we have been unable to find any evidence for this even in toy models.

I don't want to overstate this point though; I think part of the reason for the excitement around SAEs is that this was genuinely quite great science ; the Toy Models paper proposed some theoretical reasons to expect linear representations in superposition, which implied that something like SAEs should recover interesting representations, and then was quite successful! (This is why I say in the post I think there's a reasonable amount of evidence for at least the weak LRH).

I'm not entirely sure I follow here; I am thinking of compositionally as a feature of the format of a representation (Chris Olah has a good note on this here https://transformer-circuits.pub/2023/superposition-composition/index.html). I think whether we should expect one kind of representation or another is an interesting question, but ultimately an empirical one: there are some theoretical arguments for linear representations (basically that they should be easy for NNs to make decisions based on them) but the biggest reason to believe in them is just that people genuinely have found lots of examples of linear mediators that seem quite robust (e.g Golden Gate claude, neels stuff on refusal directions)